Deliverable No.: 5.5.2
Benchmark Dose Software (BMDS)
Version 2.1
User's Manual
Version 2.0
Contract No.: 68-W-04-005
Task Order No.: 53
April 30, 2009
Developed for:
United States Environmental Protection Agency
Office of Environmental Information
1200 Pennsylvania Avenue, NW
Washington, DC 20460
Developed by:
LOCKHEED MARTIN/
Systems Engineering Center (SEC)
1010 N. Glebe Road
Arlington, VA 22201
Doc No.: 53-BMDS-RPT-0028
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Lockheed Martin Enterprise Solutions and Services
BMDS 2.1 User's Manual
TABLE OF CONTENTS
1.0 GENERAL TOPICS 3
1.1 Overview 3
1.2 Main Menu and Tool Bar 4
1.3 Running a Session 9
1.4 New/Open Dataset 20
1.5 Data Transformation 24
1.6 Repeated Response Measures Data 25
1.7 Concentration x Time Data 28
1.8 Software Removal 31
2.0 MODEL OPTIONS SCREENS 32
3 MODEL DESCRIPTIONS 42
3.2 Dichotomous Model Descriptions 48
3.2.1 Gamma Model Description 51
3.2.2 Logistic Model Description 51
3.2.3 Log-Logistic Model Description 52
3.2.4 Log-Probit Model Description 53
3.2.5 Multistage and Multistage-Cancer Model Description 54
3.2.6 Probit Model Description 55
3.2.7 Quantal Linear Model Description 55
3.2.8 Weibull Model Description 56
3.3 Description of Quantal Models with Background Dose Parameter 57
3.4 Dichotomous Hill Model Description 68
3.5 Nested Model Descriptions 69
3.5.1 Logistic Nested Model Description 71
3.5.2 NCTR Model Description 72
3.5.3 Rai and Van Ryzin Model Description 73
3.6 Toxicodiffusion Model Description 74
3.7 Conc_x_Time Model Description 75
4 TEXT OUTPUT FROM MODELS 76
4.1 Continuous Model Text Output 76
4.2 Dichotomous Model Text Output 80
4.3 Nested Model Text Output 81
4.4 Toxicodiffusion Model Text Output 83
4.5 ten Berge Model Text Output 84
5 GRAPHIC OUTPUT FROM MODELS 87
6 ACRONYMS, TERMS, AND DEFINITIONS 88
7 REFERENCES 89
8 APPENDICES 90
8.1 Model Input Files Format 90
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1.0 GENERAL TOPICS
1.1 Overview
The U.S. Environmental Protection Agency (EPA) Benchmark Dose Software (BMDS) was developed as
a tool to facilitate the application of benchmark dose (BMD) methods to EPA hazardous pollutant risk
assessments. This help facility provides instruction on how to use the BMDS, but is not intended to
address the EPA BMD methods. While the EPA BMD methods guidance has not been finalized at this
time, every attempt has been made to make his software consistent with the most recent working draft
guidance and discussions of the EPA Benchmark Dose Work group. The latest draft of the "Benchmark
Dose Technical Guidance Document" (October, 2000) is undergoing an external, EPA Risk Assessment
Fourm (RAF) review. Until formal BMD methods guidance is available, users of this software are strongly
encouraged to review existing background material such as "The Use of the Benchmark Dose Approach
in Health Risk Assessment" (EPA, 1995) before using this software.
Research into model development for BMDS started in 1995 and the first BMDS prototype was internally
reviewed by EPA in 1997. After external and public reviews in 1998-1999, and extensive Quality
Assurance testing in 1999-2000, BMDS version 1.2 was released in April, 2000. Subsequent versions
were released up to version 1.4.1 b in August 2007. This latest version of BMDS, version 2.1, replaces
1.4.1b and 2.0 and contains a wholly revamped user interface and new dichotomous models
("Dichotomous-Alternative" model type) as follows: Gamma-BgDose; Dichotomous Hill; Logistic-
BgResponse; LogProbit-BgDose; Multistage-BgDose; Multistage-Cancer-BgDose; Probit-BgDose;
Weibull-BgDose. Additional information about these new models is contained in the Help option
"Alternative Models Help." Moreover, this version contains a new continuous model, Exponential, which
consists of a set of four related models that can be run together or individually. A toxicodiffusion model
has been added to model data sets where the response is measured at different times after exposure (a
repeated measures model). Finally, a model called the "ten Berge" model has been added to analyze
dichotomous responses where (at least) two independent variables are presumed to account for the
response rates; this model has been used extensively for acute inhalation exposure experiments where
the two explanatory variables are concentration and duration of exposure.
EPA uses BMD methods to estimate reference doses (RfDs) and reference concentrations (RfCs), which
are used along with other scientific information to set standards for noncancer human health effects. Until
recently, RfDs and RfCs have been determined from no-observed-adverse-effect levels (NOAELs), which
represent the highest experimental dose for which no adverse health effects have been documented.
Using the NOAEL in determining RfDs and RfCs has long been recognized as having limitations in that it
1) is limited to one of the doses in the study and is dependent on study design; 2) does not account for
variability in the estimate of the dose-response; 3) does not account for the slope of the dose-response
curve; and 4) cannot be applied when there is no NOAEL, except through the application of an
uncertainty factor (Crump, 1984; Kimmel and Gaylor, 1988). A goal of the BMD approach is to define a
starting point of departure (POD) for the computation of a reference value (RfD or RfC) or slope factor
that is more independent of study design. The EPA Risk Assessment Forum has written guidelines for the
use of the BMD approach in the assessment of noncancer health risk (U.S. EPA, 1995) and the EPA
Benchmark Dose Workgroup is in the process of drafting technical guidance for the application of the
BMD approach in cancer and noncancer dose-response assessments.
Use of BMD methods involve fitting mathematical models to dose-response data and using the different
results to select a BMD that is associated with a predetermined benchmark response (BMR), such as a
10% increase in the incidence of a particular lesion or a 10% decrease in body weight gain. BMDS
facilitates these operations by providing simple data-management tools and an easy-to-use interface to
run multiple models on the same dose-response data set. Results from all models include a reiteration of
the model formula and model run options chosen by the user, goodness-of-fit information, the BMD, and
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the estimate of the lower-bound confidence limit on the BMD (BMDL). Model results are presented in
textual and graphical output files which can be printed or saved and incorporated into other documents.
Running the models on a data set consists of five basic steps.
Step 1: Create a new session or open an existing session.
Step 2: Select the appropriate models based on the type of data set being evaluated.
Step 3: Create a data set using the BMDS spreadsheet capability or import a data file.
Step 4: Specify the parameters associated with the model selected by choosing or creating a new
option file.
Step 5: Run the Model and view the tabular and graphical results.
More complete documentation for use of BMDS is provided within the remainder of this program's online
help facility. Hard copy documentation is available from EPA's BMDS web site at
http:/epa.gov/ncea/bmds.htm.
EPA plans to continually improve and expand the BMDS system. Use the BMDS web page at
(http://epa.gov/ncea/bmds.htm) as your most up-to-date source of information and updates pertaining to
the BMDS. The entire BMDS system or model updates can be downloaded from the web site. The source
code files for the models used in the BMDS system are also available via the BMDS web site to reviewers
and programmers who might be interested in performing an in-depth analysis of the model algorithms and
features.
We welcome, in fact encourage, your comments on the BMDS software and the model source code files.
Please provide comments, recommendations, suggested revisions, or corrections, to
bmds.ncea@epa.gov.
1.2 Main Menu and Tool Bar
At all times throughout the running of the BMD software a menu bar and a tool bar appears at the top of
the window. The following section will describe the different options provided by the menu bar. The
Toolbar is the graphical representation of certain options under the "File" item on the menu bar. When
applicable, the Toolbar icon associated with those "File" items are shown next to their description below.
File
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File
Edit View Tools Wi
New
Open
New Dataset
Open Dataset
Exit
Creates a new Dose-Response session window.
Open Opens a previously saved session. Either a regular Dose-Response session (a file
with the .ssn extension; see description below) or an existing ten Berge analysis (a file with the
.ten extension) may be opened this way.
Save Session Saves the current session.
Save Session As... Saves the current session under a new file name.
New Dataset Create a new data set.
Open Dataset Opens an existing data file.
Print Prints the results of the current session.
Exit Exit the BMDS program.
Edit
The Edit menu commands assist with copying, cutting and pasting data within the BMDS output file. The
commands can be implemented by selecting them from the menu with a mouse or by using the indicated
key strokes.
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Edit Preferences
Cut
Copy
Select All
Undo Paste (Ctrl+Z) Will undo a paste or cut.
Cut (Ctrl+X) Selected data is cut from an active output file
Copy (Ctrl+C) Selected data is copied from an active output file; or a selected data file name is
copied from the "Data File" column of an active session grid.
Paste (Ctrl+V) Cut/copied data is pasted into output file at cursor location.
Select All Selects all text in current active window.
View
View
Tools Window
Tools
Tool Bar
Status Bar
Tool Bar Toggles the visibility of the tool bar and icons. A checkmark to the left of this option in
the menu indicates the tool bar is visible.
Status Bar Toggles the visibility of the status bar at the bottom of the BDMS screen. A
checkmark to the left of this option in the menu indicates the status bar is visible.
View Plot... Displays a plot file graph.
View Output File... Opens saved Output file in new window.
R Interface... Currently not implemented.
Options... Reveals option tabs for application configuration.
Report
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Report Data Grid Work Directory
Summary Report M
Group By: End Points
Cancel ,. Save & Exit
Summary Report A checkmark to the right of this option indicates a summary report and
summary plots will be displayed after a session "run." If left unchecked, the summary report is not
generated and plots displayed in separate windows.
Group By This option determines how session "run" results (summary reports and summary
plots) are grouped together. Results can be grouped by end points or by the data filename.
Data Grid
Report Data Grid Work Directory
Default Number of Rows:
Default Number of Columns:
Default Number of Rows Determines how many rows appear when creating a new dataset.
Default Number of Columns Determines how many columns appear when creating a new
dataset.
Working Directory
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HIApplication Configuration
Report Data Grid Work Directory
Work Directory:
Temp Directory:
R Wrk Directory;
Options under this tab are currently not implemented.
Session Grid
This menu is available when a session window is open.
Session Grid | Help
Insert Row
1 Row
Add Row(s)
Delete Row
Insert Row Inserts a new row above the currently selected row in the session grid. The currently
selected row is indicated by the black arrow to the left of the row number.
Drop down list Allows a predefined number of rows to be added to the session grid or all the
models of a chosen group to be added.
Add Row(s) Used in conjunction with the drop down list described above. No action is taken until
user selects from the list and clicks Add Row(s).
Delete Row Deletes the currently selected row in the session grid.
Windows
Options under the Windows menu are only available when multiple windows are open inside the BDMS
program.
Windows | Session Grid Help
Tile Horizontal
Tile Vertical
Cascade
Close All
1 C:\USEPA_LM\BMDS2\Data\Dichotomous.ssn
2 C:\USEPA_LM\BMDS2\Data\bgd.ssn
Tile Horizontal Tiles windows horizontally.
Tile Vertical Tiles windows vertically.
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Cascade Displays windows in a cascade arrangement.
Close all Closes all windows inside the BDMS program.
Window List A list of currently open windows is displayed. Clicking on a particular window name
will bring the selected window to the top. The current top window will have a checkmark to the left
of its name.
Help
Help
BMDS 2.0/2.1 Help
Dichotomous Alternative Models Help
Submit Problem Report
About.,.
BMDS 2.0/2.1 Help Displays the contents of the Help documentation in a new window.
Dichotomous Alternative Models Help Information on the Alternative models is displayed in a
new window.
Submit Problem Report Currently not implemented.
About... Window describing the BMDS Sponsors and Credits, BMDS program version, and a
disclaimer.
1.3 Running a Session
Step 1: Create a new session or open an existing session.
Use the menu or appropriate icons to create a new session or open an existing session.
FjJe,, Edit View Tools Windows Help
New Dataset
Open Dataset
Step 2: Select the appropriate model(s) based on the type of data set being evaluated.
Once a session is open, a model type can be selected with the drop down box. BMDS is capable
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of processing multiple sets of data and models. To add additional models to the session table,
select Session Grid from the main menu. The Session Grid menu allows a single row or a user-
determined number of rows to be added to the session table. There is also a Delete Row
function.
;! C:\USEPA\BMDSZBeta\Data\Dichotomou5.ssn
Model Type
Dichotomous
Model Name
v Gamma
Logistic
LogLogistic
Log Pro bit
Multistage
Multistage-Cancer
Data File Run? Model Option File Endpoint
1-23-Dicho.dax 0 1-23-Dicho.opt PERCENT
LogLogDoslL.dax 0 Logistic.opt EFFECT1
LogLogResp.dax 0 LogLogistic.opt EFFECT1
LogLogResp.dax 0 LogLogResp.opt EFFECT1
multistage.dax 0 Multistage.opt PERCENT
Multistage! J.dax 0 Multil .opt EFFECT1
Out'
Run
BBi
Editing Dichotomous->Gamma
Right click on the row under the Model Name column. A menu will appear with a choice of
models depending on the model group previously selected.
IS C:\USEPA_LM\BMDS2\Data\DichotomoU5.ssn
Model Type
^ 1 Dichotomous
2 Dichotomous
3 Dichotomous
4 Dichotomous
5 Dichotomous
6 Dichotomous
< - -
Model Name Data File Run?
v 0
v Logistic
v LogLogistic
v LopProbit
v Multistage
v Multistape-Car
.. _ ...
Logistic
LogLogistic
LogProbit
Multistage
Multistage-Cancer
Probit
dax 0
ax 0
ax 0
0
dax 0
"
Model Option File
1-23-Dicho.opt
Logistic.opt
LogLogistic.opt
LogLopResp.opt
Multistage. opt
Multil .opt
~ '""
Endpoint Out File A
PERCENT
EFFECT1
EFFECT1
EFFECT1
PERCENT
EFFECT1
V
>
Editing Dichotomous->Gamma
Step 3: Create a data set using the BMDS spreadsheet capability or import a data file.
Data are stored in files with the .dax extension. A new data set can be created by right clicking
on a field under the Data File column. Data may be created, edited or selected from an existing
*.dax file.
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H C:\USEPA_LM\flMDS2\Data\Dichotomous.ssn
>
<
Model Type
1 Dichotomous
2 Dichotomous
3 Dichotomous
4 Dichotomous
5 Dichotomous
6 Dichotomous
Model Name
v Gamma
v Logistic
v LogLogistic
v LogProbit
v Multistage
v Multistage-Cancer
Data File Run? Model Option File Endpoint Out File A
tfiumiiiffiiiBmnai^^
l4|H|tWj£!i§ ;
LogLogDosI L.dax
LogLogResp.dax
LogLogResp.dax
multistage. dax
MultiStage1_1.dax
Create New Data File (*,dax)
View/Edit Data File
Change To Another Data File
Display Model Input File (*,(d))
RCENT
FECT1
FECT1
FECT1
' tZJ "MurtlTtaOe^pt 'FEHChNI
0 Multi! .opt EFFECT1
V
»
Editing Dichotomous- >Gamma
The data entry and editing facility appears below. Right click in any column field (the column
names) to display column options.
P Dataset - C:\USEPA LM\BMDS2\Data\1 -23-Dicho. dax
File Edit Data Grid
1
2
3
4
5
DOSE
TOTAL
0
50
100
150
200
EFFECT3
Rename Column
Transform Column
100
90
93
98
PERCENT Col?
.34
.58
2.5
60
90.23
Col8
Select Rename to rename the column. Enter the new column name and use the Save and Exit
button to make the change.
Cancel Save and Exit
Select Transform Column to bring up the Variable Transformation window. Use this window to
apply transformations on specified columns.
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SE to Standard Deviation (SD)
^^B
EFFECT2
See sections 1.4, A, B, and C for additional manipulations of the data files. Once all the data are
entered/modified as desired, the user may save and close the data grid screen. The appropriate
data file name should be displayed in the session window under the Data File column.
Copy and Paste Feature
A copy and paste feature enables users to copy and paste the data file into multiple rows using
CTRL-C to copy and CTRL-V to paste. Multiple rows can be copied or pasted at the same time.
Rows are selected by holding a mouse click and dragging to highlight data. Alternatively, a
SHIFT-CLICK method can be used vertically in either direction.
Example:
The copy and paste feature is useful for setting multiple models to use the same data file all at
once instead of individually. In this example a data file is copied to multiple rows. CTRL-C is used
to copy the data file highlighted.
l|C:UJSEPA1flMDS2Beta\DataVDichotomous.ssn
Model Type
^ 1 Dichotomous
2 Dichotomous
3 Dichotomous
4 Dichotomous
5 Dichotomous
6 Dichotomous
7 Dichotomous
8 Dichotomous
9 Dichotomous
Model Name
v Gamma
v Logistic
v LogLogistic
v LogProbit
v Multistage
v Multistage-Cancer
v pmbit
v Weibull
v Quantal-Linear
Data File
^1 1 -23-Dicho.dax
LogLogDosI L.dax
LogLogResp.dax
LogLogResp.dax
multi stage. dax
MultiStage1_1.dax
ProbitBgr.dax
WeibullOS.dax
Weibull_bgd1.dax
Run?
( 0
0
0
0
0
0
0
0
0
Model Option File
1-23-Dicho.opt
Logistic.opt
LogLogistic.opt
LogLogResp.opt
Multistage-opt
Multil .opt
ProbitBgr.opt
WeibullS.opt
LinearBgr.opt
Endpoint Out File
PERCENT
EFFECT1
EFFECT!
EFFECT1
PERCENT
EFFECT1
EFFECT1
EFFECT!
EFFECT!
< >
Multiple rows under the Data File column are selected to receive the copied data file value.
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3 C:\USEPA\BMDS2Beta\Data\Dichotomous.ssn
Mode! Type
Dichotomous
Dichotomous
Dichotomc-us
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Model Name
v Gamma
v Logistic
v LogLogistic
v LogProbit
^ Multistage
v MuItistage-Cancer
v Pro bit
^ Weibull
v Quantal-Linear
Data File
1-23-Dicho.dax
tSfll-SigBMl'.UstBX
La.gLftgSespaiaej
kOflLogSsStdi itx.
fetulMStafl8l_l,daM=
ftttbjtftjsiflx;
Run? Model Option File Endpoint
Q 1-23-Dicho.opt PERCENT
0 Multistage. opt PERCENT
0 Multil .opt EFFECT1
ED Prnbit.Bgt.opl EFFECT1
0 WeibullS.opt EFFECT1
0 LmearBgr.opt EFFECT1
OutFil
CTRL-V is used to paste the data file into multiple rows.
S C:\USEPA\BMDS2Beta\Data\Dichotomous.5sn
Model Type
1 Dichotomous
^ 2 Dtchotomous
3 Dichotomous
4 Dichotomous
5 Dichotomous
6 Dichotomous
7 Dichotomous
8 Dichotomous
9 Dichotomous
Model Name
v Gamma
v Logistic
v LogLogistic
v LogProbit
v Multistage
v M u Iti sta g e-Ca n ce r
v Pro bit
v Weibull
v Quantal-Linear
Data File
1-23-Dicho.dax
^1 1 -23-Dicho. dax
1-23-Dicho.dax
1-23-Dicho.dax
1-23-Dicho.dax
1-23-Dicho.dax
1-23-Dicho.dax
1-23-Dicho.dax
1-23-Dicho.dax
Run?
0
1 ' '
0
0
0
0
0
0
0
Model Option File
1-23-Dicho.opt
Logistic.opt
LogLogistic.opt
LogLogResp.opt
Multistage. opt
Multil. opt
ProbitBgr.opt
WeibullS.opt
LmearBgr.opt
Endpoint Out File
PERCENT
EFFECT1
EFFECT1
EFFECT1
PERCENT
EFFECT1
EFFECT1
EFFECT1
EFFECT1
< >
Step 4: Specify the parameters associated with the model selected by choosing or
creating a new option file.
The option parameters are stored in files with the .opt extension. Right clicking on a field under
the Model Option File column allows new option files to be created and existing option files to be
selected credited.
!1 C:\USEPA_LM\BMDS2\Data\Dichotomous.ssn
* 1
2
3
4
5
6
Model Type
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Dichotomous
Model Name
v- Gamma
v Logistic
v LogLogistic
v LogProbit
v Multistage
v M uiti stag e-Ca n ce r
Data File
1-23-Dicho.dax
LogLogDos! L.dax
LogLogResp.dax
LogLogResp.dax
multistage. dax
MuitiStage1_1,dax
Run?
R
0
0
0
S
0
Model Option Fie Endpoint Out File AB
ll-23-Dicho oot laSrTBSjl^^^^^^^^^B
Logistic.opt
LogLogistic.opt
LogLogResp.opt
Multistage. opt
Multil .opt
Create New Option File (*.opt)
View/Edit Option File
Change To Another Option File
Display Model Input File (*.(d))
EFFECT1
Editing Dichotomous->Garrima
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The display window below is used to view and edit the parameter options. Option files may be
saved to a specified path, set to default values, and optimized using the buttons along the bottom
of the window. The status bar displays which model and model type the parameters will affect.
Data to be used in the model may also be seen by clicking the Show data button. The path to the
data is displayed to the left of the button indicated by Data File:.
BMD Calculation
BMDL Cunre. Cafe.
fie strict Po wer >=J
Dose DOSE
Subjects in Dose Group TOTAL
incidence EFFECT1
Positive
Confidence Level
BMRF
Dose Groups
iteration
Relative Function
Parameter
250)
1.00E-Q8
1.00E-08
Rift Type Extra
Parameters Active Opt.
Background Default
Slope Default
Power Default
BMDS Mode Run
C:\USEPA\BMDS21 Beta'lDataVI -23-Dicho.dax
Set values To
Default
Optimize Initial
Param Values
Gamma- >Dichotomous
Select Display Model Input File (*.(d)) from the session screen to view the input file.
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H[ C:\USEPA\BMDS21Beta\Data\1Gam1 21 2.(d)
File Edit Preferences
BMDS Model Run
C: \USEPA\BHDS21Beta\DataU-23-Dicho. dax
C:WSEPA\BMDS21Beta\Data\lGaml-21-2.out
5
250 l.OOE-08 l.OOE-08 01100
l.OOOe-4 0 0.95
-9999 -9999 -9999
0
-9999 -9999 -9999
DOSE EFFECT1 HEGATIVE_RESPOWSE
0 0 100
50 5 95
100 30 70
150 65 35
200 90 10
Step 5: Run the Model and view the textual and graphical results.
Right click in a specific cell in the Out File column to specify a file for saving output.
S C:\UStPA_LM\BMOS2\DaIa\Dichotomous.ssn
Model Type
^ 1 Dichotomous
2 Dichotomous
3 Dichotomous
4 Dichotomous
5 Dichotomous
6 Dichotomous
V
V
V1
V
V
V
Model Name
Gamma
Logistic
LogLogistic
Log Pro bit
Multistage
Multistage-Cancer
Data File
3-Dicho.dax
LogDost L.dax
LogResp.dax
LogResp.dax
tistage.dax
tiStage1_1.dax
Run? Model Option File Endpoint
0 1-23-Dicho.opt PERCENT
0 Logistic-opt EFFEOT1
0 LogLogistio.opt EFFECT1
0 LogLogResp.opt EFFECT1
0 Multistage opt PERCENT
0 Multi! opt EFFECT1
Out File
M
Set Out File To
Clear Out File
Editing Dichotomous->Gamma
|}j^S
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S C:\USEPA_LM\BMDS2\Data\Dichotomous.ssn
^ 1
2
3
4
5
6
Model Type
Oichotomous
D i ch oto m o u s
Dichotornous
Dichotornous
D i ch oto m o u s
Dichotornous
Model Name
v Gamma
v Logistic
v LogLogistic
v LogProbit
v Multistage
v Multistage-Cancer
Data File
1-23-Dicho.dax
LogLogDosI L.dax
LogLogResp.dax
LogLogResp.dax
multi stage. dax
Multistage! _1.dax
Run?
Model Option File
1-23-Dicho.opt
T
D
D
H
Check All
Unchecked All
LogLogResp.opt
Multistage. opt
Multsl .opt
Endpoint Out File A
PERCENT
EFFECT1
EFFECT1
EFFECT1
PERCENT
EFFECT1
V
Run
^H
Editing Dichotomous->Gamma
Click on the Run button on the bottom left of the session window. Two new windows will be
opened, displaying a textual Summary Report and a Summary Graph of the results. The window
below displays the variables set for each of the models run in a table format. Each lettered
column corresponds to the models previously added in the session window. Right clicking in any
lettered column will display a menu with options to Show Out/Graph, Display Array Values, Open
Data File, or to Open Option File. To display array values, users must right click on a cell
containing the word "Array."
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^
File
Variables
Model Name
Data File Name
Option File Name
Maximum number of iterations
Relative Function Convergence
has been set to
Parameter Convergence has
been set to
Initial/Specified Background
Initial/Specified Slope
Initial/Specified Intercept
Initial/Specified Power
Initial/Specified Beta(1)
Initial/Specified Beta(2)
Initial/Specified Beta(3)
Asymptotic Correlation Matrix of
A B
Logistic LogLogistic
LogLogDos"! L.dax LogLogResp.dax
Logistic.opt Log Logistic, opt
250 250
1e-008
1e-008
0
0.846976
-1.56202
1e-OQ8
1e-008
0.02
1.24527
-2.6972
C
Log Pro bit
LogLogResp.dax
LogLogResp.opt
250
1e-008
1e-008
0.2
1.32603
0.748336
Parameter Estimates
Parameter Estimates
Analysis of Deviance Table
AIC
Goodness of Fit
Chi"2
d.f.
P-value
Specified effect
Risk Type
Confidence level
BMD
BMDL
waiffi^^^m
Array
Array
54.9629
Array
0.96
3
0.8101
0.1
Extra risk
0.95
0.585511
0.403496
Show Out/Graph
Display Array Values
Open Data File
Open Opbion File
' Array
0.01
2
0.9952
0.1
Extra risk
0.95
1.26305
0.46166
!37
' Array
0.38
2
0.8289
0.1
Extra risk
0.95
0.444256
0.117746
Individual graphs and .OUT File data are displayed when Show Out/Graph is selected by right
clicking in the Summary Report window.
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Logistic Model. (Version: 3.0; Date: 09/23/2007)
Input Data File: C:\USEPA\BHD52Beta\Data\2LogLogLog.(c
Gnuplot Plotting File: C:\USEPA\BHD32Beta\Data\2LogLc
Tue Sep 25 13:;
BMDS Model Run
The form of the probability function is:
P[response] = 1/fl+EXP(-intercept-slope*dose)]
Dependent variable = EFFECT1
Independent variable = DOSE
Array data is displayed by selecting Display Array Values from the Summary Report window.
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The Summary Graph displays graphs corresponding to each model run. Individual graphs my be
copied to the clipboard and inserted into other files such as MS Word documents.
PI Summary Graphs->Dichotomous.ssn [Endpoint: EFFECT1]
Multiple Sessions
In addition to running a session, BMDS 2.1 is capable of running multiple sessions
simultaneously. The results of a session may be computed while computations on a separate
session are being run. Simply open multiple sessions and click the Run button of each session
window.
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File Edit View Tools Session Grid Windows Help
J - A J -S 3
Model Name
Hill
Linear
Po lyn o m i a
Power
Data File Run? Model Option File Endpomt
CONTINUOUS! .dax 0 Hill.opt Mean
CONTINUOUS!.dax 0 Linear.opt Mean
CONTINUOUS!.dax 0 Poly.opt Mean
CONTINUOUS! .dax 0 Power.opt Mean
2 Continuous
3 Continuous
4 Continuous
Run
Editing Continuous->Hill
Model Name
Gamma
Logistic
LogLogistic
LogProbit
Multistage
Mnlti <-!.=, n«=-
Data File
1-23-Dicho.dax
LogLogDosI L.dax
LogLogResp.dax
LogLogResp.dax
multistage,dax
Run? Model Option File Endpomt
0 1-23-Dicho.opt PERCENT
0 Logistic.opt
0 Log Logistic, opt
Log Log Res p. opt
0 Multistage.opt
(71 MnltM nnt
Dichotomous
Dichotomous
Dichotomous
Dichotomous
EFFECT1
EFFECT1
EFFECT1
PERCENT
Bun
^m
tina Dithotomaus->Gamma
Model Name
N Logistic
NCTR
R a i_a n d_Va n_Ryz i n
Data File
NESTED.dax
NESTED.dax
NESTED.dax
Run? Model Option File Endpoint
0 NLogist.opt Response
0 NCTR.opt Response
0 Rai.opt Response
2 Nested_Dichotomous
3 Nested Dichotomous
Bun
ting Nested Dichotomous->NLogistic
1.4 New/Open Dataset
The following section will explain the functions of this window, as well as inform the user of the different
options presented by the window. A user may run a single model on a single data set by creating a new
data set or opening an existing data set in this manner. Analyses pursued in this manner are most similar
to the way in which model runs were done in BMDS versions 1 .xx.
A) Entering Data
Data will already be present in the grid (spreadsheet) if the Open Dataset option was chosen. If the New
Dataset option is chosen a blank grid (spreadsheet) will appear allowing the user to manually enter data
into the spreadsheet or to paste data from another spreadsheet (e.g., Excel) using most standard
spreadsheet operations. Adding rows or columns can be accomplished simply by putting data in the
cells of the row or column. The default number of rows and columns allowed is 100 and 50, respectively,
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but this can be changed on the "Data Grid" tab under "Options ..." found under the "Tools" menu item.
When Open Dataset is chosen from the File menu or the Open Dataset button is pressed the user will be
prompted for a file to load or import. By default the system initially displays any BMDS dataset files (*.dax)
in the "USEPA\BMDS21\Data" directory (i.e., in the folder Data in the folder created when BMDS was
installed). These files are in the BMDS format and can be loaded directly.
To import delimited DOS text files or files created in Excel 2003, select New Dataset and then, under the
File option on the Data Grid, select Import Data From and selected the type of file you want to import:
Save Dataset
Save Dataset As...
Import Data From
Tab Delimited Text File (*.txt)
Space Delimited Text File (*.brt)
Comma Separated Values (*.csv)
Excel File (*.xls)
BMDS 1.xx Dataset (*.set)
Export Data To
Close Dataset
Note that: The first row of the imported file is reserved for column headers (variable names). Once
imported, one can change the name of a column header by clicking with the right mouse button the
column header (name) and selecting "Rename Column" from the menu. Column headers must be one
word (no spaces allowed).
The Dataset files created by the BMDS program are stored as DOS text files delimited with blanks (i.e.,
each line will represent a row in the spreadsheet and each blank will signify the start of a new value within
the row). If your file is of this format you can choose either "BMDS 1 .xx Dataset" if the file has a .set
extension or "Space Delimited Text File" from the format menu options. Then the user will have to find the
file in the folder in which it is saved on the computer being used (the default directory is again the Data
directory where BMDS was installed).
B) Modifying Data
1) Cutting and Pasting
Spreadsheet data can be modified using the keystrokes or Edit menu selections for cut (Ctrl+X),
copy (Ctrl+C), paste (Ctrl+V) and Undo (Ctrl+Z) in the normal manner. These operations can also
be used to transfer data to and from other spreadsheet applications such as Excel and Lotus. The
keystrokes shown below for these operations work in all sections of BMDS, including the
Create/Edit spreadsheet.
U_ndo Paste(Ctrl+Z) Will undo a paste or cut.
Cut (Ctrl+X) Selected data is cut from the spreadsheet
Copy (Ctrl+C) Selected data is copied from the spreadsheet
Paste (Ctrl+V) Cut/copied data is pasted into spreadsheet at cursor location.
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Select All Selects the entire spread sheet contents.
2) Adding and Deleting Columns and Rows
Data in columns and rows can be deleted by highlighting the data or the entire column/row (left
clicking on its header/label highlights the entire column/row) and hitting the Delete key. Note that
when all of the cells in a column/row are empty the column/row is removed when the data set is
saved. However, if a column/row contains any data at all, the column/row is retained when the
data set is saved.
3) Sorting
Left clicking on the column header will sort the data set by the values in that column. Additional
left clicks in the column header will toggle between ascending order and descending order for the
sort. If a data field in the selected column is blank the row representing that field will sort to the
top of the spreadsheet (regardless of whether the sort order is ascending or descending). You
must save your data set after sorting if you want the sort to be retained.
4) Transforming Columns of Data
This is accomplished by clicking with the right mouse button in the header of the column where
you want the new (transformed) data to appear and selecting "Transform Column" from the menu
(see the Data Transformation help section, 1.6, below).
5) Renaming Columns of Data
This is accomplished by clicking with the right mouse button in the header of the column where
you want the new column name to appear and selecting "Rename Column" from the menu.
C) Saving the Dataset
The dataset file name is shown in the upper left corner of the data grid screen. Newly created data sets
are initially assigned a default name of "Untitled." If a model is run on a data set before it is saved to
another name, the results of the model run are saved to the root directory of the BMDS program. To save
the dataset to a different name and directory location (it is recommended that you save datasets to a
unique directory) click on the "Save As" button. If "Save As" is selected, the system will prompt for a
filename and a file location. The new file will be saved for future use as a BMDS dataset with a .dax
extension (.dax files are actually text files delimited with blanks). If "Save" is selected, changes will be
saved to the dataset file name that is in use (i.e., the name that appears in the Selected File window).
Note: All result files (e.g., .out and .pit) from model runs on a single dataset (not when run from a session)
are given the same prefix and are saved to the same directory as the .dax file.
D) Selecting a Model to Run
1) Model Type - Select from six model types:
Continuous,
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Dichotomous,
Dichotomous_Alternative,
Nested,
Rptd_Resp_Measures (repeated response measures),_and
Conc_x_Time (concentration x time).
2) Model - Select from a list of models available for the chosen model type.
E) Model Options / Defining Dataset Variables
When the Proceed button is pressed a Model Option Screen appears. That option screen is the one
appropriate to the model chosen. From that option screen the user assigns columns in the data set to the
required variables and selects the model options (e.g., parameter constraints and BMRF values). Once
those choices are complete the user may hit the Run button to complete the analysis of the data set
selected.
In the cases where the Model Type is "Rptd Resp Meausures" or "Conc_x_Time," see sections 1.6 and
1.7, respectively, for a description of the option screens and how to complete an analysis. For all other
model types, the remainder of this section and Section 2.0 describes how to work with the Option
Screens and complete a model run.
All of the variables required for a model must be linked to a column in the spreadsheet. Variables
required for running BMDS on a data set will differ according to the Model Type selected, and will appear
in the "Column Assignments" section of the Model Option Screen for the model chosen. For
Dichotomous andDichotomous_Alternative models, Dose, # Subjects in Dose Group, and Incidence or %.
Positive columns must be identified. For Continuous models, Dose, # Subjects in Dose Group,, Mean and
Standard Deviation columns must be identified if response data are reported by dose group. Dose and
Response columns must be identified if response data are reported for each individual animal. For
Nested models, Dose, Litter Specific Covariate, Incidence and Litter Size must be defined. The
requirements for a Rptd_Resp_Measures or Concx Time model are somewhat different and are
discussed in separate sections of this Help Manual.
Dose
Variable representing the amount of a substance an experimental subject consumes (e.g., oral
drinking water or food studies), is injected with (e.g., gavage or intravenous injection studies) or is
exposed to (e.g., inhalation studies). For inhalation studies, this column would represent the
concentration of the substance in the air being inhaled. Most of the time Dose will be an
independent variable under the control of the experimenter. However, for epidemiological studies
Dose, as well as confounding factors such as age, smoking habits and duration of exposure, are
not under the control of the experimenter and may be different for each individual responder.
While BMDS allows for the entry and analysis of individual Dose information, provisions for
factoring the impact of confounders have not as yet been incorporated.
#Subjects in Dose Group
Independent variable representing the total number of subjects within a dose group for which a
continuous Response is measured ordichotomous Incidence is identified.
Incidence
Dependent variable used for Dichotomous and Nested Models to represent the number of
subjects within a Dose group responding in a positive, generally considered adverse, manner.
% Positive
Dependent variable used for Dichotomous Models to represent the percent of the total number of
subjects within a Dose group that responded positively. The data for this column must be entered
as a percent (not a fraction).
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Mean
Dependent variable used for Continuous Models to represent the average response within a
group (sum of all responses in group divided by Subjects/Group).
Standard Deviation
The positive square root of the variance for a Dose group, which is the sum of the squared
deviations of the individual responses from the mean, divided by # Subjects in Dose Group-1.
Response
This dependent variable refers to the individual continuous data responses by subject. If this
variable is used, the Subjects/Group, Mean and Standard Deviation continuous data variables are
not used and are grayed out.
Litter Size
Number of live pups per litter.
Litter Specific Covariate
This is a covariate such as body weight of dams, number of implants, or litter size that is felt to
best explain response variability between litters. It is used in the nested models to try to account
for that variability. See Nested Model Descriptions for more details.
As indicated above, when these user-specified choices are completed, and the model options are
selected (see the sections below on the options for the specific models) the Run button may be clicked to
compete the analysis.
1.5 Data Transformation
As an option in the Create/Edit Dataset window the user has the ability to create a new data column by
performing a mathematical operation on existing data fields. To perform a transformation double-click with
the right mouse button anywhere in the column where the new data will appear. Select "Transform
Column." Select an operation from the pull down menu. Select the Column(s) on which the operation will
be performed. Enter any operators that may be required. Click OK. The transformed data will appear in
the designated column. The following transformations are available.
1) Log Base 10 of a single column
This option will return the LogQ base 10 of all values in the selected column.
2) Log Base e (Natural Log) of a single column
This option will return the LogQ base e of all values in the selected column.
3) Exponential Base 10 of a single column
This option will return 10 to the x where x is the value in the column for each row in that particular
column.
4) Exponential Base e of a single column
This option will return e to the x where x is the value in the column for each row in that particular
column.
5) Raise column to Power X
This option will raise each value in a column to a specified Power x, where x is a user specified
number.
6) Multiply column by constant X
This option will multiply each value in a column by a specified constant x, where x is a user
specified number.
7) Add two columns
This option will return the value of one column added to the value of a second column for each
row in that particular column.
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8) Subtract two columns
This option will return the value of one column minus the value of a second column for each row
in that particular column.
9) Multiply two columns
This option will return the value of one column multiplied by the value of a second column for
each row in that particular column.
10) Divide two columns
This option will return the value of one column divided by the value of a second column for each
row in that particular column.
11) Quantilize column
This option will return either a 0 or a 1 for all rows based on whether the value in the selected
column is Larger or Smaller than a user specified value. If the selected adverse direction is
"Larger," a 0 will be returned for values lower and a 1 will be returned for values larger than the
user specified value. If the selected adverse direction is "Smaller," a 1 will be returned for values
lower and a 0 will be returned for values larger than the user specified value.
12) Add X to column
This option will add a constant X to each value in a column, where x is a user specified number.
13) SE to Standard Deviation (SD)
This option will convert standard errors (SE) from a designated column to standard deviations
and place them in a designated SD column. The user must also designate the column that
contains the number of subjects in each dose group as that value (n) is used in the calculation.
1.6 Repeated Response Measures Data
Once a data set has been created and saved with a name that is not "Untitled" the user can initiate a
repeated response measures analysis by selecting the Model Type as "Rptd_Resp_Measures" and hitting
the Proceed button. Note that currently there is only one model of this type (the so-called Toxicodiffusion
model) so no model selection needs to be done. An example data set for use with the Toxicodiffusion
model is shown here:
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Hitting the Proceed button will open a special Option Screen specifically designed to facilitate modeling
with the Toxicodiffusion model:
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Animal ID ID
Dose dose
Time time
Response fore, grip
Exposure Time
Ba ckgro und Degre e
BMR Risk Type Extra
BMR Risk Level
Adverse Direction Lowertail
Adverse Definition Background R "
Adverse Level
Low Cut-off
High Cutoff
Chart Title (optional)
Time Axis Scale Natural
f of Time Points
Parameters Options
AO Default
BO Default
CO Default
KO Default
ToxicoDiffusion Bootstrap BMDS MODEL RUN
Chemical Name
Exposure Type
Species Name
C:\USEPA\BMDS21Beta\Data\TETacForeGrip.dax
C:\USEPA\BMDS21Beta\Data\ToxTETSet.out
Set Values To
Default
Optimize Initial
Pafam. Values
ToxicoDiffusion_beta->Rptd_Resp_Measures
This Option Screen is very similar to that for other BMDS models, so the following information will focus
on the unique aspects.
The data for such an analysis will consist of one or more measurements from any given experimental unit
(animal) at different times before or after the exposure. Thus, the data set must include a column that
identifies which animal the observations come from (the "ID" column in the above example). Even though
it is assumed that each animal is exposed to only one dose level, each row of data must include the dose
value; the column assignment for that dose value is specified as shown above. The time of each
observation (row) must be given (the "time" column in the above example) and the value of the response
at that time must be recorded (in the "fore.grip" column in the above example).
There is a section specifying the Plotting Assignments. The properties of the resulting graphs can be
identified here.
As with other BMDS model Option Screens, the Parameter Assignments section allows the user to let the
program find initial values for the optimization runs (Default - the values "-9999" shown in the option
screen are merely flags to pass to the input file that indicate this default option, they are not real initial
values) or to initialize the parameter values to values of the user's choice (the "Initialize" option).
Currently, the Toxicodiffusion model does not allow users to specify values of the model parameters.
The "Other Assignments" section allows the user to define other important components for the analysis.
The time at which exposure occurs (time zero in many experiments) must be specified. So too must the
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user specify the background degree, which is an integer between 0 and 2 that determines how the
responses are assumed to vary overtime in the absence of exposure. This background (without-
exposure) variation is defined by a polynomial of the specified degree (constant, linear, or quadratic for
the choices 0, 1, or 2, respectively).
Adverse responses can be defined in one of two ways. Either a background rate of adverse response is
specified (e.g., a 5% rate of adverse response in the absence of exposure) or cut-off value(s) can be
specified, with the assumption that values above or below (depending on the adverse direction) the cut-
offs) are adverse. The background rate of response need only be defined of the definition is in terms of
background rate (probability) of response; the cut-off(s) need only be defined if the definition is in terms of
cut point(s).
"Other Assignments" also allows specification of the number of bootstrap iteration to run to estimate
confidence bounds. As shown below, those bounds can be one-sided or (if the "Use Two Sided Cl?" box
is checked) two-sided:
Adverse Definition
Adverse Level
Low Cut-off
High Cut-off
Use Two Sided Ci?
Confidence Levei
Bootstrap Iterations
Bootstrap Result?
The number of bootstrap iterations should be large enough to provide a stable estimate of the bounds.
The value shown above (100) is almost certainly too low for a final, stable estimate of those bounds.
Values on the order of 100 or more will probably be required in most cases; the user should perhaps do
several runs to determine that the bound estimates have stabilized for the number of iterations chosen.
Increasing the number of iterations will noticeably increase the time it takes to run the model.
IMPORTANT NOTE: For the field "Confidence Level" the user must actually enter an a value such that
the level of confidence is (1-a)*100%. For example, in the screen shot above, the "Confidence Level field
has the value 0.05. This corresponds to requesting 95% confidence limits: (1 - 0.05)*100% = 95%.
Finally, the "Study Description" section is where the user can supply any additional experiment-specific
information that s/he wished to have reported in the output files.
Once all the options have been specified as desired, clicking on the Run button will initiate the repeated
measures analysis. The run will produce a set of five graphs which will flash momentarily on the screen.
when the run is complete the full set of five plots will be available in a summary plot screen. The
individual plots can be copied and pasted into other files (e.g., a Word document file).
1.7
Concentration x Time Data
Once a data set has been created and saved with a name that is not "Untitled" the user can initiate an
analysis of Concentration/Time data by selecting the Model Type as "Conc_x_Time" and hitting the
Proceed button. Note that currently there is only one model of this type (the so-called ten Berge model),
so no model selection needs to be done. Hitting the Proceed button will open a special Option Screen
specifically designed to facilitate modeling with the ten Berge model:
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jnc maPer n Minutes
t « Column Assignments »
Description Column
f Subjects
Incidence
Explanatory Varl
Explanatory Var2
Model ^^^^^
Description
Calculations Desired?
Compuie Confidence Interval?
Sfd. Deviation for Confidence Interval
Y- « Product Terms » ^
Transform. Main Effect
A
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none " O
none " O
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Calculate Dose For Calc'd Response For Ratio of Parameters **"
Given Response Given Exp. Vars For Two Exp. Vars
0 0 O
0 0 0
1.96 1.96 1.96 v
At the top of this Option Screen are the data from the data set that was used to get to this screen. The
data should include a variable corresponding to the number in each group ("Exposed" in this example)
and the number in each group responding ("Dead" in this example). When the user fills in those two
choices in the Column Assignments section of the screen, the remaining column names will appear as
possible explanatory variables (Explanatory Var1, etc.) automatically. Currently, there is a limit of five
possible explanatory variables. There must be at least two possible explanatory variables; if there is only
one possible explanatory variable, the user does not need the Conc_x_Time model - a standard dose-
response model from among the Dichotomous or Dichotomous_Alternative model types will suffice.
Not all the possible explanatory variables need be included in the model as main effects or in the product
terms. Moreover, explanatory variables included as main effects (by checking the corresponding box in
the "Main Effect" column) need not be in the product terms and the product terms need not be restricted
to variables included as main effects. One example is shown below:
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« Column Assignments »
Description Column
f iiuoje cfs hxp o s e d
Transform.
Main Effect
Incidence Dead "
Explanatory Varl Conc_mg_Per_m " logarithmic -
Explanatory Var2 Minutes 'none "
Explanatory Var3 BW_grams "none '
0
D
« Product Terms »-
1 BW_grams
2
3
The variables can be used as is or transformed. The transformations available are the logarithmic (y =
Ln(x)) and reciprocal (y = 1/x) transformations. Whatever transformation is chosen will be used
everywhere that variable occurs in the specified model (main effect and any product terms).
A logit or a probit model may be selected as the basis for the concentration-time modeling:
Probit
Background Correction
Logit
Calculate Dose For
Given Response
Calc'dResponse For
Given Exp. Vars
Ratio of Parameters
For Two Exp. Vars
In addition, the user may specify what type of estimates are desired. A BMD type of calculation would
correspond to the choice "Calculate Dose for Given Response" where the user specifies a response level
(e.g., 10) as a percentage (strictly between 0 and 100) and then requests the valye for one of the
explanatory variables included in the model when the other explanatory variables are set to specific
values. And example is shown below:
Description
Calculations Desired?
Compute Confidence Interval?
Std. Deviation for Confidence Interval
% Response of Interest
Given Response
0
0
1.96
10
Given Exp. Vars
0
0
1.96
For Two Exp. Vars
0
0
1.96
V
Fmd Corr. Value For Conc_rng_Per_r '
When Minutes '
When BW grams '
The "Std. Deviation for Confidence Interval can be determined from the table below. Note that this
approach was used here because one might often be using a value from a t-distribution rather than a
normal distribution. See the documentation for the ten Berge model for additional information.
Table 1: Deviates Corresponding to Confidence Levels of Interest for Confidence Interval Estimation
(from Standard Normal Distribution)
a
0.2
0.1
0.05
0.01
Confidence Level
80%
90%
95%
99%
Deviate
1.282
1.645
1.960
2.576
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The user can determine the deviate to use for other confidence levels of interest from a table of quantiles
of a standard normal distribution, available in many elementary statistics books (or s/he may compute
them using Microsoft Excel function "NORMSINV" and putting in (1-a/2) as the argument to that function
when interest is in the 100*(1-a) confidence interval).
If the user is more interested in estimates of the response when all the explanatory variables are at
specified values or in the ratio of the parameters of given main effects (often considered when
concentration and time are logarithmically transformed as a measure of "n," the slope of the response
contours on the Ln(conc)-Ln(time) plots). In all of these cases, if the user indicates that such estimates
are desired (the appropriate box in the "Calculations Desired?" row is checked by clicking on it), then the
cells corresponding to the remaining required fields will no longer be grayed out and values must be
entered for all such fields.
Once a ten Berge modeling option screen has been completed, it may be saves using the Save or Save
As buttons on the screen. The extension for a ten Berge model run is ".ten" and should be used with all
such saves. If, later, the user want to revisit a saved ten Berge analysis, the File menu item can be used
to do so:
File; | Edit View Tools Windows Help
New
Open
New Dataset
Open Dataset
Exit
Dose Response Session
ten-Berge
gmw,
I
Clicking on the ten-Berge option shown will open a window showing all the ten Berge (.ten) files in the
Daya folder of the directory where BMDS was installed. As usual, the user may navigate in that window to
the location where the desired ten Berge analysis file is located.
1.8 Software Removal
Users need to uninstall (remove) prior versions of the BMDS 2.1 software before installing a new version
to their computer. To uninstall the BMDS application, go to Control Panel, open the Add or Remove
Programs utility, select the BMDS 2.1 program in the list, and click on the "Remove" button. Simply
deleting the application files doesn't uninstall the software. Note: If the user doesn't have the proper rights
in the computer, the "Remove" button will not be shown and the user should uninstall BMDS by re-starting
the original setup.exe file and then choosing "Remove Benchmark Dose Software"
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2.0 MODEL OPTIONS SCREENS
The Model Option Screen allows users to change options available for a model run. When BMDS is
initially run or when the "Reset to Defaults" button is selected all options are set to their default values
(identified below). Options chosen and saved in to an Option file (opt extension) will be retained for later
use.
BMD Calculation
BMDL Curve. Cafe.
He strict Po war >= 7
Dose Dose
f Subjects in Dose Group N
incidence
Positive
Confidence Level
BMRF
Dose Groups
Iteration
Relative. Function
250
1.00E-08
1.00E-08
Parameter
Risk Type Extra
Parameters Active Opt.
Background Default
Slope Default
Power Default
BMDS Model Run
C:\USEPA\BMDS21 Beta\Data\CONTINUOUS1 .dax
Set Values To
Default
Optimize Initial
Pa ram. Values
Gamma- >Dichotomous
Each Model Option Screen contains features which are unique to the model being run. For a discussion
of these model specific features see the above Related Topics. All Model Option Screens have the
following common features:
Model Type and Name
In the lower left corner of the option screen the name of the specific model being employed and the
model type (Dichotomous, Continuous, Nested, Dichotomous-Alternative, or Repeated Response
Measures) are displayed.
Data File
A field displaying the name of the data file (*.dax) file.
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User Notes
This is an editable field of up to 80 characters in length. The content of this field will be displayed in a
single line of text under the date in the *.out file.
Column Assignments Section
This section allows the user to assign columns from the data file to the parameters that are required
for model runs.
Optimizer Assignments Section
This section specifies information controling the determination of convergence of the model runs. In
general, the user need not be concerned about modifying these values.
Iteration: An upper limit to the number of interations that will be used in the optimizations (default
= 250).
Relative Function: This specifies the criterion for ascertaining relative function convergence
(default = 1 .Oe-8)
Parameter Function: This specifies the criterion for ascertaining parameter convergence (default
= 1 .Oe-8)
Parameter Assignments Section
The user can choose one of three options related to parameter values:
Default option: the initial estimated value for a parameter is determined by the program and its
value will vary during optimizations;
Specified option: the initial value for a parameter is as specified by the user and its value will
remain at that specified value during all optimizations;
Initialized option: the initial estimated value for a parameter is entered by the user but its value
will vary during optimizations. If the initialize option is checked for any parameter, the user must
choose the Specified or Initialized option for all parameters.
Other Assignments Section
This section contains information on parameter constraints and choices for BMD and BMDL
calculations. All models contain the following fileds in the Other Assignments section.
BMD Calculation: Specifies whether ot not the user wants a BMD (with associated BMDL)
calculated.
BMDL Curve Calc: When this option is selected, the graph resulting from the model run will
display a blue BMDL curve. The BMDL curve is estimated by calculating the BMDL for BMDs at
BMRs of 1, 5, 10, 20 and 30%, and connecting these points via either a straight line. The
calculation of the BMDL curve has been known to cause some convergence problems and can
significantly increase computer run time, particularly if several models are being run in a session.
Thus, the current default and recommended option is to not request calcuation of the BMDL curve
unless absolutely necessary (the BMDL for the requested BMRF will still be estimated and
displayed in the output file regardless of the choice for this option).
Confidence Level: The confidence level (default 0.95) associated with the BMDL calculation.
BMRF: The factor defining the benchmark response level. Its value will depend on the Risk Type
or BMR Type specified by the user (one of these types will also be in the Other Assignments
section, depending on the model type).
Other Buttons
The option file screen also have buttons to Set values to their Defaults, to Save the option file (or
"Save As ..." if one wants to change the option file name), to Run the model, and to Close the option
file screen.
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2.1 Dichotomous and Dichotomous_Alternative Model Option Screens
All of the common options described above are available on the Model Option Screens for Dichotomous
and Dichotomous_Alternative models. In addition, the following ttw options are available in all Option
screens for dichotomous models.
Dose Dose
Subjects in Dose Group N
Incidence
Positive
iteration
Relative Function
Parameter
Risk Type Extra
Parameters Active Opt.
Background Default
Slope Default
Power Default
BMDS Model Run
C:\USEPA\BMDS21 Beta\Data\CGNTINUOUS1 .dax
Set Values To
Default
Optimize Initial
Param. Values
Gamma->Dichotomous
Dose Groups
This is a read-only field indicating the number of Dose groups recorded from the data set file for
input into the model.
Risk Type
Choices are "Extra" (Default) or "Added." Added risk is the additional proportion of total animals
that respond in the presence of the dose, or the predicted probability of response at dose d, P(d),
minus the predicted probability of response in the absence of exposure, P(0). Extra risk is the
additional risk divided by the predicted proportion of animals that will not respond in the absence
of exposure, 1 - P(0). Thus, extra and additional risk are equal when background rate is zero.
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The BMRF for all dichotomous models must be between 0 and 1 (not inclusive).
Note about BMRF and Graphs
The response associated with the BMP that is displayed in the graphical model output will only be
the same as the BMR when P(0) = 0. This is because to obtain the actual response value one
must solve for P(d) in the equation for added or extra risk discussed above.
In addition to the two options listed above for all dichotomous models, the following options are available
for specific models of the Dichotomous or Dichotomous_Alternative Type.
Restrict Slope >= 1
Models: LogLogistic, Log-Probit, Dichotomous-Hill, LogProbit-BgDose
If the slope is allowed to be less than 1, the slope of the dose-response curve is infinite at zero
dose.
Restrict Power >= 1
Models: Gamma,, Weibull, Gamma-BgDose, Weibull-BgDose
Selecting this feature (Default) restricts the power parameter (a) to a value of 1 or greater. If a <
1, then the slope of the dose-response curve becomes infinite at the control dose. This may be
biologically unrealistic, and can lead to numerical problems when computing confidence limits, so
several authors have recommended restricting a >= 1.
Degree of Polynomial
Models: Multistage, Multistage-Cancer, Multistage-BgDose, Multistage-Cancer-BgDose
This is the degree of the polynomial model that will be used, or the number of times dose is
factored into the model equation (maximum = 23). A value must be entered here before the
model will run. Polynomial degree should not exceed the number of dose groups unless the beta
coefficients of the model are specified or restricted (beta coefficients are always restricted in the
multistage-cancer model).
Restrict Betas >= 0
Models: Multistage, Multistage-BgDose
Selecting this feature (Default) restricts all of the beta (p) parameter coefficients in the multistage
model to a value of 0 or greater.
2.2 Continuous Model Option Screens
All of the common options described at the beginning of section 2.0 are available on the Model
Option Screens for Continuous models. In addition, the following three options are available in all
Option screens for continuous models.
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Constant Variance(Hno.
BMD Calculation
BMDL Curve. Gale.
He -strict Po wer >=J
f Subjects in Dose Group N
Mean Mean
Std. Deviation Std
Response
Confidence Level
BMRF
Iteration
Relative Function
Parameter
250
1.00E-08
1.00E-08
Adverse Direction Automatic
8MB Type Std. Dev.
Parameters Active Opt. Value
Alpha Default v
Rho Default v
Control Default
BMDS Model Run
C:\USEPA\BMDS21 Beta\Data\CONTINUOUS1 .dax
, Show Data
Set Values To
Optimize Initial
'Value?
Power- ><_ontinuous
Constant Variance
When selected (Default), the model assumes a constant variance across all dose groups. If not
selected, then the model assumes that the variance can be different for each dose group, and
varies as a power function of the mean response (see Continuous Model Descriptions for more
details).
Adverse Direction
Choices for the Adverse Direction option are "Automatic," (Default), "Up" or "Down." This option
refers to whether adversity increases as the dose-response curve rises "up" or falls "down." If
automatic is chosen, the software chooses the adverse direction based on the shape of the dose-
response curve. Manually choose the adverse direction if you know the direction of adversity for
the endpoint being studied. This selection only impacts how the user-designated BMR is used in
conjunction with model results to obtain the BMD.
BMR Type
The BMR type is the method of choice for defining the response level used to derive the
benchmark dose (BMD). The choices allowed are "Rel. Dev." (Default), "Abs. Dev.," "Std. Dev.,"
"Point" and "Extra" (Hill model only). "Rel. Dev." (Relative Deviation) means the response
associated with the BMR will be the background estimate plus or minus (depending on the
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Adverse Direction) the product of the background estimate times the BMRF entered by the user.
"Abs. Dev." (Absolute Deviation) means the response associated with the BMR will be the
background estimate plus or minus the BMRF. "Std. Dev." (Standard Deviation).means the
response associated with the BMR will be the background estimate plus or minus the product of
the BMRF times the standard deviation for the control group data. "Point" means the response
associated with the BMR will be the BMRF value itself. "Extra" (Hill and some exponential models
only) means the response associated with the BMR will be the background estimate plus or
minus the product of the BMRF times the difference between the background estimate and the
model estimate of the maximum/minimum response. "Extra" is similar to Extra risk for
dichotomous data, except that the maximum (or minimum) achievable response is not 1, but is
estimated from the model.
Rel. Dev.Response = m(0) + (BMRF* m(0)) (Default)
Abs. Dev.Response = m(0) + BMRF
Std. Dev.Response = m(0) + (BMRF*STD)
Point Response = BMRF
Extra (Hill and some exponential models only)
for "up" Response = m(0) + (BMRF*(mmax - m(0)))
for "down" Response = m(0) - (BMRF*( m(0) - mmin))
where m(0) is the mean response when exposure equals zero, STD is the standard
deviation when exposure equals zero, mmax is the maximum predicted mean from the Hill or
exponential model, and mmin is the minimum predicted mean from the Hill or exponential model.
In addition to the three options listed above for all continuous models, the following options are available
for specific continuous models.
Degree Poly
Models: Linear, Polynomial
This is the degree of the polynomial model that will be used, or the number of times dose is
factored into the model equation (maximum = 21). A value must be entered here before the
model will run. Polynomial degree should not exceed the number of dose groups unless the beta
coefficients of the model are restricted. For the linear model, this field is set to 1 and is not
editable.
Restrict Power >= 1
Models: Power, Exponential
The power parameter can be restricted to be greater than or equal to one. The power is
unrestricted if this option is not selected.
This option is currently disabled for the exponential models.
Restrict n >1
Models: Hill
The n parameter of the Hill model can be restricted to be greater than one. The n parameter is
unrestricted if this option is not selected.
Restriction
Models: Linear, Polynomial
Restrictions on coefficients of the dose terms can be "None" (Default), "Non-negative" (>0), or
"Non-positive" (<0). Note that, while no restrictions (None) is the current default for this option,
the user should specify that the parameters be restricted to either Non-negative or Non-positive
values whenever possible to avoid "wavy" model responses (see details in Polynomial Model
description). Since there is only one dose coefficient in the continuous Linear model, this is
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sometimes referred to as restricting the slope of this model.
Unique Options for Exponential Models
The exponential model choice actually allows the user to run up to four models that have
exponential-dose terms. These models are referred to as exponential Models 2-5 (following a
designation by Wout Slob, wherein the restricted (flat) model was model 1). See the section on
the definition of the continuous models for additional details.
The user may choose to run any or all of the exponential models when running from a Session
screen. (When running on a single data set by use of the data grid - see section 1.4 - all
exponential models will be run.) Moreover, the user may select to have the exponential model
runs reported (grouped) together in one output file or on separate output files. These choices are
made in the "Model Selection" section of the exponential model option screen:
' «Cotuma Assignmenfs»~
Dote Dose
f Subjects in Dose Group N
Mean Mean
Std. Delation Std
Response
' «Ofher Assignments»
«Opfimizer A ssignments»
Iteration
Ftelafive Function
Parameter
250
1.00E-08
1.00E-08
Distribution Normal
Solution
Confidence Level
Constant Variance(Ftrto=0) 0
BMD Calculation 0
fJe strict Po wer >= 7
Adverse Direction
BMR Type Std. Dev.
BMHF
°-95
Parameters Options
/nA/pfta Default
flho Default
a Default
6 Default
c Default
IBMDS Model Run
Mode/ 2
Mode/ 3 ;0
Model 4 '0
ModelS 0
Grouped
Other options unique to the exponential model option screen are as follows:
Distribution: The user may choose to assume that the data are normally or lognormally
distributed around the dose-group-specific means. The choice of the distribution affects
that type of MLE solution that may be obtained (see next option). Moreover, when a
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lognormal distribution is assumed, only constant (log-scale) variance models will be fit to
the data; such models correspond to an assumption of a constant coefficient of variation.
Solution: The user may choose to get an exact or approximate MLE solution. When the
data are assumed to be normally distributed, the choice is fixed at "Exact" because the
exact solution is available no matter how the data are presented (either as group-specific
means and variances or as individual responses). When the data are assumed to be
lognormally distributed and the data are presented in terms of group-specific means and
standard deviations, then the exact MLE solution can not be obtained. In that case, the
"Solution" option is fixed at "Approximate" and the means and standard deviations of the
log-transformed data are estimated as follows:
log-scale mean = In(mean) - ln(1+(std/mean)2)/2
log-scale std = sqrt[ln(1+(std/mean)2)]
When the data are assumed to be lognormally distributed and the individual responses
are available the user may choose between the exact and approximate solutions. In this
case, the user is advised to select the exact solution; the only reason to select the
approximate solution in this case would be to compare it to other calculations that were
done approximately out of necessity.
The "Extra" BMR Type is available for the exponential models. Note, however, that only
exponential models 4 and 5 estimate a maximum (or minimum) mean response, so it is
only for those two models that extra risk can be defined. If running models 2 and 3 along
with models 4 and 5 with the Extra BMR Type, no BMD or BMDL will be calculated for
models 2 and 3.
Also note that in the "Parameter Assignments" section, each model has a separate tab to
allow model-specific parameter designations (the default, specified, and intialized options
discussed above.
2.3 Nested Model Option Screens
All of the common options described at the beginning of section 2.0 are available on the Model
Option Screens for Nested models. Note that in the "Column Assignments" section, the
parameter "Litter Size" has replaced "#Subjects in Group" and an additional parameter, "Litter
Specific Covariate" has been added; these designations reflect the primary use of the nested
models, i.e., for modeling data from reporductive or developmental assays in which the number of
responders within litters of certain sizes are recorded. The following six options are available in all
Option screens for nested models..
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Re strict Power >=J
BMD Calculation
BMDL Curve. Calc.
Litter Size Total
incidence Response
Litter Specific Covariate Litter
Dose Groups
BMR
Confidence Level
Iteration
Relative Function
Parameter
250
1.00E-OS
1.00E-08
Risk Type Extra
Fixed Litter Size
Parameters Active Opt.
Alpha i Default
Rho Default
Beta ' Default
Litter Specific Covariate Use
Infralitfer Correlafionsl Estimate
Set Values To
Default '"
Optimize Initial
Rai_and_Van_Ryzin->Nested_DichQtQmQus Model
Dose Groups
This is a read-only field indicating the number of Dose groups recorded from the data set
file for input into the model.
Restrict Power >=1
Power parameter can be restricted to be > 1 (Default)
Risk Type
Choices are "Extra" or "Added." Additional risk is the additional proportion of total animals
that respond in the presence of the dose, or the probability of response at dose d, P(d),
minus the probability of response in the absence of exposure, P(0). Extra risk is the
additional risk divided by the proportion of animals that will not respond in the absence of
exposure, 1 - P(0). Thus, extra and additional risk are equal when background rate is
zero.
Fixed Litter Size
Choices are "Control Group Mean" (Default) or "Overall Mean." See Nested Model
Descriptions for an explanation as to why this option is necessary, and which choice
would be preferred for your given data set. Basically, if the Litter Specific Covariate is not
affected by dose, the Overall Mean should be used. If the Litter Specific Covariate is
affected by dose, consider using the Control Group Mean.
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Litter Specific Covariate
Provides user with the option to allow the models to attempt to account for a litter specific
covariate or not. If "Use Litter Specific Covariate" is selected (Default), all of the Theta
values are estimated . If "Don't Use Litter Specific Covariate" is chosen, all of the Theta
values are set to zero.
Intralitter Correlations
Provides user with the option to allow the models to attempt to estimate intralitter
correlations or assume they are zero. If "Estimate Intralitter Correlations" is selected
(Default), all of the Phi values are estimated (one for each dose group). If "Assume
Intralitter Correlations Zero" is chosen, all of the Phi values are set to zero.
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3 MODEL DESCRIPTIONS
3.1 Continuous Model Descriptions
Special Considerations for Models for Continuous Endpoints in Simple Designs
Models in this section are for continuous endpoints, such as weight or enzyme activity measures, in
simple experimental designs that do not involve nesting or other complications. The models predict the
mean value of the response, A(ctose), expected for a given dose.
Models for continuous endpoints require consideration of more details than do those for dichotomous
endpoints in similar designs. While for dichotomous models, we normally model the incidence of
adversely affected individuals, and so expect the response to increase with increasing dose, in
continuous models the change in a measure is modeled without regard for "adversity", and the response
may increase or decrease. Thus, just what constitutes an adverse change, and how to specify it, must be
made explicit. The models in BMDS allow that specification to be made in several ways, which will be
described below (BMP Computation').
Another important contrast with dichotomous models is the nature of the probability distribution of
response. In dichotomous models, the nature of the experimental design guarantees that the binomial
probability distribution is appropriate. There are many more options for continuous distributions, however.
In the current version of BMDS, the distribution of continuous measures is assumed to be normal, with
the exception of the Exponential Models, for which the user may assume either a normal or a lognormal
distribution (see the section on the Lognormal Distribution below). Moreover, for all models and normally
distributed data, one may assume either a constant variance (that is, the variance is the same regardless
of dose group), or a variance that changes as a power function of the mean value:
which is the modeled variance for the ith dose group, the expression A(c/ose/) is the observed mean (from
the model) for the ith dose group, and a (alpha) and p (Rho) are estimated parameters. This formulation
allows for several commonly encountered situations. For example, if p = 2, then the coefficient of variation
is constant, a common situation especially for biochemical measures; if p = 1, then the variance is
proportional to the mean, which is sometimes appropriate for large counts (especially if the constant of
proportionality, k, is 1.0). When a lognormal distribution is assumed, the Exponential Models assume a
constant (log-scale) variance, equivalent to a constant coefficient of variation.
Likelihood Function
Suppose there are g doses,
dose i*,,., dose-g
with NI subjects per dose group, and that y,y is the measurement for they"1 subject in the ith dose group.
The form of the log-likelihood function depends upon whether the variance is assumed to be constant, or
to vary among doses.
For constant variance, the log-likelihood function is:
L = -|
i
where
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- jv< - i
is the sample variance for the ith dose group,
is the sample mean for the ith dose group, g is the number of doses, N, is the number of subjects in the
ith dose group, and o2 the variance which is same in all dose groups. Generally, o2 and the parameters
hidden here in A() are to be estimated.
If the variance is allowed to be a power function of the mean, the log-likelihood function is:
where
tt_ -
J * 1 *~fc r ,-" T 'ii 1 *> , _ .. , n, 1 1
with
B, = Nifa.
BMD Computation
In the continuous models, the benchmark dose is always the dose that results in a prespecified change in
the mean response. The change can be expressed in several ways
an absolute change in the mean (Abs. Dev.);
a change in the mean equal to a specified number of control standard deviations (Std. Dev);
a specified fraction of the control group mean (Rel. Dev.);
a specified value for the mean at the BMD (i.e., not a change, but a fixed value) (Point);
a change equal to a specified fraction of the range of the response, applicable only when the dose-
response has an asymptote at high doses (Extra) [Hill and some Exponential models only].
Symbolically, these are (where 6 represents the BMRF designated by the user):
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5 Abs. Dev,
5 - (Jl Std, Dev,
5-MO) ReL Dev,
fi(BMD) = ff Point
= d Extra
MO)
BMDL Computation
BMDS currently only calculates one-sided confidence intervals, in accordance with current BMD practice.
The general approach to computing the confidence limit for the BMD (called the BMDL here) is the same
for all the models in BMDS, and is based on the asymptotic distribution of the likelihood ratio (Crump and
Howe, 1985). Two different approaches are followed in these models. In one, the equations that define
the benchmark response in terms of the benchmark dose and the dose-response model are solved for
one of the model parameters. The resulting expression is substituted back into the model equations, with
the effect of reparameterizing the model so that BMD appears explicitly as a parameter. A value for BMD
is then found such that, when the remaining parameters are varied to maximize the likelihood, the
resulting log-likelihood is less than that at the maximum likelihood estimates by exactly
In the polynomial and exponential models, it is impractical or impossible to explicitly reparameterize the
dose-response model function to allow BMD to appear as an explicit parameter. For this model, the BMR
equation is used as a non-linear constraint, and the minimum value of BMD is determined such that the
log-likelihood is equal to the log-likelihood at the maximum likelihood estimates less
Lognormal Distributions
In previous versions of BMDS, continuous data were always assumed to be normally distributed. In the
current version of BMDS, for the exponential models only, the user has the option of specifying that the
continuous data being analyzed are lognormally distributed. Lognormal distributions are appropriate only
for data that are strictly positive and may be preferable for such data (since the normal distribution allows,
in theory, both positive and negative values, no matter what the mean and standard deviation). When a
lognormal distribution is specified, the models assume a constant log-scale variance, which is equivalent
to an assumption of a constant coefficient of variation (CV).
The likelihood function shown above is then correct for data on the log scale (log-transformed) and is the
basis for fitting the log-transformed version of the model in question. That is, if u.L(dose) is the log-scale
mean as a function of dose, the model being fit is u.L(dose) = ln{m(dose)}, where m(dose) is the specified
model (e.g., one of the exponential models parameterized as shown in the section on Exponential
Models). Therefore, m(dose) will then be a description of the change in the median response as a
function of dose since the anti-log of the log-scale mean is the median.
Note: when the input data are summarized in terms of the sample mean and sample standard deviation
(or standard error or variance), the exact likelihood of the data can not be determined if the data are
lognormally distributed. In such cases, BMDS gives an approximate MLE solution by estimating the log-
scale sample mean and log-scale sample standard deviation for each dose group as follows:
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estimated log-scale sample standard deviation (s, ): sqrt{ln[1 + s2/m2]}
estimated log-scale sample mean (mL): ln[m] - SL 12
where m and s are the reported sample mean and sample standard deviation. When individual responses
are available, the user may input those values (where the input dax file will have two columns reporting
the dose and the response for each experimental unit) and may request that the exact MLE solution be
obtained (which the software does by first log-transforming the individual responses) or that the
approximate solution using the estimates shown above be obtained (which the software does by first
computing sample means and sample standard deviations). This option allows the user to compare
estimates and determine the impact of the approximation or to provide consistency across data sets if
some data sets have individual responses while others do not.
3.1.1 Linear Continuous Model Description
Model Form
The Linear model is a form of the polynomial model. The formula for the polynomial model is
- fto + ftidose + fkdose* + + findasen
The linear model is a special case of the polynomial model, with n restricted to 1 .
Parameters
Alpha is a from the variance model (see Continuous Model Description)
Rho is p from the variance model (see Continuous Model Description)
BetaO ... Betan is pi ... pn; polynomial coefficients.
Special Options
Degree Poly is Degree of polynomial.
Restriction
One of "None", "Non-Positive", "Non-Negative". Determines restrictions on the polynomial
coefficients. Restricting them to be either non-positive or non-negative guarantees that the
resulting function will be strictly decreasing, strictly increasing, or perfectly flat (when all the
coefficients are zero). If the coefficients are unrestricted, more complicated shapes are possible,
and, particularly as the degree of the polynomial approaches the number of dose groups minus
one, the polynomial will often be quite "wavy". When the coefficients are unrestricted and the
degree is one less than the number of dose groups (for example, if there are four dose groups,
including control, if the degree of the polynomial is three), then the model will exactly reproduce
the means of the dose groups.
BMD Computation
The appropriate relationship for the BMR is solved (see Continuous Models: BMD Computation) using
numerical methods.
BMDL Computation
The BMR equation (see Continuous Models: BMDL Computation) is used as a non-linear constraint, and
the minimum value of BMD is determined such that the log-likelihood is equal to the log-likelihood at the
maximum likelihood estimates less
3.1.2 Polynomial Continuous Model Description
Model Form
The formula for the polynomial model is
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ji(dose) fto + ftidoxK + fadose" + + findo.= 1
Restrict 6 >= 1. If 6 < 1, then the slope of the dose-response curve becomes infinite at the control
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dose. This may be biologically unrealistic, and can lead to numerical problems when computing
confidence limits, so several authors have recommended restricting 6 >= 1.
BMD Computation
The appropriate relationship for the BMR is solved (see Continuous Models: BMD Computation)
analytically.
BMDL Computation
The equations that define the benchmark response in terms of the benchmark dose and the dose-
response model are solved for the slope. The resulting expression is substituted back into the model
equations, with the effect of reparameterizing the model so that BMD appears explicitly as a parameter. A
value for BMD is then found such that, when the remaining parameters are varied to maximize the
likelihood, the resulting log-likelihood is less than that at the maximum likelihood estimates by exactly
2
3.1.4 Hill Continuous Model Description
Model Form
The form of the Hill model is:
r
, n . ,
k +d
Parameters
Intercept (Control) = y
Slope = k
Power = n
Sign = v
Special Options
Restriction
When the "Restrict n > 1" box is checked, the power parameter will be estimated to be greater
than or equal to 1.
BMD Computation
The appropriate relationship for the BMR is solved (see Continuous Models: BMD Computation)
analytically.
BMDL Computation
The BMR equation (see Continuous Models: BMDL Computation) is used as a non-linear constraint, and
the minimum value of BMD is determined such that the log-likelihood is equal to the log-likelihood at the
maximum likelihood estimates less
3.1.5 Exponential Beta Continuous Models Description
Introduction
Dr. Wout Slob of RIVM in The Netherlands has proposed a set of nested models known as the
exponential models. Currently, these models should be fit only to data having positive (mean) values.
There are four exponential models fit by BMDS and they are defined and labeled as follows.
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Model Form
Model 2: m(dose) = a*exp{sign*b*dose}
Model 3: m(dose) = a*exp{sign*(b*dose)d}
Model 4: m(dose) = a*(c - (c-1)*exp{-1*b*dose})
Model 5: m(dose) = a*(c - (c-1)*exp{-1*(b*dose)d})
[Model 1, as defined by Dr. Slob, is the constant-mean model, called R in BMDS, which is estimated for
every continuous data run.] The parameter "sign" is the indicator of the direction of change: +1 for data
trending up, -1 for data trending down. It is very important that the user correctly specify the direction of
change in the data - for the Exponential Models the "automatic" choice of adverse direction has not been
included. Some indicators that the wrong direction has been used for any given run include the
observation that one or more models result in a flat curve fit, that optimal solutions for MLE parameters or
BMDLs have not been obtained, and/or that the likelihoods associated with the models are much worse
than models A1 to A3 (and are more like model R).
Parameters
For all the exponential models the following restrictions apply:
Background Response: a (> 0)
Slope: b (> 0)
Asymptote Parameter: c [Models 4 and 5 only]
c >1 for increasing data
0 < c < 1 for decreasing data
Power: d (> 1) [Models 3 and 5 only]
Restrictions
There are no restrictions beyond the parameter constraints shown above for each model.
BMD Computation
The appropriate relationship for the BMR is solved (see Continuous Models: BMD Computation)
analytically.
BMDL Computation
The BMR equation (see Continuous Models: BMDL Computation) is used as a non-linear constraint, and
the minimum value of BMD is determined such that the log-likelihood is equal to the log-likelihood at the
maximum likelihood estimates less
3.2 Dichotomous Model Descriptions
Special Considerations for Models for Dichotomous Endpoints in Simple Designs
BMDS includes in this category models for dichotomous endpoints in which the observations are
independent of each other. In these models, the dose-response model provides the probability that an
animal will have an adverse response at a given dose. The actual number of animals that have an
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adverse response is assumed to be binomially distributed. An example of such a data set is a study in
which adult animals are exposed to different concentrations of a toxicant and then evaluated for the
presence of liver toxicity. For models for dichotomous endpoints in which the responses are nested (for
example, pups in litters, and litters nested within doses), see the section Nested Dichotomous Endpoints.
BMDS contains ten models for dichotomous endpoints (the Probit, Log-Probit, Logistic, Log-Logistic,
Weibull, Quantal Linear, Gamma, Multistage, and Multistage-Cancer models). They may all be written in
the form:
Prob{response> = y + (1 - v)F(ctose; a, p, . . .)
Here F(dose; a, p, . . .) is a cumulative distribution function and y, a, P, , are parameters to be
estimated using maximum likelihood methods. Sometimes Prob{response> is written as P[ctose; y, a, p,
. . .] to indicate the relationship between the response probability and the dose as well as parameters.
When the function F(ctose; a, /3, . . .) approaches zero as dose approach zero, the parameter y
represents the background incidence. In the Logistic and Probit models, F(0) is not zero, unlike in the
Log-Logistic and Log-Probit models. In these models, y is set to 0.
Special Options for Models
In addition to the options that are available to all dichotomous models, there may be model-specific
options. Generally, these are options to restrict the legal range of a parameter or set of parameters. The
range of a parameter may be restricted for two reasons:
the slope of the dose-response curve becomes infinite at a dose of 0 if the parameter falls below 1 , so
that the default is to restrain that parameter to be at least 1 , or
the quantal polynomial dose-response curve can become non-monotonic if the coefficients are
allowed to be negative, often resulting in the curve looking "wavy", so the default is to restrict the
coefficients to be non-negative.
The applicable special options are listed in the sections for the specific models.
Likelihood Function
All models in the current version of BMDS are fit using maximum likelihood methods. This section
describes the likelihood function used to fit the dichotomous models.
Suppose we employ k doses:
do He i . do,
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k
L = V^ L i ( Ni , «.j , dos e.j ; 0
i=i
where
BMD Computation
The BMD is computed as a function of the parameters of the model, which must have already been
estimated. The BMDs for dichotomous models are expressed as the dose that would give an (estimated)
increase in incidence of x% above the control incidence (where x is often in the range of 1 to 10 percent).
This increase in incidence is referred to here as the "BMRF", for benchmark response factor. Note that,
although the word "response" is used here, we are really talking about an increase of the incidence over
the control incidence (added risk). The actual response associated with the BMR, will only be the same
as the BMR when P(0) = 0. This is because to obtain the actual response associated with the BMR one
must solve for P(d) in the equation for added or extra risk.
Two formulations for computing the excess over background are in common use, the extra risk model and
the additional risk model. In the extra risk model,
while in the additional risk model,
BMR = p(BMD: 7, a,/I,,,) - p(0: 7, a, ft,...).
The equation appropriate to the risk type formulation that the user requests is solved to get the BMD for a
specific model and data set. Details of this computation are included in the descriptions of the models.
BMDL Calculation
BMDS currently calculates one-sided confidence intervals, in accordance with current BMD practice.
(Note: the Multistage and Multistage-Cancer models also acalculate one-sided upper confidence limits).
The general approach to computing the confidence limit for the BMD (called the BMDL here) is the same
for all the models in BMDS, and is based on the asymptotic distribution of the likelihood ratio (Crump and
Howe, 1985). Two different approaches are followed in these models. In one, the equations that define
the benchmark response in terms of the benchmark dose and the dose-response model are solved for
one of the model parameters. The resulting expression is substituted back into the model equations, with
the effect of reparameterizing the model so that BMD appears explicitly as a parameter. A value for BMD
is then found such that, when the remaining parameters are varied to maximize the likelihood, the
resulting log-likelihood is less than that at the maximum likelihood estimates by exactly
In a few models, it is impractical or impossible to explicitly re parameterize the dose-response model
function to allow BMD to appear as an explicit parameter. For these models, the BMR equation is used as
a non-linear constraint, and the minimum value of BMD is determined such that the log-likelihood is equal
to the log-likelihood at the maximum likelihood estimates less
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3.2.1 Gamma Model Description
Model Form
The Gamma Model formula is:
8 dose.
I r ose.
Probjresponse} p(dose: j,a,fl} 7 + (1 7) / tn~le,~tdt
i(oj Jo
Here, 0< v < 1 , p >= 0, and a > 0 with an option to restrict a >= 1 .
Parameters
"background" is Y
"power" is a
"slope" is p
Special Options
Restrict power >= 1
Restrict a >= 1 . If a < 1 , then the slope of the dose-response curve becomes infinite at the control dose.
This is biologically unrealistic, and can lead to numerical problems when computing confidence limits, so
several authors have recommended restricting a >= 1
BMD Computation
Let
be the incomplete Gamma function and
be its inverse function. Then
. ,
-j extra risk
BMD = ^ -i BASK \
i-T *"' additional
9
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the slope parameter p, which is
then replaced in the original model equations. This makes BMD appear in the model equations as a
parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.2 Logistic Model Description
Model Form
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The form of the probability function for the Logistic model is
i
P rob {r e span $ e } p (do& e; or, fi)
] -I. p (n+ddose)
Parameters
"intercept" is a
"slope" is p
Special Options
None
BMD Computation
The BMD estimate for the Logistic model is defined implicitly by the following equation. An iterative
numerical method is used to determine the value of BMD:
ln<
BMD = - -
where
1 1 e~ft
., BMR y - ; added risk
/. - \ e'" «
I BMR; extra risk
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the intercept parameter a,
which is then replaced in the original model equations. This makes BMD appear in the model equations
as a parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.3 Log-Logistic Model Description
Model Form
The form of the probability function for the Log-Logistic model is
if cfose > 0:
i -7
P rob {r espon.se} = »(close: 7, o?, ft) = 7 +
l- * ' * * .,..!/ t | i
and if cfose = 0:
Probf response} = p( dose: 7, a..fi) = 7;
0 < Y < 1, P >= 0 (with an option to restrict p >= 1).
Parameters
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"background" is v
"intercept" is a
"slope" is p
Special Options
Restrict slope > 1: If the slope is allowed to be less than 1, the slope of the dose-response curve is
infinite at zero dose.
BMD Computation
The BMD estimate for the Log-Logistic model is:
BMR \
- «
extra risk
addedrisL
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the intercept parameter a,
which is then replaced in the original model equations. This makes BMD appear in the model equations
as a parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.4 Log-Probit Model Description
Model Form
The form of the probability function for the Probit model is
if cfose > 0:
Prob {re,sponge} p( rfo.se 57, a,/?) 7 + (1 7)$ (a + ftln(dose)),
and if cfose = 0:
Prob{ re .spon.se}- p(dose:^,o:.,fi) 7;
where
and
(that is, is the normal distribution function), 0 < y < 1, P
>= 0 (with an option to restrict p >= 1).
Parameters
"background" is y
"intercept" is a
"slope" is p
Special Options
Restrict slope > 1: if the slope is allowed to be less than 1, the slope of the dose-response curve
is infinite at zero dose.
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BMD Computation
The BMD estimate for the Log-Probit model is:
. ,
extra, risk
]ii(BMD) =
^g-3-^ added risk,
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the intercept parameter a,
which is then replaced in the original model equations. This makes BMD appear in the model equations
as a parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.5 Multistage and Multistage-Cancer Model Description
Model Form
The Multistage and Multistage-Cancer Model formula is:
V"*-^ ;*{ fl -,. ?
Proh{responsej- p(dose,: 7, ft,..., fln) 7 + (I 7) - (1 e ^-?=1' '" )
Here, 0 < v < 1, and there is an option to restrict p/> 0 for all is. The degree of the polynomial is n. The
Multistage-Cancer model is exactly the same as the Multistage model except that the p parameters are
always restricted to be positive (the Multistage model allows them to be positive or negative).
Parameters
"Background" is y
Dose Coefficients (Beta1 ... Betan) are (31 ... pn
Special Options
Degree Poly
The maximum degree polynomial to fit. (maximum = 23)
Restrict Betas >= 0
When this box is checked, the polynomial coefficients are restricted to be non-negative. This
guarantees that the dose-response function will either be perfectly flat or always increasing, with
no "bumps". This restriction option is not available for the Multistage-Cancer model because it is
always implemented for that model.
BMD Computation
There is no general analytic form for the BMD in terms of the BMR and the estimated model parameters
for the multistage model. Instead, BMD is the root of the equation
fiiBMD + + pnBMDn + ln(l - A) = 0
where
,4 < BMR extra risk
additional risk
BMDL Computation
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The BMR equation is used as a non-linear constraint, and the minimum value of BMD is determined such
that the log-likelihood is equal to the log-likelihood at the maximum likelihood estimates less
3.2.6 Probit Model Description
Model Form
The form of the probability function for the Probit model is
Prob{reA'|w»i.,se| p(dose:ni\Q^0) <&(& + ftdose),
and for the Log-Probit model is:
where
and
(that is, v is the standard normal density function, and = 0 (with an option to restrict p >= 1).
Parameters
"background" is v (Log-Probit only)
"intercept" is a
"slope" is p
Special Options
Log of Dose: This results in the Log-Probit model.
Restrict slope > 1 (Log-Probit only): if the slope is allowed to be less than 1, the slope of the
dose-response curve is infinite at zero dose.
BMD Computation
The BMD estimate for the Probit model is defined implicitly by the following equation. An iterative
numerical method is used to determine the value of BMD:
extra risk
addedrisk,
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the intercept parameter a,
which is then replaced in the original model equations. This makes BMD appear in the model equations
as a parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.7 Quanta! Linear Model Description
Model Form
The Quantal Linear model is a form of the Weibull model. The Weibull Model formula is:
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re*po«.«*e} - p(doae\ 7, a,/*) = 7
The Quantal Linear model results from setting a equal to 1 in the Weibull Model.
Parameters
"Background" is y, restricted to fall in 0< y < 1 .
"Slope" is p
"Power" is a = 1
Special Options
None
BMD Computation
The BMD estimate for the Weibull model is:
BMD =
i
extra risk
i
additional risk
BMD estimates for the quantal linear model is found by substituting 1 for a.
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the slope parameter 0, which is
then replaced in the original model equations. This makes BMD appear in the model equations as a
parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.2.8 Weibull Model Description
Model Form
The Weibull Model formula is:
Prob{ response} = p(doae: 7, a, ft] = 7 + (1 - 7)(l -
Note: The Quantal Linear model results from setting a equal to 1 in the Weibull Model.
Parameters
"Background" is y, restricted to fall in 0< y < 1.
"Slope" is p
"Power" is a, and is restricted to a >= 0 with an option to restrict a >= 1.
Special Options
Restrict power >= 1
Restrict a >= 1. If a < 1, then the slope of the dose-response curve becomes infinite at the control
dose. This is biologically unrealistic, and can lead to numerical problems when computing
confidence limits, so several authors have recommended restricting a >= 1.
BMD Computation
The BMD estimate for the Weibull model is:
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i
'-\nn-BMR)] « . ,
^-j extra nsk
/?MD I "" ' i
BMU - \ _|nn-2MJ«M^
additional risk
BMDL Computation
To calculate the BMDL, the defining equations for the BMD are solved for the slope parameter p, which is
then replaced in the original model equations. This makes BMD appear in the model equations as a
parameter. See BMDL Computation in Dichotomous Model Description^for further details.
3.3 Description of Quanta! Models with Background Dose Parameter
Users should consult the Help file for a specific model for details on that model. With a few obvious
changes, those details apply also to models with a background dose parameter.
Two Forms of Each Quanta! Model
For each of four 'traditional' quantal models in BMDS (multistage, log probit, gamma, and Weibull),
alternative models were developed that incorporate a background dose parameter in place of a
background response parameter. Such a model was also developed for the log logistic function but is not
included in this release for technical reasons1.
The "cancer model" is a version of the multistage model for which the user cannot relax the restriction on
coefficients that requires them to be non-negative, and which reports the "cancer slope factor" (calculated
as BMR/BMDL). A new version of this model is provided with a background dose parameter.
The original logistic and probit models (without log-transformation of the dose) implicitly allow for a
background dose effect, although a background dose parameter is not explicitly estimated. These models
do not have a background response parameter. Thus, new versions of these models are provided which
add an explicit background response parameter y, increasing the number of parameters from two to three
for these new models.
Thus, for each type of quantal model in BMDS, there are now two alternative versions available, one with
a background dose parameter and another with a background response parameter.
The alternative forms of model can be represented as follows:
Backp'owuct response parameter, y: P(p. x. y) = y + (l-y)*F{p. x}
Background dose parameter, \\: P(p, x, v|) = F{p, (x~ i})}
Here, F{p, x} represents the functional form specific to each model (multistage, logistic, etc.). F{p, x} is a
probability distribution function taking values between 0 and 1 for positive dose values. For more details,
see Table 1. In the background dose version of a model, parameter y is dropped and the parameter n is
added.
1 The log-logistic model with background dose parameter has an especially "flat" log-likelihood surface, making it difficult, for some
datasets, for the software to converge to a maximum likelihood solution and especially difficult to solve the BMDL. In general,
that model often fails to converge on a BMDL solution when the control response is larger than approximately 0.2 - 0.4.
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Table 1. Comparison of current BMDS quanta! models with new models allowing a background
dose or background response parameter
Model Name1
Multistage2
mu!tistage_bgd
Logistic
legist ic_bgr
Probit
probif_bgr
Logjogistic
log_logistic_bgd
Log_probit
!og_probit_bgd
Gamma
gamma_bgd
Weibull
Weibui!_bgd
Functional Form of the Model
V + (1-y)[1-exp{-£^}]
/-i
1-exp{- T^.(^ + ;?)J'}
j-i
[1 + exp{-(a + pX)}]-1
V + (1-V)[1 + exp{-(a + pX)} ]-1
0{a + pX}
y + (1-v) 0{a + pX}
Y + (1-Y)[1 + exp{-(a + plog{X})}]-1
[1 + exp{-(a + plog{X + n})}]-1
y + (1-V)*{a + Plog{X}}
*{ a + p log{X + n } }
Y + (1-Y)[fYV^]/r(a)
G(p(d+n).a)/r(a)
G is the incomplete gamma function
V + (1-V)[1-exp{-pX«}]
[1 - expfp (X + n) a> ]
Explicit
Background
Parameter
V
n
None
V
None
V
V
n
V
n
V
n
V
n
Low Dose
Linearity?
Yes if ^>0
No if fr=0
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No3
Yes
No3
Yes
n
Parameters
1+k
1+k
2
3
2
3
3
3
3
3
3
3
3
3
1 Names in regular type denote modules (i.e., *.exe files) that currently exist within BMDS. Names in
italics denote modules that are new to BMDS and represent alternative forms of the models with a new
background parameter.
2 The cancer model is identical to the multistage model except that p > 0 is enforced and the cancer
slope factor is reported.
3 If power parameter is > 1, slope -> 0 as dose -> 0; if power parameter is < 1, slope -> «° as dose -> 0.
Confidence Limits for the Benchmark Dose (BMD)
The new models report both lower and upper confidence limits for the benchmark dose, that is, BMDL
and BMDU. The confidence level selected by the user applies to a one-sided confidence limit (as for all
the quantal models). Thus, if the user selects a 95% confidence level, "Confidence level = 0.95" is
reported in the *.out file with the BMD, BMDL, and BMDU. This confidence level applies to a one-sided
interval for BMD, e.g., [BMDL, «). If the user reports the two-sided interval [BMDL, BMDU], the
appropriate confidence level in this example is 90%; in general, if the user selects a confidence level 1-a,
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the two-sided interval has confidence level 1-2a.2
Parameter Constraints
This section applies to BMDS quantal models generally and is not specific to the new versions of those
models. Two sorts of constraints are applicable to the quantal models: natural constraints, which limit
parameters to those values permitting 0 < P(dose; p, n.) ^ 1, and user-selectable constraints. The latter
will default to standard settings in BMDS with no need for user actions. Examples of user-selectable
constraints are restrictions on the multistage coefficients, which normally are required to be non-negative
in order to provide a monotonically increasing dose response function, and a restriction on the power
parameter of the gamma and Weibull models, which BMDS requires by default to be no smaller than 1.
Natural parameter constraints are shown in Table 2. Advice and observations on user-selectable
constraints are provided in the Benchmark Dose Technical Guidance document (on EPA's website
"http://cfpub.epa.gov/ncea/" select Publications).
Table 2. Natural parameter constraints in BMDS quantal models.
2 In some cases, the 2-sided confidence limits may have coverage larger than stated (e.g., greater than 95%), because in some
cases they may bound a collection of confidence regions rather than an unbroken interval.
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Model Name1
Multistage2
multistage_bgd2
Logistic
legist ic_bgr
Prabit
probit_bgr
Logjogistic
log_!ogistic_bgd
Log_probit
log_probit_bgd
Gamma
gamma_bgd
Weibull
Weibutt_bgd
Functional Form of the Model
v + (i-v)[i-exp{-y;^}]
.7-1
1-exp{- £^.(X +?)''}
.7-1
[1 + exp{-(a + pX)}]-1
y + (1-V)[1 + exp{-(a + (3X)}]-i
*{a + pX}
V + (1-y) 0{a + pX}
V + (1-V)[1 + exp{-(a + plog{X})}]-1
[1 + exp{-(a + plog{X + n})}]-1
y + (1-V)*{a + plog{X}}
*{ a + p log{X + n } }
Y + d-Y)[f t-V*]/l~(a)
G(p(d+n),a)/r(a)
G is the incomplete garnrna function
V + (1-V)[1-exp{-pXn]
[l-expfPCX + nm
Parameter Constraints
0o
-CO < Q < +CO [3 > 0
-CO < Q < +00 p > 0
0 < y < 1
-CO < Q < + |3 > 0
-« < a < +«> i p > 0
0 < y < 1
°° < a < +00 p > 0
0 0
n> 6
-CO < Q < +00 p > 0
0 o
n> o
a >0 , p >0
0 < v < 1
a >0 , p >0
n> o
a >0 , p >0
0 < v < 1
a >0 , p >0
n> o
1 Names in regular type denote modules (i.e., *.exe files) that currently exist within BMDS. Names in
italics denote modules that are new to BMDS and represent alternative forms of the models with a new
background parameter.
2 The cancer model is identical to the multistage model except that Pj > 0 is enforced and the cancer
slope factor is reported.
In some cases, BMDS software will report that a parameter has "... hit a bound implied by some inequality
constraint and thus has no standard error." In that case, the printed parameter estimate will equal some
natural or user-selectable constraint (for example, p = 0 for multistage, or power a =1 for gamma3). In
5 There is also an arbitrary upper bound of 18 for the power parameter for the gamma and Weibull models
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such cases, the Wald confidence intervals for the other parameters are not even asymptotically correct.4
The 2-sided profile-likelihood confidence intervals for the BMD and Extra or Added Risk are
asymptotically correct in such cases.5 (However, whether or not a boundary has been 'hit', a 1- sided
profile-likelihood confidence interval may not have the nominal coverage - if the nominal coverage is 1-a,
the asymptotic coverage for BMDL could be anything between 1 and 1-2a.)
Also, if the power parameter for the gamma or Weibull models is reported equal to 18 and the warning "...
hit a bound... " appears, the parameter estimates are maximum likelihood estimates only in the restricted
sense that the power parameter has been assigned a value and the other parameters are MLEs
conditional on that assigned value. Such model results are not strictly comparable with others in terms of
AIC. In such a case, the BMD and BMDL could depend on the choice of power parameter; thus,
sensitivity analysis is indicated if one intends to rely on the reported BMD or BMDL.
Origin and Properties of Background Parameters
The background response parameter has been said to represent"... independent action between the
chemical and the background." (NRC, 1980), or, in the case of cancer, "...carcinogens that cause a
response of cancer in a way that is completely independent of the mechanisms by which the primary
carcinogen causes a response." (Crump et al., 1976). Thus, it has also been called an independent
background (Crump et al., 1976; Hoel, 1980). The background dose parameter has been said to
represent additivity between the applied dose of a chemical and the background (NRC, 1980), or to
represent"... carcinogens (including spontaneous biochemical accidents) that somehow act in
conjunction with the primary carcinogen ..." (Crump et al., 1976). Thus, it has also been termed an
additive background (Crump et al., 1976; Hoel, 1980).
Models with a background dose parameter will have an approximately linear response to dose at very low
doses (Crump et al., 1976). Only some of the original quantal models will behave in this way (see Table
1). The specification of the background term can have a substantial influence over risk estimates made
well below the range of experimental doses (Krewski and van Ryzin, 1981; NRC, 1980). The original
logistic and probit models (without log-transformation of the dose) implicitly allow for a background dose
effect, although a background dose parameter is not explicitly estimated, and these models exhibit low-
dose linearity. The new versions of these models provide an explicit background response parameter,
and also exhibit low-dose linearity.
Table 1. Comparison of current BMDS quantal models with new models allowing a background
dose or background response parameter
4 See G. Molenberghs and G. Verbeke (2007) American Statistician 61: 22-27; B. Sinha et al. technical report at
http://www.math.umbc.edu/~kogan/technical_papers/index2007.html.; Self, S.S. and K-Y. Liang (1987) Asymptotic properties of
maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, J.Am. Stat. Assoc. 82: 605-610.
5 B. Sinha et al. technical report at http://www.math.umbc.edu/~kogan/technical_papers/index2007.html.
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Model Name1
Multistage2
muftistage_bgd
Logistic
logistic_bgr
Probit
probit_bgr
Logjogistic
log_iogistic_bgd
Log_probit
tog_probit_bgd
Gamma
gamma_bgd
Weibull
Weibull_bgd
Functional Form of the Model
y + (1-Y)[1-exp{-f;,^J}]
/-i
1-exp{- 7^(^+37)'}
j-i
[1 + exp{-(a + pX)}]-1
V + (1-Y)[1 + exp{-(a + PX)} ]-1
*{a + (3X}
V + (1-y) ${a + (3X}
y + (1-V)[1 + exp{-(a + plog{X})}]-1
[1 + exp{-(a + plog{X + n,})}]-1
Y + (1-V){a + Plog{X}}
*{ a + p log{X + n } }
Y + (1-V)[jVV^]/r(a)
G(p(d+n).oO/r(a)
G is the incomplete gamma function
V + (1-Y)[1-exp{-pX«}]
[1-exp{-p(X + n)a}]
Explicit
Background
Parameter
V
n
None
V
None
V
V
n
V
n
V
n
V
n
Low Dose
Linearity?
Yesif pi>0
No if Pi =0
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No3
Yes
No3
Yes
#
Parameters
1+k
1+k
2
3
2
3
3
3
3
3
3
3
3
3
1 Names in regular type denote modules (i.e., *.exe files) that currently exist within BMDS. Names in
italics denote modules that are new to BMDS and represent alternative forms of the models with a new
background parameter.
2 The cancer model is identical to the multistage model except that p > 0 is enforced and the cancer
slope factor is reported.
3 If power parameter is > 1, slope -> 0 as dose -> 0; if power parameter is < 1, slope -> «° as dose -> 0.
Model Behavior in Relation to Background Parameter
The effects of the two sorts of background parameters, y and n, are illustrated for the log-probit models:
P(dose; y, a, p) = y + (1-y) 0(a + p log{X})
P(dose; n, a, p) = * (a + p log{X + n})
Models with a background response parameter can represent the functional shape of F(dose; p) starting
from a "floor" at P(0) = y (Figure 1). The response curve may appear sigmoidal, concave ("supralinear"),
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convex ("sublinear") or nearly linear, depending on the values of the other parameters.
Figure 1. Log-probit model with background response term, P(dose; v, a, P) = Y + (1
P*log(X)}. Here a = 2, p = 2, and v is varied from 0 to 0.4.
0
so
o
'-O _
"c5
£
0 ""
0 "
o
o
log-probit mode! with alpha - 2, beta - 2,
and gamma - 0, 1, 2. ,3, and 4
. ._ ,:srn^ -
-
-
_,,/
.11
00 02 04 06 0,8 10
Dose
Models with a background parameter additive to dose (n) can shift the response curve left or right (Figure
2), for fixed a (intercept) and p (slope). The background dose model can successfully fit datasets that
appear concave ("supralinear"), appearing as if the response had been truncated on the left. Figure 2 also
suggests that the background dose model may have difficulty fitting a convex or sigmoidal data pattern
that begins with a high control response, but may be successful in fitting a linear to concave (supralinear)
response that begins with a high response at zero dose. (In this Figure, the other two parameters are
fixed; however, experience with maximum likelihood fitting of various datasets suggests that these
qualitative generalizations are correct).
Figure 2. Log-probit model with background dose term. The background-dose parameter (n) was
varied, taking values of 3 to 0 from left to right. For this plot, a = -0.1 and (3 = 1. This illustrates how
increasing the background dose parameter shifts the response curve leftward (observed doses would of
course be non-negative; the horizontal axis was extended to negative doses to illustrate the functional
forms of these models).
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Log-probit with background dose, alpha = -01, beta
tig_dose = 3. 2.5, 2. 1.5, 1. 0.5. 0. left 10 right
CO
o
ID
>. Q
£L
r-j
o
p
o
-2
-I
0
Dose
Figure 3 shows an example of fitting an artificial dataset generated using a known log-probit function. In
this case, the two log-probit models fit equally well. They differ almost 2-fold in BMDL, and of course one
is linear at low doses and the other is sublinear. Figure 4 shows an example of fitting log-probit models to
data generated using a log-logistic function, illustrating how the two models, differing in background
parameter, will differ in the low-dose region.
Figure 3. Log-probit model with background dose term fitted to data. The model P = O(a +
p*(log(dose + n)), with parameters n = 0.75, a = 0.1, p = 1, was used to generate probabilities for doses
0, 0.5, 1.0, 1.5, and 2.0. Expected numbers out of 50 animals were rounded to the nearest integer, giving
numbers affected of 21,31, 37, 41, and 43. The model was fitted to these artificial data, yielding
estimated parameters n = 0.727918, a = 0.108666, b = 0.982273. The solid line shows the exact model
used to generate the data, and the dashed line shows the estimated model. Circles show the data as
observed proportions of 50 animals affected. Goodness of fit statistics: Chi-square(2) = 0.01, P-value =
0.9929. The log-probit model with background response was also fitted (Chi- square(2) = 0.01, P-value =
0.9942). These models predicted BMDL values of 0.0216005 and 0.0126529, respectively, for extra risk
0.1 at the 95% level.
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CO
o
ra
O
DL
r-j
d
q
d
-1
I
0
Dose
Figure 4. Log-probit model with background dose term fitted to data. The log-logistic model P = 1/(-a
-p *(log(dose + n,)), with parameters n = 1.5, a = -5, p = 10, was used to generate probabilities for doses
0, 0.25, 0.5, 0.75, and 1.0. Expected numbers out of 50 animals were rounded to the nearest integer,
giving numbers affected of 14, 32, 44, 48, and 49. The logprobit model with background dose was fitted to
these artificial data, yielding estimated parameters n = 0.567585, a = 0.946006, and b = 2.71885. The
solid line shows the log-logistic model which generated the data. The dashed line shows the estimated
log-probit model with background dose. The dotted line shows the estimated log-probit model with
background response. Circles show the data as observed proportions of 50 animals affected. Both log-
probit models fit well (Chi-square goodness of fit statistic 0.21 and 0.03, resp.); they estimated BMDs of
0.044 and 0.10, and BMDLs of 0.025 and 0.047, resp.
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o
to
o
>- 10
t C)
J
m
fiQ
O
ce *
OL O
IN
O
q
o
00
04
08
1 0
DOSE
Application
The primary reason to apply and compare models differing in the background parameter is to better
appraise model uncertainty and its implications, including uncertainty about low-dose linearity. Also, for
users interested in the maximum likelihood estimate of a response at low doses and its confidence limits,
it will be informative to compare these two types of models. Models with and without low-dose linearity
can differ greatly in the relative risk predicted at low doses (Krewski and van Ryzin, 1981; NRC, 1980).
Some of the models with a background dose parameter may not fit data well, or may have trouble
converging on a solution for the BMD or BMDL, when the observed response at zero dose is large (e.g.,
20% to 50% of subjects or more) and the dose-response pattern is unusual (either "flat" or non-monotonic
at two or more doses). In other cases, especially when the control response probability is low, the two
forms of model may fit a dataset almost equally well. In general, then, users are advised always to review
the AIC and goodness-of-fit statistics (including the goodness-of-fit residuals) and to examine plots of the
fitted model and data, before deciding whether any model, including a background dose model, fits the
data adequately.
Model Fitting and Model Selection Issues
Some of the models with background dose parameter (gamma, Weibull, and log-probit models) may fail
to converge on a BMDL solution in one of two situations: (1) when the response data are not strictly
increasing, and (2) when the response at zero dose is positive (esp., when it is large, e.g., over 20%).
When the response is not strictly increasing, most or all models may not fit well, and the following
questions need to be considered: (a) is the response lower at a high dose because a competing risk is
removing animals before the response can occur? If so, should responses be adjusted to account for
this?6 (b) Is it reasonable to remove the high-dose group and fit a model to the reduced dataset? (c) Is the
6 Piegorsch, W.W. and A.J. Bailer (1997) Statistics for Environmental Biology and Toxicology, London: Chapman & Hall. Gart, J.J.,
K.C. Chu and R.E. Tarone (1979) Statistical issues in interpretation of chronic bioassay tests for carcinogenicity, J. Natl. Cancer
Inst. 62: 957-974. Portier, C.J. and A.J. Bailer (1989) Testing for increased carcinogenivity using a survival-adjusted quantal
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response inherently non-monotonic, requiring a different type of model? Advice on these questions is
provided in the Benchmark Dose Technical Guidance document (on EPA's website
"http://cfpub.epa.gov/ncea/", select Publications).
When the response at zero dose is zero or very small, the models with background dose parameter are
expected to produce a BMDL. Most cancers in rodent bioassays have zero or very low incidence in the
control group.7 With such data, models with a background dose parameter provide a useful alternative to
those background-response models (i.e., the log-probit, loglogistic, gamma and Weibull quantal models)
that can have extreme slopes (zero or infinite) as dose nears zero. However, when the response at zero
dose is large, BMDL solutions may fail for some background dose models and parameter standard errors
may be unusually large. These are signs of problems with near-non-identifiability of parameters and/or a
very 'flat' and difficult-to solve likelihood.8 These should be taken as warning signs that the model is
probably not suitable and that the model estimates should not be relied upon.
A question of model selection could arise in comparing the traditional 2-parameter probit or logistic to the
new, 3-parameter, background response versions of these models. That is, the chisquare goodness of fit
may be enhanced merely by the addition of a parameter. Two considerations are pertinent. First, if either
the chi-square value or the AIC value is substantially smaller for one model, it is to be preferred. Second,
if the model versions differ only slightly in this respect, the generally accepted practice is to prefer the
model with fewer parameters, but if the models predict substantially different BMDLs, it seems best to
acknowledge the uncertainty about the true model and its BMDL. It is possible to fit a 2-parameter version
of the new background response logistic and probit models by specifying that the intercept parameter be
set to zero. However, this is appropriate only when the data are consistent with a response probability of
0.5 or greater for the control (because F{a=0,p} > 0.5 for dose > 0). This 2-parameter model could be
compared to the traditional logistic or probit model with 2 parameters, and the new background response
model with 3 parameters.
Interpretation
In some cases, similar models differing only in the type of background parameter (dose vs. response)
may fit data almost equally well; even when they do not, there is no way to infer from mere curve-fitting
which model is truer to reality. It is possible to invent even more models that might fit the data adequately
but could suggest other interpretations.
The motivation for the background dose parameter was to represent an external dose or internal process
acting additively to the applied dose. The background dose parameter may, but does not necessarily,
represent a background exposure to the chemical applied in a bioassay or its metabolites (e.g., possible
exposure from food, water or air in addition to the experimental exposure). It could also represent the
outcome of biological processes generating natural metabolites that act by the same mechanism or that
interfere with natural mechanisms which inhibit the mechanism; still more hypotheses could be adduced.
Thus, the background dose parameter should not be interpreted literally as support for a particular
mechanism unless there is independent evidence to support the particular mechanistic interpretation.
Nevertheless, it seems natural to evaluate the fit of background dose models when there is independent
evidence about pre-existing or ongoing background exposure.
The background response parameter usually provides a close fit to the response of control animals if the
response test, Fund. Appl. Toxicol. 12: 731-737. Bailer, A.J. and C.J. Portier (1988) An illustration of dangers of ignoring survival
differences in carcinogenic data, J. Appl. Toxicol. 8: 185-189. Kodell, R.L., D.W. Gaylorand J.J. Chen (1986) Standardized tumor
rates for chronic bioassays, Biometrics 42: 867-873.
7 Portier, C.J., J.C. Hedges and D.G. Hoel (1986) Age-specific models of mortality and tumor onset for historical control animals in
the National Toxicology Program's carcinogenicity experiments, Cancer Research. 46: 4372-4378. Gaylor, D.W. (1992) Relationship
between the shape of dose-response curves and background tumor rates. Reg. Toxicol. Pharmacol. 16: 2-9.
8 One useful (but not infallible) diagnostic is to plot a suitable transformation of the empirical probabilities (p = y/n) against the dose
metric. If the pattern can be fit well by a linear function, then problems with near-nonidentifiability (Seber and Wild 1989) may be
anticipated when fitting the corresponding model with background dose. Transformations: for the log-probit or log-logistic model with
background dose, the probitsor logitsof p; for the Weibull model with background dose, log(-log(1-p)).
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overall model fit is good. As with the background dose parameter, one should beware of too literal an
interpretation. The model could be interpreted literally to mean that a proportion y of animals will have
cancers of'natural' origin at every dose and that a proportion (1-y) F(dose; p) of animals will have cancers
attributable to the carcinogen. This clearly goes beyond the data and its support would require
experiments especially designed to test this interpretation.
3.4 Dichotomous Hill Model Description
Model Form
The form of the probability function for the Dichotomous Hill model is:
Prob{response}
v*g +(v-v*g)/[1 +Exp(-a-b*l_n(dose))]
When d = 0, Prob{response}
Parameters
v*g.
"v" is the maximum probability of response predicted by the model (0 < v < 1)
"g" multiplied by v (v*g) is the background estimate of the probability of response
"intercept" is a
"slope" is b
Special Options
Restrict Slope > 1: if the slope is allowed to be less than 1, the slope of the dose-response curve
is infinite at zero dose.
BMD Computation
The BMD estimate for the Dichotomous Hill model is defined by the following equation.
Added risk:
I BMR-v+g*v
-a-Log I
BMD^e
Extra risk:
-a - Log -
(-
BMR-v+g *v-BMR*g *v
BMD=e-
BMDL Computation
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To calculate the BMDL, the defining equations for the BMD are solved for the intercept parameter which
is then replaced in the original model equations. This makes BMD appear in the model equations as a
parameter. See BMDL Computation in Dichotomous Model Description:_for further details.
3.5 Nested Model Descriptions
Special Considerations for Models for Nested Dichotomous Endpoints
The most common application of the models in this section will be to developmental toxicology studies of
organisms that have multiple offspring per litter, as do rodents. In these study designs, pregnant females
("dams") are given one or several doses of a toxicant, and the fetuses, embryos, or term offspring
("pups") are examined for signs of abnormal development. In such studies, it is usual for the responses of
pups in the same litter to be more similar to each other than to the responses of pups in different litters
("intra-litter correlation", or "litter-effect"). Another way to describe the same phenomenon is that the
variance among the proportion of pups affected in litters is greater than would be expected if the pups
were responding completely independently of each other.
The models in this section make available two approaches to this feature of developmental toxicology
studies: they use a probability model that provides for extra inter-litter variance of the proportion of pups
affected (the beta-binomial probability model: see "Likelihood Function"); and they incorporate a litter-
specific covariate that is expected to account for at least some of the extra inter-litter variance. This latter
approach was introduced by Rai and Van Ryzin (1985), who reasoned that a covariate that took into
account the condition of the dam before dosing might explain much of the observed litter effect. Those
authors suggested that litter size would be an appropriate covariate. For the reasoning to apply strictly,
the measure of litter size should not be affected by treatment; thus, in a study in which dosing begins after
implantation, the number of implantation sites would seem to be an appropriate measure. On the other
hand, the number of live fetuses in the litter at term would not be an appropriate measure if there is any
prenatal death or resorption (this has apparently been ignored in most of the literature).
Carr and Portier (1991), in a simulation study, warn that in situations in which there is no effect of litter
size, statistical models that incorporate a litter size parameter, as do the models in BMDS, will often
erroneously indicate that there is a litter size effect. Thus, the user should use litter size parameters with
caution. Unfortunately, there are currently no good diagnostics for determining whether a litter size effect
actually exists.
Likelihood Function
Let g represent the number of dose groups. For the ith group, there are n, pregnant females administered
dose dose,. In Vnejth litter of the ith dose group there are s,7 fetuses, x,7 affected fetuses, and,
potentially, a litter-specific covariate r,7 which will often be a measure of potential litter size, such as
number of implantation sites, though this is not a requirement of the models. In what follows, the dose-
response model, which gives the probability that a fetus in Vnejth litter of the ith dose group will be
affected is represented by
The beta-binomial distribution can be thought of as resulting from sampling in two stages. First, each litter
is assigned a probability, P,yfrom a beta distribution (beta distributions represent a two parameter family
of probability distributions defined on the interval (0,1)). The parameters of the beta distribution are
determined by the administered dose, the litter specific covariate r,y and the degree of intra-litter
correlation, v/. Note that the intra-litter correlation parameter varies among doses. It is well known
(Williams et al., 1988) that when the true intra-litter correlation differs among doses, unbiased estimates
of the other parameters in a dose-response model can only be obtained if dose-specific intra-litter
correlation parameters are estimated. As a special case, if v/ =0, then this part of the process is
completely deterministic, and
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This allows for the possibility of no litter effect at all.
In the second stage of sampling, Sy fetuses are assigned to the litter, and the number of affected fetuses,
Xjj is sampled from a binomial distribution with parameters Py and s,7.
The log-likelihood function that results from this process is:
9 | n,
r \^ )
L= 2^1
rx,j
Lfe=l
k=l
where
and
B-)=o
if a> 6 by convention.
BMD Computation
BMD computation is similar to that for dichotomous models with the added wrinkle that a value for the
litter-specific covariate is required. The user has the option of specifying either the control group mean of
the covariate, or the overall mean. Probably, the overall mean should be preferred, if the covariate is not
expected to be affected by dose. Of course, if the covariate is affected by dose, then it should probably
not be used, anyway!
BMDL Computation
BMDS currently only calculates one-sided confidence intervals, in accordance with current BMD practice.
The general approach to computing the confidence limit for the BMD (called the BMDL here) is the same
for all the models in BMDS, and is based on the asymptotic distribution of the likelihood ratio (Crump and
Howe, 1985).
The approach used for all the nested dichotomous models is the same. The equations that define the
benchmark response in terms of the benchmark dose and the dose-response model are solved for one of
the model parameters, using either the control group mean or the overall mean of the litter-specific
covariate. The resulting expression is substituted back into the model equations, with the effect of
reparameterizing the model so that BMD appears explicitly as a parameter. A value for BMD is then found
such that, when the remaining parameters are varied to maximize the likelihood, the resulting log-
likelihood is less than that at the maximum likelihood estimates by exactly
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3.5.1 Logistic Nested Model Description
Model Form
The Nested Logistic Model is the log-logistic model, modified to include a litter-specific covariate. The
model form for the Nested Logistic Model is:
Prob{response} = a+Q^y + (1 - a - e^y) / (1 + exp[-p-e2ry - p*Ln(dose)])
if dose > 0, and a + B^ if dose = 0.
In the above equation r,y is the litter-specific covariate for Vnejth litter in the ith dose group; a >= 0, p >=
0, p >= 0 with an option to restrict p >= 1; and a+9iry > 0 for every r-,-t.
In addition there are g intra-litter correlation coefficients, 0 < <$>/< 1 (i = 1, ..., g).
Parameters
Intercept = a
Power = p
Slope = p
First coefficient for litter-specific covariate = 01
Second coefficient for liter-specific covaritate = 02
Intralitter correlation coefficients = 1 . . . g
Special Options
Restriction
Power parameter (Rho) can be restricted to be >. 1 (Default)
Risk Type
Choices are "Extra" or "Added." Additional risk is the additional proportion of total animals that respond in
the presence of the dose, or the probability of response at dose d, P(d), minus the probability of response
in the absence of exposure, P(0). Extra risk is the additional risk divided by the proportion of animals that
will not respond in the absence of exposure, 1 - P(0). Thus, extra and additional risk are equal when
background rate is zero.
BMD Computation
If rm represents either the control mean value for the litter-specific covariate or the overall mean, then the
BMD is computed as:
BMD = Exp{[ln(A/(1 -A)) - p - 92rm] / p}
where
A = BMRF for extra risk
= BMRF/0 - a - 9irm) for added risk
BMDL Computation
The parameter p is replaced with an expression derived from the BMD definition (above) in the dose-
response function, with the effect of reparameterizing the model so that BMD appears explicitly as a
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parameter. A value for BMD is then found such that, when the remaining parameters are varied to
maximize the likelihood, the resulting log-likelihood is less than that at the maximum likelihood estimates
by exactly
3.5.2 NCTR Model Description
Model Form
The NCTR model is a Weibull model modified to include a litter-specific covariate. The model form is:
Prob{response} = 1 - Exp{-(a+ G^ry - rm) - (p+ 02(rjj - rm) »dosep}
where r,7 is the litter-specific covariate for the jth litter in the ith dose group, rm is the overall mean for the
litter-specific covariate, a >= 0, p >= 0, p >= 0 with an option to restrict p >= 1, and
9i(ry-rm)>0 and 02(ry - rm) > 0
for every r,y.
In addition there are g intra-litter correlation coefficients, 0 < 1 . . . g
Special Options
Restriction
Power parameter p (Rho) can be restricted to be > 1 (Default)
Risk Type
Choices are "Extra" or "Added." Additional risk is the additional proportion of total animals that respond in
the presence of the dose, or the probability of response at dose d, P(d), minus the probability of response
in the absence of exposure, P(0). Extra risk is the additional risk divided by the proportion of animals that
will not respond in the absence of exposure, 1 - P(0). Thus, extra and additional risk are equal when
background rate is zero.
BMD Computation
BMD = [-(Ln(1-A)) / (p + 025r)](1/p)
where 5r is the average of (ry - rm) over either the control group or over all observations, depending upon
the option selected for "Fixed Litter Size" (when using the overall mean, 5r is always 0), and
A = BMRF for extra risk
BMRF/(l-a-0i5r) for added risk
BMDL Computation
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The parameter p is replaced with an expression derived from the BMD definition (above) in the dose-
response function, with the effect of reparameterizing the model so that BMD appears explicitly as a
parameter. A value for BMD is then found such that, when the remaining parameters are varied to
maximize the likelihood, the resulting log-likelihood is less than that at the maximum likelihood estimates
by exactly
3.5.3 Rai and Van Ryzin Model Description
Model Form
The Rai and Van Ryzin model is a Weibull model modified to include a litter-specific covariate. The model
form is:
Prob{response} = [1 - Exp{-a-p»dosep}] Exp{-(91 + 92dose)»rjj}
where r-,-t is the litter-specific covariate for the jth litter in the ith dose group, a >= 0, p >= 0, 0 >= 0 with an
option to restrict 0 >= 1, and
(61 + 92dosei) > 0, for all doses (i = 1, ..., g).
In addition there are g intra-litter correlation coefficients, 0 < <$>/< 1.
This is a generalization of the model described in Rai and Van Ryzin (1985) by the addition of the power
parameter, p. To get the conventional Rai and Van Ryzin model, fix the power parameter to 1.
Parameters
Intercept = a
Power = p
Slope = p
First coefficient of litter-specific covariate = 01
Second coefficient of litter-specific covariate =02
Intralitter correlation coefficients = 1 . . . g
Special Options
Restriction
Power parameter p (Rho) can be restricted to be > 1 (Default)
Risk Type
Choices are "Extra" or "Added." Additional risk is the additional proportion of total animals that respond in
the presence of the dose, or the probability of response at dose d, P(d), minus the probability of response
in the absence of exposure, P(0). Extra risk is the additional risk divided by the proportion of animals that
will not respond in the absence of exposure, 1 - P(0). Thus, extra and additional risk are equal when
background rate is zero.
BMD Computation
The BMR formulas are solved numerically for the BMD.
BMDL Computation
The parameter p is replaced with an expression derived from the BMD definition in the dose-response
function, with the effect of reparameterizing the model so that BMD appears explicitly as a parameter. A
value for BMD is then found such that, when the remaining parameters are varied to maximize the
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likelihood, the resulting log-likelihood is less than that at the maximum likelihood estimates by exactly.
3.6 Toxicodiffusion Model Description
Model Form
The Toxicodiffusion model has the following form for describing the time course of responses before and
after an exposure to a dose:
7j(d, t) = A(t) + B-t-d- exp(-k -1) 1(1 + C - d -1 - exp(-k - f))
where
Aft) = Ao or
Aft)= A0+Ait or
Aft)= A0_A1t + A2f
depending on the "background degree" specified by the user. A(t) applies before exposure and for all
times in the absence of exposure (or to "sham" exposures to dose=0). Thus the Toxicodiffusion model is
applicable to data with the following characteristics:
An outcome (response variable) measured on a continuous scale.
Single exposure (or exposure interval), to several (4-5 recommended) "dose" levels.
Duration of the experiment (the time component) coded between 0 and a maximum
positive value, with 0 being the beginning and the maximum positive value the last time
point at which data are available. The time at which exposure took place must be known
and coded by a value between 0 and the maximum value.
The outcome is observed (and recorded) repeatedly over time on each study subject; the
timing of the observation is given. It is not required, however, that each subject
(experimental unit) yield an equal number of observations at the same time points.
Observations should not be aggregated over subject, and data must be identifiable with
each subject.
Multiple subjects per dose group.
Dose effects are preferably observed at more than one dose level.
Differences in dose effects are seen at some time points.
The model fitting is accomplished by maximizing the likelihood of the data, assuming a random effects
model for the parameter A0 (normally distributed across individuals) and a normal error distribution
(observations are normally distributed around the model-predicted individual-, dose-, and time-specific
means).
Parameters
Background parameters = A0, A-,, A2
Time-course parameters = B, C, k
Special Options
None
Risk Type
Risk is defined in terms of added or extra risk. Because the Toxicodiffusion model is for continuous
responses, this requires specification of response levels that are considered adverse. That is done in one
of two ways. First, the assumed background rate (probability) of adverse response may be specified; in
that case the cut-off(s) that yield that probability of response are determined from the fit of the model.
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Second, the cut-off value(s) may be specified directly; that yields an estimated background rate of
response once the model is fit. In either case, the extra or added risk is calculated for any dose (and
time) based on the model-predicted increase in the proportion of responses beyond the cut-off(s).
BMD Computation
The BMD output from a Toxicodiffusion model run is the lowest dose for which, at some time after
exposure, the extra or added risk is equal to the BMR Risk Level specified by the user. Note that
because the response rates vary over time, there will be several dose levels that yield the BMR response
at various time points. The minimum of those doses is the reported minimum BMD.
BMDL Computation
The BMDL is estimated via bootstrap resampling of residuals and random effects. The residuals and
random effects are estimated from the original fitting of the model. They are resampled (within or across
dose groups) treating the vector of residuals for an individual as the sampling unit if need be. BMDs are
calculated as discussed above for each set of bootstrapped observations. The percentiles over all the
bootstrapped BMDs are used to define confidence bounds for the BMD (e.g., the 5th percentile would be
reported as the 95% lower bound on the BMD).
3.7 Conc_x_Time Model Description
Model Form
The only concentration-time model currently in BMDS 2.1 is the ten Berge model which has the following
form:
Prob{response} = h(z)
where hQ is either the logit or the probit function
h(z) = exp(z) / (1 + exp(z)) for Logit link function
= O(z-5) for Probit link function.
and OQ is the standard normal cumulative distribution function. The variable z is a linear function of the
terms in the model as follows:
z = BQ + B^fcCC) + B2*fT(T) + B3*fx(x) + B4*r4(C, T, x) + B5*r5(C, T, x) + ...
where f,(u) = transformation of concentration (i=C), time (i=T), or covariate (i=x);
Tj(C, T, x) = interactions (products) of the fc(C), fT(T), and fx(x) terms.
The f, transformations that have been implemented include:
fi(u) =
u
ln(u)
1/u
Transformation
Identity
Logarithmic
Reciprocal
Note that the covariable "x" is actually a place holder for any number of possible explanatory variables of
interest (think of x as a vector of variables above and beyond the C and T variables).
Parameters
Intercept = B0
Coefficients of the model terms = B-,, ..., Bn
(currently the BMDS version of the model allows up to five main effects variables and three product terms,
so that n is less than or equal to 8).
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Special Options
None
Risk Type
There are no specific risk type choices. The model calculates a concentration (or the value of any other
variable) given the values of the other variables in the model such that the probability of response is equal
to some specified value. If the background probability is 0, as it would be if the logarithmic transformation
is used for all the explanatory variables in the model, then the probability of response for a set of values
for the model variables is equal to the added or extra risk for that set of values.
BMD Computation
The BMD (concentration yielding a specific probability of response, given the values of the other model
variables) is computed numerically from the set of MLE parameter values.
BMDL Computation
A Wald-type confidence interval is determined for all model parameters (including the "BMD" as defined
above). The confidence bounds determined in this manner for the BMD yield the BMDU and BMDU. The
user must specift a deviate value corresponding to the confidence level of interest; this deviate can be
determined from the standard normal distribution or, perhaps more appropriately, from a T distribution
with degrees of freedom determined from the number of observations and the number of fitted
parameters.
Note about model graphics: because the graphical representation of the ten Berge modeling results is
quite different from that obtained from other BMDS models, the currentl version of BMDS does not
include a graphical output for the ten Berge model. Users desiring plots of contours of response
probabilities on the Concentration-Time plane should consider porting the modeling results to Excel and
creation of plots using that software.
4 TEXT OUTPUT FROM MODELS
The purpose of the BMDS output pages is to provide the user with goodness-of-fit criteria and model
results to aid in determining the appropriateness of the subject model to the benchmark dose derivation.
While BMDS will estimate parameters etc. for the user, it is the users responsibility to interpret these
results before making use of the BMDL. The BMDS model text output also provides information relevant
to whether or not the function maximization problem was actually accomplished. That is, for each model,
parameters are estimated using Maximum Likelihood procedures through an iterative routine. There is no
guarantee that the model parameters will in fact achieve the true maximization, and by inspecting the
output pages, the user should be able to obtain at least some idea as to whether or not it was achieved.
While all models tend to follow a similar format, there are some differences in the output pages given by
certain models.
The output pages also give the user a quick verification of the options they had selected on the model run
screen. For instance, when two users may be comparing results and obtained different answers, they
may consult the output pages to make sure the settings were the same or if they had used the same (or
most current) version of the software/models.
4.1 Continuous Model Text Output
The continuous output page starts with a few explanatory lines that the user can reference quickly to:
check the version number, the date and time of run, the input data set used, verify that all the correct
options were set, check which model was used, see the explicit form of the mean function for the model
run, and get some basic data summaries (number of dose levels, etc). The output page is designed so
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that it will provide a reliable basis for reentering BMDS and accurately reproducing the results of a run
(e.g., with an updated model) at a later date. The "form of the response function" is provided on each
model's text output page, and is the model function that BMDS will estimate parameters for in order to
derive the Benchmark Dose.
Default Initial Parameters:
These are computer generated values that provide the starting point for the iterative maximization routine
used by BMDS. This may give the user a basis for appropriate parameter values should they want to
rerun the program if a maximum wasn't found, not believable, etc.
Parameter Estimates:
The parameter estimates are the actual estimates the program routine has found for the particular model
run. This table includes both the estimates for the true parameter values as well as their estimated
standard errors. The standard errors are given for two reasons: (1) If standard errors are extraordinarily
high, then the user should suspect that the probability function may not have reached a maximum, and
they may want to use different starting points. There is not a guarantee if these are high that the function
has not, in fact, been maximized. The user should use this in conjunction with other output to make a
decision. (2) To make inferences about the population parameters themselves. Under certain
assumptions, the user maybe able to formulate tests for the true value of the parameter.
Asymptotic Correlation Matrix of Parameter Estimates
This table provides the user with a matrix of correlation estimates between each of the parameters.
Again, if these values seem to be high (in this case, very close to 1), there may have been a problem in
the maximization. However, as stated before, high correlation does not confirm that the problem of
maximization in fact failed.
Table of Data and Estimated Values of Interest
This table gives a listing of the data as well as estimated means and standard deviations from the model.
This is a good place for the user to look, along with the Tests of Fit and Maximum Likelihood below, to
judge the appropriateness of the model. If a model fits well, the observed and estimated means should be
relatively close. The scaled residual values printed at the end of the table are defined as follows:
(Obs. Mean - Predicted Mean)/SE,
where the Predicted Mean is from the model and SE equals the estimated standard deviation (square
root of the estimated variance) divided by the square root of the sample size.
The overall model should be called into question if the scaled residual value for any individual dose
group, particularly a low dose group, is greater than 2 or less than -2.
Tests of Fit and Maximum Likelihood
Continuous Model Maximum Likelihood Help
The BMDS uses likelihood theory to estimate function parameters and ultimately to make inferences
about risk assessment data. Maximum likelihood is the process of estimating the models parameters such
that a likelihood function is maximized according to the data. In other words, parameter values are
"chosen" such that the subject model (i.e. polynomial or power) obtains the best possible fit to the data,
given the constraints of the model's parameter structure. For example, suppose one wishes to fit a
second degree polynomial model with a constant variance to a data set. The particular form of this model
would be:
Y = bO + b1 * X + b2 * XA2
The parameters we wish to estimate in this case would be bO, b1, and b2, as well as the constant
variance parameter, call it SigmaA2. To estimate these parameters, BMDS uses maximum likelihood
procedures. The end result being a vector of parameters that maximizes the likelihood function for the
model specified. The "Log(likelihood)" value given on the BMDS output page is the maximum value of the
natural logarithm of the likelihood function. Also note that there are an associated number of degrees of
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freedom at each likelihood calculated. The degrees of freedom in each case is the number of parameters
estimated in that particular model. In the example above, 4 parameters were estimated, and thus, this
likelihood has 4 degrees of freedom.
The Akaike's Information Criterion (AIC) (Akaike, 1973; Linhart and Zucchini, 1986; Stone, 1998) value
given on the BMDS output page is -2L + 2p, where L is the log-likelihood at the maximum likelihood
estimates for the parameters, and p is the number of model parameters estimated. It can be used to
compare different types of models which use a similar fitting method, as do all dichotomous, continuous
and nested model types within BMDS. The model with the lowest AIC would be presumed to be the better
model under this method. Although such methods are not exact, they can provide useful guidance in
model selection.
The BMDS output page gives four or five likelihood (and AIC) values, depending on the variance model
chosen, that may be of interest to the user. These values are later used in asymptotic Chi-Square tests
of fit. Each of these likelihood values represents a model a user may consider in the analysis of the data.
The five models are:
"Full-constant variance" Model - A1 :Yij = Mu(i) + e(ij), Var{e(ij)} = SigmaA2
"Fullest" Model - A2:Yij = Mu(i) + e(ij), Var{e(ij)} = Sigma(i)A2
"Full-modeled variance" Model - A3:Yij = Mu(i) + e(ij), Var{e(ij)} = alpha*(Mu(i))Arho
"Reduced" Model - R: Yi = Mu + e(i), Var{e(i)} = SigmaA2
Fitted Model: The user specified model.
Model A1 would be a "full" model that fits all the means at the user specified dose levels. This model also
implies a constant variance at each dose level. This likelihood may be of interest in order to determine
whether or not a constant variance model adequately describes the data. Model A2 would be the "fullest"
model. It would describe a data set that has an individually estimated mean at each dose level, as well as
a non-constant variance that does not have any functional relationship to the mean. Model A3 is similar to
model A2, and only differs in its variance parameters. In this case, the model is considered to have a non-
constant variance over the dose levels, but this variance is modeled as a function of the mean. The
reduced model is the model that implies no real difference in mean or variance over the dose levels. In
other words, if this model is deemed adequate to describe the data, risk assessment may not be
appropriate, as there is no adverse effects over the dose levels considered (i.e., the mean and variance
do not fluctuate). The last model, the fitted model, is the user specified model. A user may have reason to
believe that a certain model may describe the data well, and thus uses it to make inferences about the
population in order to calculate the BMD and BMDL.
Tests of Fit
The BMDS software provides three or four different Tests of Fit that the user may use to determine an
appropriate model for fitting their data. These Tests of Fit are based on asymptotic theories of the
likelihood ratio. Without getting too technical, the likelihood ratio is just the ratio of two likelihood values,
many of which or given in the BMDS output. Statistical theory proves that -2*log(likelihood ratio)
converges to a Chi-Square random variable as the sample size gets large and the number of dose levels
gets large. These values can in turn be used to obtain approximate probabilities to make decisions about
model fit. Chi-Square tables can be found in almost any statistical book.
Each of the four/five models, described in Help under likelihood, has a likelihood value. The BMDS
program uses these values to create ratios from two models that form a meaningful test. Suppose the
user wishes to test two models for fit, A and B. One assumption that is made for these tests is that the
"true" model is in fact B, but it can be simplified in such a way that the simplified model describes the data
as well as B. Also suppose A is a much simpler model in that it has much fewer parameter values (the
goal is to simplify the model as much as possible without losing information about the data). Assume
each model has a maximum likelihood value, call them L(A) and L(B). A ratio can be formulated easily:
L(A)/L(B) (Note: The model with a higher number of parameters is always in the denominator of this ratio).
Now, using the theory, -2*log{ L(A)/L(B)} approaches a Chi-Square random variable. This can be
simplified by using the fact that the log of a ratio is equal to the difference of the logs, or simply put, -
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2*log{ L(A)/L(B)} = -2*( log{L(A)} - log{L(B)}) = 2*log{L(B)} - 2*log{L(A)}. The likelihood values given by
BMDS are in fact the log likelihoods, so this becomes just a subtraction problem. This value can then in
turn be compared to a Chi-Square random variable with a specified number of degrees of freedom.
As mentioned on the Likelihood Help screen, each log likelihood value has an associated number of
degrees of freedom. The number of degrees of freedom for the Chi-Square test statistic is merely the
difference between the two model degrees of freedom. In the mini-example above, suppose L(A) has 5
degrees of freedom, and that L(B) has 8. In this case, the Chi-Square value you would compare this to
would be a Chi-Square with 8-5 = 3 degrees of freedom.
In the A vs B example, what is exactly being tested? In terms of hypotheses, it would be:
HO: A models the data as well as B
H1: B models the data better than A
Keeping these tests in mind, suppose 2*log{L(B)} - 2*log{L(A)} = 4.89 based on 3 degrees of freedom.
Also, suppose the rejection criteria is a Chi-Square probability of less than .05. Looking on a Chi-Square
table, 4.89 has a p-value somewhere between .10 and .25. In this case, HO would not be rejected, and it
would seem to be appropriate to model the data using Model A.
The BMDS software provides three or four default tests, depending on the variance model the user has
specified (constant variance model, or a non-constant variance model where the variance is a function of
the mean, namely, Sigma(i)A2 = alpha*(Mu(i))Arho). BMDS assumes rejection criteria is a Chi-Square
probability of less than .05 for all of the tests, however p values are presented so that the user is free to
use any rejection criteria they want. Each test in each model will be discussed in some detail below.
Test 1 (A2 vs R): Tests the hypothesis that response and variance don't differ among dose levels.
If this test accepts, there may not be a dose-response.
Using Model A2 and model R, a likelihood ratio is formulated to determine whether the data vary at all
among dose groups. If this test accepts, then there may not be a dose-response, although it is probably
possible for some data sets with a slightly significant trend to not reject this test. This model implies no
differences in the mean, nor in the variance at each dose level, and thus, there would be no adverse
effect as dosage is increased. If this test rejects, then modeling the data is appropriate, and the user
should consider the tests below.
Test 2 (A1 vs A2): Tests the hypothesis that variances are homogeneous. If this test accepts, the
simpler constant variance model may be appropriate.
Recall that the goal is to simplify the model. If this test accepts, it may be appropriate to go with the
simpler constant variance model. If this test rejects, the user may want to run a non-constant variance
model, or if the non-constant variance model was run, then the user should look at the second test 3
below to make further decisions.
Test 3 (Test 4 in non-constant variance model) (Fitted vs A3): Tests the hypothesis that the model
for the mean fits the data. If this tests accepts, the user has support for the selected model.
This test is used to give some indication as to whether or not the user specified model is appropriate to
model data. On the BMDS user screens, the user specifies a model that they may believe is the true, or
near true, model. If this test accepts, the user has support for the choice of model, and may deem it
adequate for data modeling. If this test rejects, the user may want to try a different model.
Test 3 (Non-constant variance model) (A3 vs A2): Test the hypothesis that the variances are
adequately modeled. If this test accepts, it may be appropriate to conclude that the variances have
been modeled appropriately.
Here, the test is one to see whether or not the variance model, Sigma(i)A2 = alpha*(Mu(i))Arho, is an
appropriate assumption. Again, the purpose is to reduce the parameter space, and by modeling the
variances as a function of the mean (which also intuitively makes sense that variance may have some
dependence on the mean value) we achieve some reduction. If this tests accepts, it may be appropriate
to conclude that the true variances have the form above. If this test rejects, unfortunately BMDS has no
further way to model variance. Look for different variance models in future releases of BMDS.
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4.2 Dichotomous Model Text Output
The dichotomous output page starts with a few explanatory lines that the user can reference quickly to:
check the version number, the date and time of run, the input data set used, check which model was
used, see the explicit form of the response function, verify that all the correct options were set and get
some basic data summaries (number of dose levels, etc). The output page is designed so that it will
provide a reliable basis for reentering BMDS and accurately reproducing the results of a run (e.g., with an
updated model) at a later date. The "form of the response function" is provided on each model's text
output page, and is the model function that BMDS will estimate parameters for in order to derive the
Benchmark Dose.
Default Initial Parameters:
These are computer generated values that provide the starting point for the iterative maximization routine
used by BMDS. This may give the user a basis for appropriate parameter values should they want to
rerun the program if a maximum wasn't found, they just don't believe the answer, etc.
Parameter Estimates:
The parameter estimates are the actual estimates the program routine has found for the particular model
run. This table includes both the estimates for the true parameter values as well as their estimated
standard errors. The standard errors are given for two reasons: (1) If standard errors are extraordinarily
high, then the user should suspect that the probability function may not have reached a maximum, and
they may want to use different starting points. There is not a guarantee if these are high that the function
has not, in fact, been maximized. The user should use this in conjunction with other output to make a
decision. (2) To make inferences about the population parameters themselves. Under certain
assumptions, the user maybe able to formulate tests for the true value of the parameter.
Asymptotic Correlation Matrix of Parameter Estimates
This table provides the user with a matrix of correlation estimates between each of the parameters.
Again, if these values seem to be high (in this case, very close to 1), there may have been a problem in
the maximization. Also, as stated before, high correlation does not confirm that the problem of
maximization in fact failed. The Weibull model, for instance, tends to give high correlation between the
slope and power parameters, even when the likelihood was maximized.
Analysis of Deviance Table
The analysis of deviance table lists three maximum likelihood values. The first is the "full model". The full
model would be any model that would perfectly fit all the positive response proportions at the dose levels
specified by the user. The second model is the "fitted model" maximum likelihood value. This is the value
of the maximum likelihood function for the particular model selected and using the estimated parameter
values. The last likelihood value is the "reduced model" value, which would be the value of the likelihood
function if all data points where assumed to come from the same population with the same population
parameter. That is, for each dose level, the actual probability of an adverse effect would be the same.
These values are just the likelihood functions evaluated according to the assumptions made at each step
(i.e., the model assumption for the fitted model).
Next to the likelihood values there are three values: Deviance, degrees of freedom (DF), and P-value.
The Deviance is the difference between the fitted or reduced model and the full model likelihood values.
This deviance measures whether or not the smaller model (i.e., the fitted or reduced model) describe the
data as well as the full model does. This deviance is then used to formulate a Chi-Square random
variable that tests exactly that. The user may choose a rejection level (.05 is common) to test whether or
not the model fit is appropriate. The p-value for testing whether or not the fitted model adequately
describes the data is given next to the fitted model likelihood, and the user can reject or not reject a
hypothesis according to the p-value given . The reduced model p-value would be used in the same way,
but here the user would be testing whether or not there is in fact a dose/response relationship where the
true population proportion is a function of dose, as opposed to a single population with one parameter
(the proportion of affected animals).
It will often happen that several models provide an adequate fit to a given data set. These models may be
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essentially unrelated to each other (for example a logistic model and a probit model often do about as
well at fitting dichotomous data) or they may be related to each other in the sense that they are members
of the same family that differ in which parameters are fixed at some default value. One can consider the
log-logistic, the log-logistic with non-zero background, and the log-logistic with threshold and non-zero
background to all be members of the same family of models. Generally, within a family of models, as
additional parameters are introduced the fit will appear to improve. Goodness-of fit statistics presented in
the main body of the Analysis of Deviance Table can be used to compare such related models, but are
not designed to compare unrelated models. Alternative approaches are need for selecting between
models that are not related (not in the same family).
The Akaike's Information Criterion (AIC; Akaike, 1973; Linhart and Zucchini, 1986; Stone, 1998) is
defined as -2L + 2p, where L is the log-likelihood at the maximum likelihood estimates for the parameters,
and p is the number of model parameters estimated. The AlCs for the model run are provided at the
bottom of the Analysis of Deviance Table. They can be used to compare different types of models which
use a similar fitting method (for example, least squares or a binomial maximum likelihood), as do all
dichotomous, continuous and nested model types within BMDS. The model with the lowest AIC would be
presumed to be the better model under this method. Although such methods are not exact, they can
provide useful guidance in model selection.
Goodness of Fit
This table gives both a listing of the data as well as residual and overall Chi-Square Goodness of Fit
tests. This is a good place for the user to look outside of the Analysis of Deviance table to judge the
appropriateness of the model. The table lists estimated probabilities, the expected and observed number
of affected animals and scaled residuals for each dose group. If a model fits well, the observed and
expected number of affected animals should be relatively close. The overall scaled residual value, and it
corresponding p-value are indications of that "closeness". If the p-value is larger than some
predetermined critical p-value, then the user may be able to conclude that the model is appropriate to
model the data. The scaled residual values printed at the end of the table are defined as follows:
(Obs. - Expected)/sd,
where "Expected" is the expected number of responders from the model and sd equals the estimated
standard deviation (square root of the estimated variance) of the expected number. For these models, the
estimated variance is equal to n*p*(1-p) where n is the sample size and p is the model-predicted
probability of response. The overall model should be called into question if the scaled residual value for
any dose group, particularly a low dose group, is greater than 2 or less than -2.
Slope at ED(10) - Cancer Model Only
Some additional assessment tools are imparted by the draft beta Cancer model at this time. The output
page for the draft beta cancer model includes an estimate of the slope of the BMD curve at the ED(10)
(the 10 percent extra risk response level) and the two sided 95.0% confidence interval for the slope at the
ED(10). The two sided 95.0% confidence interval for the linear term of the model is also provided. Finally,
scaled residuals are reported to aid in determining how well the model fits the data at low doses.
Benchmark Dose Computation
This is the ultimate goal of the BMDS software (see Overview). The BMD or BMDL is the value that the
user will use when determining the RfD or RfC for the particular toxicant being studied. The user should
investigate all the output to this point, and then make the decision to accept this as a valid BMDL.
4.3 Nested Model Text Output
The nested model output page starts with a few explanatory lines that the user can reference quickly to:
check the version number, the date and time of run, the input data set used, verify that all the correct
options were set, check which model was used, see the explicit form of the mean function for the model
run, and get some basic data summaries (number of dose levels, etc). The output page is designed so
that it will provide a reliable basis for reentering BMDS and accurately reproducing the results of a run
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(e.g., with an updated model) at a later date. The "form of the response function" is provided on each
model's text output page, and is the model function that BMDS will estimate parameters for in order to
derive the Benchmark Dose.
Default Initial Parameters:
These are computer generated values that provide the starting point for the iterative maximization routine
used by BMDS. This may give the user a basis for appropriate parameter values should they want to
rerun the program if a maximum wasn't found, they just don't believe the answer, etc.
Parameter Estimates:
The parameter estimates are the actual estimates the program routine has found for the particular model
run. This table includes both the estimates for the true parameter values as well as their estimated
standard errors. The standard errors are given for two reasons: (1) If standard errors are extraordinarily
high, then the user should suspect that the probability function may not have reached a maximum, and
they may want to use different starting points. There is not a guarantee if these are high that the function
has not, in fact, been maximized. The user should use this in conjunction with other output to make a
decision. (2) To make inferences about the population parameters themselves. Under certain
assumptions, the user maybe able to formulate tests for the true value of the parameter.
Analysis of Deviance Table
The analysis of deviance table list three maximum likelihood values. The first is the "full model". The full
model would be any model that would perfectly fit all the positive response proportions at the dose levels
specified by the user. The second model is the "fitted model" maximum likelihood value. This is the value
of the maximum likelihood function for the particular model selected and using the estimated parameter
values. The last likelihood value is the "reduced model" value, which would be the value of the likelihood
function if all data points where assumed to come from the same population with the same population
parameter. That is, for each dose level, the actual probability of an adverse effect would be the same.
These values are just the likelihood functions evaluated according to the assumptions made at each step
(i.e., the model assumption for the fitted model).
Next to the likelihood values there are three values: Deviance, degrees of freedom (DF), and P-value.
These are asymptotic Chi-Square test that investigate the appropriateness of the model fit, as well the
reduced model. The Deviance is the difference between the fitted or reduced model and the full model
likelihood values. This deviance measures whether or not the smaller model (i.e., the fitted or reduced
model) describe the data as well as the full model does. This deviance is then used to formulate a Chi-
Square random variable that tests exactly that. The user may choose a rejection level (.05 is common) to
test whether or not the model fit is appropriate. The p-value for testing whether or not the fitted model
adequately describes the data is given next to the fitted model likelihood, and the user can reject or not
reject a hypothesis according to the p-value given . The reduced model p-value would be used in the
same way, but here the user would be testing whether or not there is in fact a dose/response relationship
where the true population proportion is a function of dose, as opposed to a single population with one
parameter (the proportion of affected animals).
Goodness of Fit Information - Litter Data and Grouped Data
Both of these tables provide a listing of the data, expected and observed responses and Chi-Square
residuals (observed - expected). The "Litter Data" table contains this information for each litter. To obtain
the "Group Data" table, the Litter Data were sorted on Dose (first), and by Litter Specific Covariate within
Dose. Within dose, litters adjacent to each other with respect to Litter Specific Covariate were grouped
together until the expected number of affected pups was at least one. This grouping was done prior to the
estimation of an overall Chi-Square and p-value to improve the validity of the Chi-Square approximation
for the goodness of fit statistic. Goodness of Fit statistics. Both tables list estimated probabilities, the
expected and observed number of affected animals and Chi-Square residuals for each dose group. If a
model fits well, the observed and expected number of affected animals should be relatively close. The
overall Chi-Square value, and it corresponding p-value are an indication of that "closeness". If the p-value
is larger than some predetermined critical p-value, then the user may be able to conclude that the model
is appropriate to model the data.
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The scaled residual values printed at the end of the table are defined as follows:
(Obs. - Expected)/sd,
where "Expected" is the expected number of responders from the model and sd equals the estimated
standard deviation (square root of the estimated variance) of the expected number. For these models, the
estimated variance is equal to n*p*(1-p) where n is the sample (litter) size and p is the model-predicted
probability of response. The overall model should be called into question if the scaled residual value for
any individual dose and litter-specific covariate combination, particularly for a low dose group, is greater
than 2 or less than -2."
Benchmark Dose Computation
This is the ultimate goal of the BMDS software (see Overview). The BMD or BMDL is the value that the
user will use when determining the RfD or RfC for the particular toxicant being studied. The user should
investigate all the output to this point, and then make the decision to accept this as a valid BMDL.
4.4 Toxicodiffusion Model Text Output
The Toxicodiffusion model output file begins with a section that echoes user-specified information (e.g.
Study Name and Study Description) as well as some information about the contents of the data set: what
the dose levels are, at what times observations were available, and the sample size (i.e., the number of
distinct combinations of experimental unit ID and time). The user should verify that these values are
correct; if they are not, then the data file should be checked for data entry errors.
In addition, this section shows the form of the model.
Likelihood-Related Estimates
The AIC and BIG as well as the log-likelihood for the model fit to the data being analyzed are shown here.
Random Effects
This section shows which parameters were selected to have random effects around the main (fixed)
effect. At this time, the only parameter for which random effects are specified is the parameter A0 (the
constant term in the background response polynomial). So, in this section there will be a standard
deviation reflecting the variability of the random effects around the corresponding fixed effect. There will
also be a "Residual" standard deviation reflecting the remaining variability that is not part of the random
effect (reflecting the remaining lack of fit of the model to the data and therefore associated with residuals).
The distributions of the random effects and of the residuals are assumed to be independent of one
another. [At a later time, when more than one random effect is allowed, the distributions of the random
effects will not be assumed to be independent of one another, though they all will still be assumed
independent of the residual distribution. In the case of more than one random effect, pair-wise correlation
estimates will be provided as well. When those correlations are close to 1 or -1, that may be a strong
indication that the data cannot support that many random effects and alternative assumptions should be
tried by the user.]
Parameter Estimates
In this section, the additional results related to the model fitting are provided. Parameter estimates for the
fixed effects are shown with their standard errors. In addition the degrees of freedom, t-test statistic
value, and associated p-value for that test are shown, in order to facilitate evaluation of the significance of
the parameters.
In addition, parameter correlations and a summary of the within-group residuals are shown.
Initial Values
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In this section one finds the set of initial values that were used when the model apparently converged to
an acceptable answer. Below that is the list of the initial values that the model was scheduled to try; it
starts with the first set listed and continues until it uses a set that resulted in apparent convergence.
BMP Estimation
In this section the summary BMD results are presented. First, the user-specified choices for risk type,
spontaneous risk level (adverse level; if a Cut Point was used instead of Background Rate, then the value
of the cut point would be printed here), the area of adverse effects (Adverse Direction), and the BMR level
are shown. If these are not the choices the user wants to have, the option file should be revisited and
correct values entered for these fields. The same is true of the number of bootstrap iteration which is
shown next.
The minimum BMD is what is shown (the BMD, as a rule, varies as a function of time). The time at which
that minimum BMD was obtained is also given. The value shown for "Confidence Level" is (1-a)*100%
(where a is what was entered on the option screen). The lower limit presented is based on the user-
specified number of bootstrap iterations. As discussed elsewhere, the user should test for stability of that
estimate if the accuracy of the BMDL (or BMDU if that too is estimated) needs to be assured to some
desired number of significant digits.
In addition to the text output file, five plots are produced with each run.
4.5 ten Berge Model Text Output
The ten Berge model output file begins with a section giving information about the version number and
build date of the program, as well as identifying the input data set used to create the output and the name
of the file that has the information needed to later produce graphics. [Currently, BMDS does not produce
graphics for the ten Berge model.]
Model Specifications
This section provides the overview of the framework for the model, including the reference for Finney
(1971) from which Wil ten Berge identified the probit analysis approach. The general form of the model
as it is now implemented is presented here as is a basic summary of the number of input parameters
(possible explanatory variables) and the number of observations in the data set.
Input Data Set Echo
This section should contain exactly the data that the user has included in the input file. If there are any
errors here, the user should go back to the input file and correct the input values, and then rerun the
analysis.
Modeling Choices
In this section, the following information is provided: the choices for the range of observations to analyze,
the transformations of the input parameters to use, the link function (logit or probit), and the variable
identifier numbers associated with the selected explanatory variables (single input parameters or products
of pairs of input parameters). If any of this information does not correspond to the desired analysis, the
user must go back to the input file to make corrections to the coding in the modeling section.
Fit and Parameter Estimates
The chi-square evaluation of fit and the degrees of freedom associated with the model fit to the selected
data are given. The fit is assessed in relation to the "saturated" model having as many parameters as
observations. The maximum likelihood estimates of the Bi coefficients are shown as is a Student t value
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that can be used to determine whether each of those terms is "statistically significant." Variance and
covariance estimates for each of the B, terms are provided.
Notes: When the model fails, one or more of the parameter values may have a value of the form "-1.#J" or
a similar non-number. This is an indication that the model has not converged to an answer. The user
should check the input file (also reflected in the data echo section of the output file) to see if some data
entry errors are contributing to that problem.
If there are no errors in the input data, it is entirely possible that there is no solution for some data; this
happens, for example, when there are only groups with either 0% or 100% response. In such cases, the
model cannot determine a maximum likelihood and returns values for one or more of the parameters (and
estimates depending on those parameters) that are of the form "-1 .#IOe+000," "1 .#R," "1 .#QOe+000,"
"1 .#QNANO," or similar indications that no numerical answer was available. It is known, for example, that
probit slope estimates can be infinite in some situations where concentrations with and without response
are not suitably intermingled. A sufficient (but not necessary) condition to avoid this is to have two distinct
doses with partial response.
"Dose" Estimation
In this section one finds the estimate of an input variable value that, for a given response and for specified
values of the other input parameters, gives that response rate. Confidence limits are estimated if
requested. Some reviewers have strongly suggested that the Student T-based deviates always be used
and (confidence intervals obtained when a standard normal deviate is used are "too tight") and so one
might want to obtain from statistical tables the deviate for a T-distribution having degrees of freedom
equal to the number of observations minus the number of estimated parameters (e.g., the 95th percentile
from such a T-distribution). These same comments also apply to the next two sections giving estimates
and confidence intervals for response rates and for the ratios of model parameters.
Notes: The use of the terminology "probability of correct model" in the output file is not a good choice for
describing the results of the chi-squared goodness-of-fit test that is the basis for the reported p-value.
Subsequent versions of this software will replace that terminology with a statement like "The p-value
associated with the chi-square goodness of fit test equals x" where x is the calculated p-value. The
terminology as shown in the example output file has been retained so that comparisons between the new
version and the original version of the ten Berge software could be more easily made (the same
description has been retained in both cases). Similarly, the statement that the "prediction of the model is
not sufficient" will be modified to simply indicate whether or not the p-value is greater than or less than
0.05, with the appropriate statement regarding adequate fit of the model or not (similar to the evaluations
of fit in other BMDS models) and a suggestion that (if the model is not fitting the data well) the correction
factor be applied to the variance and covariance estimates as well as selecting the deviate from the
Student T distribution rather than the standard normal distribution. Currently, neither the variance-
covariance correction nor the choice of the deviate are done automatically for the calculation of
confidence limits.
Response Estimation
Much like the previous section, this section provides estimates of the response associated with specified
values of the input variables used in the model. When a deviate is given, the corresponding confidence
interval is also calculated for that estimate. Note that the deviate supplied need not be the same as the
one provided for the "dose" estimation, in case different confidence levels may be desired for dose and
response estimates.
Notes: See notes in previous section about terminology related to the model fit.
Ratio Estimation
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In this section the ratio of the Bi coefficients request by the user will be reported. As in the previous
sections the confidence interval is also shown, if requested, at a level consistent with the specified
deviate.
Notes: See notes in previous section about terminology related to the model fit.
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5 GRAPHIC OUTPUT FROM MODELS
The graphic output plot should display along with the text output file after each model run. The BMD and
BMDL are identified on the plot as green vertical lines and are associated with the response level
associated with the user selected BMR, the horizontal green line. The BMD curve estimated by the model
is represented by a red line and the BMDL curve (which is basically just connecting 5 BMDL estimates) is
represented by the blue line. Data points are shown in green with their individual group confidence
intervals.
The graphic display features can be modified by either using WGNUPIot edit features or copying the plot
to your computer's clip board and pasting it into another application capable of performing vector graphic
editing (e.g., Microsoft PowerPoint). These copy and edit features are accessible by left-clicking on the
small graphic icon at the top of the plot page or right-clicking on the graph. A menu will appear which
allows you to modify the plot window in various ways. Among the "Options" available are copying to the
clipboard, changing background, color and font specifications, and printing. Under the "Print" option, you
can choose to print landscape or portrait. Various sizing options are then offered, which should allow for
full page, and other displays options.
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6 ACRONYMS, TERMS, AND DEFINITIONS
ACRONYM EXPANDED
BMDS
BMR
CatReg
CRAN
CSF
EPA
IRIS
IT
ITS-ESE
LM ES&S
NCEA
NIST
ORD
PROAST
RIVM
RfC
RfD
RTP
TO
TOPO
Benchmark Dose Software
Benchmark Response
Categorical Regression
Comprehensive R Archive Network
Cancer Slope Factor
Environmental Protection Agency
Integrated Risk Information System
Information Technology
Information Technology Solutions- Environmental System Engineering
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National Center for Environmental Assessment
National Institute of Standards Technology
Office of Research and Development
Continuous Exponential Model
National Institute for Public Health and the Environment (Netherlands)
Reference Concentrations
Reference Doses
Research Triangle Park
Task Order
Task Order Project Officer
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REFERENCES
Crump, K. 1984. A new method for determining allowable daily intakes. Fund. Appl. Toxicol. 4:
854-871.
Kimmel, C.; Gaylor, D. 1988. Issues in qualitative and quantitative risk analysis for developmental
toxicology. Risk Anal. 8: 15-21.
U.S. EPA. 1995. The use of the benchmark dose approach in health risk assessment. Office of
Research and Development, Washington, DC: EPA/630/R-94/007, February, 1995.
Crump, K.S., D.G. Hoel, C.H. Langley and R. Peto. 1976. Fundamental carcinogenic processes
and their implications for low-dose risk assessment. Cancer Research 36:2973-2979.
Hoel, D.G. 1980. Incorporation of background in dose-response models. Federation Proceedings
39(1): 73-75.
Krewski, D., and J. van Ryzin. 1981. Dose response models for quantal response toxicity data.
pp. 201-231 IN: Statistics and Related Topics. Proc. International Symposium on Statistics and
Related Topics, Ottawa, May 5-7, 1980. Eds. M Csorgo, D.A. Dawson, J.N.K. Rao, and
A.K.Md.E. Saleh Amsterdam: North-Holland.
NRC (National Research Council). 1980. Drinking Water and Health, volume 3. Washington, DC :
National Academy Press.
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8 APPENDICES
8.1 Model Input Files Format
Each model listed above is a separate executable file that makes use of DOS text input files. The DOS
text files provide the "instructions" for the model run. The BMDS interface software assists users in the
creation of properly formatted input files for the model executables. The text file format for these data
input files are model specific and can be obtained by following the Related Topics links above. Each
model can be run from the DOS command line of your computer by typing the model file name followed
by the complete name (including directory location and extension) of an associate data input file (BMDS
expects these files to be labeled with a .(d) extension, but the model executables will accept any
extension).
The model will generate both a text output (.out) and a graphic (.002) file with the same name prefix as
the .(d) file. The .out file can be read with any text editor. The BMDS interface automatically creates a plot
(.pit) file from the .002 file and displays it using the GNUPIot program you should have installed with
BMDS. Plot files can also be created from the DOS command line of your computer by typing the name of
the scripter file associated with the continuous (00*.exe), nested (05*.exe) or dichotomous (10*.exe)
model that was used, followed by the complete name (including directory location and extension) of the
.002 file associated with the model run. The wgnupl32.exe program included with the BMDS installation
can then be used to view or edit the plot (.pit) file.
BMDS 2.0 operates in a Windows environment and automatically performs the DOS process commands
when a session is run.
Cancer Dichotomous Model Input File Format
[1] Model name, in this case, the string Multistage-Cancer
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[6] Degree of Polynomial
[7a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[7b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[7c] Parameter Convergence
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[8] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[9] Restrict Betas >= 0
= 1 if Restrict Betas >= 0 box is checked
= 0 otherwise
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NOTE: In the cancer model, this parameter will always be set equal to 1.
[10] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Betal Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Beta2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18+] Etc. for BetaS, Beta4...
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[20] Background Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[21] Betal Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
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[22] Beta2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22+] Etc. for BetaS, Beta4,...as necessary
[23] Dose Name
[24] Response Name
[25] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] Multistage
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
[4] EXAMPLE
[5] 4
[6] 2
[7a] [7b] [7c] [8] [9] [10] [11] [12]
250 2.22045e-16 1.49012e-8 1101 1
[13]
0.10
[16]
-9999
[19]0
[20]
-9999
[14]
0
[17]
-9999
[21]
-9999
[15]
0.95
[18+]
-9999
[22+]
-9999
[23] [24] [25]
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Dose Resp NEGATIVE_RESPONSE
0 3 47
50 6 44
100 10 40
150 19 31
Gamma Dichotomous Model Input File Format
[1] Model name, in this case, the string Gamma
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Restrict Power >= 1
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[11] Smooth Option
= 0 if Unique
= 1 if C-Spline
[12] BMR (BMR level)
= User input value (or default of .100)
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[13] Risk Type
= 0 if Extra
= 1 if Added
[14] Confidence Level
= User input value (or default of .950)
[15] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[16] Slope Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Power Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[19] Background Parameter.
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[20] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[21] Power Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22] Dose Name
[23] Response Name
[24] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] Gamma
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
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[4] EXAMPLE
[5] 4
[6a]
250
[12]
0.10
[15]
-9999
[18]0
[19]
-9999
[22]
Dose
0
50
100
150
[6b]
2.22045e-16
[13]
0
[16]
-9999
[20]
-9999
[23]
Resp
3
6
10
19
[6c] [7] [8] [9] [10] [11]
1.49012e-8 1111 0
[14]
0.95
[17]
-9999
[21]
-9999
[24]
NEGATIVE_RESPONSE
47
44
40
31
Hill Continuous Model Input File Format
[1] Model Name, in this case, the constant string Hill
[2] User Notes
[3] Input file name
[4] Output data file name
[5] In put Type
= 1 if entered as group data (e.g., Dose, N, Mean, Std.)
= 0 if individual animal data (e.g., Dose, Response) is entered
[6] A count of the number of observations
[7] Adverse Direction
= 0 if Automatic (adverse direction with increasing dose estimated by model)
= 1 if Up (dose-response curve trends up with increasing dose)
= -1 if Down (dose-response curve trends down with increasing dose)
[8a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[8b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[8c] Parameter Convergence.
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= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[9] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[10] Restrict n>1?
= 1 if Restrict n > 1 box is checked
= 0 otherwise
[11] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[12] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface andean only be changed by
manually editing the .(d) file!!!!
[13] Smooth Option
= 0 if Unique
= 1 if C-Spline
[14] BMRType
= 0 if Absolute Dev.
= 1 if Std. Dev.
= 2 if Relative Dev.(Default)
= 3 if Point
= 4 if Extra
[15] BMR (BMR Level)
= User input value (Default = 0.1000)
[16] Constant Variance
= 0 if not (the variance is to be modeled as Var(i) = alpha*mean(i)Arho)
= 1 if box is checked (rho is set to 0 in the above equation)
[17] Confidence Level
= User input value (or default of .950)
[18] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Rho Parameter
= 0 if Constant Variance box is checked
If Constant Variance box not checked,
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] Intercept Parameter
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= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] v Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] n Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] k Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[25] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[26] Rho Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] Intercept Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] v Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29] n Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[30] k Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[31]-[34] IN THIS ORDER, by checking the column assignment pull down menus, these fields should
contain:
If Group data is entered:
[31] [32] [33] [34]
Dose name N name Mean Name Std Name
If Individual data is entered:
[31] [32]
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Dose name Response name etc.
In the same column order as above, this should just be a data listing.
Example Format
[1] Hill
[2] BMDS MODEL RUN
[3] HYBRID1.SET
[4] HYBRID1
[5] [6] [7]
1 6 1
[8a]
250
[14]
1
[18]
-9999
[24] 0
[25]
-9999
[31]
DOSE
0
8
20
30
40
50
Linear
[8b]
2.22045
e-16
[15]
1.00
[19]
-9999
[26]
-9999
[8c] [9]
1.49012
e-8
[16]
1
[20]
-9999
[27]
-9999
[32]
Nl
4
5
4
4
4
5
Continuous
Model Input
[10]
0
[17]
095
[21]
-9999
[28]
-9999
[33]
MEAN
38.45
39.56
40.9
41.95
42.725
43.42
File Format
[11] [-
1 1
[22]
-9999
[29]
-9999
[34]
STD
1.1683
1.28218
1.303
1.418203
1.438
1 .45932
Use Polynomial Continuous Model Input File Format, but maf
[13]
1
[23]
-9999
[30]
-9999
set to 1.
Logistic and Log-Logistic Dichotomous Model Input File Format
[1] Model name, in this case, the string Legist
[2] User notes
[3] Input file name
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[4] Output file name
[5] Number of Observations
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Log Transformation
= 1 if Log transformation is to be used
= 0 otherwise
[9] Restrict Slope >= 1
= 1 if Restrict Slope >= 1 box is checked
= 0 otherwise
[10] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value or if Log transformation not selected
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[17] Slope Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Intercept Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[20] Background Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected or if Log transformation not selected
[21] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22] Intercept Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[23] Dose Name
[24] Response Name
[25] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] Legist
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
[4] EXAMPLE
[5] 4
[6a] [6b] [6c] [7] [8] [9] [10] [11] [12]
250 2.22045e-16 1.49012e-8 1001 1 0
[13]
0.10
[16]
-9999
[14]
0
[17]
-9999
[15]
0.95
[18]
-9999
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[19]0
[20]
-9999
[23]
Dose
0
50
100
150
User's Manual
[21]
-9999
[24]
Resp
3
6
10
19
[22]
-9999
[25]
NEGATIVE_RESPONSE
47
44
40
31
Logistic Nested Model Input File Format
[1] Model name, in this case, the string Nlogist
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[5a] Number of Dose groups
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Restrict Power >= 1 (Note: Power = Rho parameter in model)
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Fixed Size
= 1 if Ctrl Group Mean selected
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= 0 if overall mean selected
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Rho Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Beta Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Thetal Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] Theta2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] Phil Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] Phi2 Parameter
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= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Phi3 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24] Phi4 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24+] Phi5 through PhMO if necessary (as many Phi parameters as dose groups)
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[25] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[26] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] Rho Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] Beta Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29] Thetal Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[30] Theta2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[31] Phil Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[32] Phi2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[33] Phi3 Parameter
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= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34] Phi4 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34+] Phi5 through PhMO if necessary (as many Phi parameters as dose groups)
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[35] Dose Name
[36] Response Name
[37] Constant String: NEGATIVE_RESPONSE
[38] Column 4 name
[39] Column 5 name
Data:
Dose in first column
Response in Second
Total (Litter Size) minus Response in third column
Litter Size
Group number, or anything you want, really, so long as its integers
Example Format
[1] Nlogist
[2] BMDS MODEL RUN
[3] NCTR31 .SET
[4] NCTR31
[5]
40
[6a]
250
[13]
0.05
[16]
-9999
[21]
-9999
[25] 0
[26]
[5a]
4
[6b] [6c] [7] [8] [9]
2.22045 1.49012 , n ,
e-16 e-8
[14] [15]
0 0.95
[17] [18] [19] [20]
-9999 -9999 -9999 -9999
[22] [23] [24+]
-9999 -9999 -9999
[27] [28] [29] [30]
[10] [11] [12]
1 1 0
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-9999
[31]
-9999
[35]
Dose
0
0
0
0
0
0
0
0
0
0
25
25
25
25
25
25
25
25
25
25
50
50
50
50
50
50
50
50
50
50
100
100
100
100
100
2.1 User's Manual
-9999
[32]
-9999
[36]
resp
0
4
1
2
2
2
2
0
2
0
4
4
3
7
5
3
1
5
3
5
3
10
10
3
5
7
5
3
8
6
10
2
13
3
10
-9999 -9999
[33]
-9999
[37]
nega_resp
13
10
12
10
10
9
5
12
10
9
9
8
11
3
6
9
11
8
8
11
6
6
3
5
4
4
3
9
3
3
4
1
1
3
1
-9999
[34+]
-9999
[38] [39]
column4 columns
13
14
13
12
12
11
7
12
12
9
13
12
14
10
11
12
12
13
11
16
9
16
13
8
9
11
8
12
11
9
14
3
14
6
11
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100
100
100
100
100
User's Manual
9
9
6
5
7
1
1
3
4
2
10
10
9
9
9
Multistage Dichotomous Model Input File Format
[1] Model name, in this case, the string Multistage
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[6] Degree of Polynomial
[7a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[7b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[7c] Parameter Convergence
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[8] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[9] Restrict Betas >= 0
= 1 if Restrict Betas >= 0 box is checked
= 0 otherwise
[10] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
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= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Betal Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Beta2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18+] Etc. for BetaS, Beta4...
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[20] Background Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[21] Betal Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22] Beta2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22+] Etc. for BetaS, Beta4,...as necessary
[23] Dose Name
[24] Response Name
[25] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] Multistage
[2] BMDS MODEL RUN
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[3] EXAMPLE.SET
[4] EXAMPLE
[5] [6]
4 2
[7a] [7b] [7c] [8] [9] [10] [11] [12]
250 2.22045e-16 1.49012e-8 1001 1
[13] [14] [15]
0.10 0 0.95
[16] [17] [18+]
-9999 -9999 -9999 ...
[19]0
[20] [21] [22+]
-9999 -9999 -9999 ...
[23] [24] [25]
Dose Resp NEGATIVE_RESPONSE
0 3 47
50 6 44
100 10 40
150 19 31
NCTR Nested Model Input File Format
[1] Model name, in this case, the string NCTR
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[5a] Number of Dose groups
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence
= Default of 1.49012e-8 if user does not input a value
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= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Restrict Power >= 1 (Note: Power = Rho parameter in model)
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Fixed Size
= 1 if Ctrl Group Mean selected
= 0 if overall mean selected
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Rho Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Beta Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
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[19] Thetal Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] Theta2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] Phil Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] Phi2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Phi3 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24] Phi4 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24+] Phi5 through PhMO if necessary (as many Phi parameters as dose groups)
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[25] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[26] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] Rho Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] Beta Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29] Thetal Parameter
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= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[30] Theta2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[31] Phil Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[32] Phi2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[33] Phi3 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34] Phi4 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34+] Phi5 through Phi9 if necessary (as many Phi parameters as dose groups)
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[35] Dose Name
[36] Response Name
[37] Constant String: NEGATIVE_RESPONSE
[38] Column 4 name
Data:
Dose in first column
Response in Second
Total (Litter Size) minus Response in third column
Litter Size
Example Format
[1] NCTR
[2] BMDS MODEL RUN
[3] NCTR31 .SET
[4] NCTR31
[5] [5a]
40 4
[6a] [6b] [6c] [7] [8] [9] [10] [11] [12]
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250
[13]
0.05
[16]
-9999
[21]
-9999
[25] 0
[26]
-9999
[31]
-9999
[35]
Dose
0
0
0
0
0
0
0
0
0
0
25
25
25
24
25
25
25
25
25
25
50
50
50
2.1 User's Manual
2.22045
e-16
1.49012
e-8
01110
[14] [15]
0
[17]
-9999
[22]
-9999
[27]
-9999
[32]
-9999
[36]
resp
0
4
1
2
2
2
2
0
2
0
4
4
3
7
5
3
1
5
3
5
3
10
10
0.95
[18] [19]
-9999 -9999
[23]
-9999
[28] [29]
-9999 -9999
[33]
-9999
[37]
nega_resp
13
10
12
10
10
9
5
12
10
9
9
8
11
3
6
9
11
8
8
11
6
6
3
[20]
-9999
[24+]
-9999
[30]
-9999
[34+]
-9999
[38]
column4
13
14
13
12
12
11
7
12
12
9
13
12
14
10
11
12
12
13
11
16
9
16
13
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50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
User's
3
5
7
5
3
8
6
10
2
13
3
10
9
9
6
5
7
Manual
5
4
4
3
9
3
3
4
1
1
3
1
1
1
3
4
2
8
9
11
8
12
11
9
14
3
14
6
11
10
10
9
9
9
Polynomial Continuous Model Input File Format
[1] Model Name, in this case, the constant string Polynomial
[2] User Notes
[3] Input file name
[4] Output data file name
[4a] Degree of polynomial
= Default of 2 if user does not input a value
= 1 if Linear model is chosen
= User input value otherwise
[5] In put type
= 1 if entered as group data (e.g., Dose, N, Mean, Std.)
= 0 if individual animal data (e.g., Dose, Response) is entered
[6] A count of the number of observations
[7] Adverse direction
= 0 if Automatic (adverse direction with increasing dose estimated by model)
= 1 if Up (dose-response curve trends up with increasing dose)
= -1 if Down (dose-response curve trends down with increasing dose)
[8a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[8b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
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= User input value otherwise
[8c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[9] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[10] Restriction on polynomial coefficients
= 0 if none
= -1 if non-positive
= 1 if non-negative
[11] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[12] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[13] Smooth Option
= 0 if Unique
= 1 if C-Spline
[14] BMRType
= 0 if Absolute Dev.
= 1 if Std. Dev
= 2 if Relative Dev.(Default)
= 3 if Point
= 4 if Extra
[15] BMR (BMR Level)
= User input value (or default of 0.1)
[16] Constant Variance
= 0 if not (the variance is to be modeled as Var(i) = alpha*mean(i)Arho)
= 1 if box is checked (rho is set to 0 in the above equation)
[17] Confidence Level
= User input value (or default of .950)
[18]-[22+] Parameter values, either user specified or default values. If the parameter is not specified, the
default value is -9999
[18] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Rho Parameter
= 0 if Constant Variance box is checked
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If Constant Variance box not checked,
= user input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20]-[22+] Beta parameters in order of appearance on run screen.
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[24] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[25] Rho Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[26]-[28+] Beta parameters in order of appearance on run screen
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29]-[32] IN THIS ORDER, by checking the column assignment pull down menus, these fields should
contain:
If Group data is entered:
[29] [30] [31] [32]
Dose name N name Mean Name Std Name
If Individual data is entered:
[29] [30]
Dose name Response name
In the same column order as above, this should just be a data listing.
Example Format
[1] Polynomial
[2] BMDS MODEL RUN
[3] Polyl.SET
[4] Poly
[4a]2
[5] [6] [7]
1 6 0
[8a]
250
[8b] [8c] [9]
2.22045e 1.49012e ,
-16 -8
[10]
0
[11]
1
[12]
1
[13]
0
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[14]
1
[15]
1.00
[16]
1
[17]
0.95
[18]
-9999
[23] 0
[24]
-9999
[19]
-9999
[25]
-9999
[26]
-9999
[20]
-9999
[27]
-9999
[21]
-9999
[28 +...]
-9999
[22 +...]
-9999
[29]
DOSE
0
8
20
30
40
50
[30]
Nl
4
5
4
4
4
5
[31]
MEAN
38.45
39.56
40.9
41.95
42.725
43.42
[32]
STD
1.1683
1.28218
1.303
1.418203
1.438
1 .45932
Power Continuous Model Input File Format
[1] Model Name, in this case, the constant string Power
[2] User Notes
[3] Input file name
[4] Output data file name
[5] In put Type
= 1 if entered as group data (e.g., Dose, N, Mean, Std.)
= 0 if animal data (e.g., Dose, Response) is entered
[6] A count of the number of observations
[7] Adverse Direction
= 0 if Automatic (adverse direction with increasing dose estimated by model)
= 1 if Up (dose-response curve trends up with increasing dose)
= -1 if Down (dose-response curve trends down with increasing dose)
[8a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[8b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[8c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[9]
BMDL Curve Calculation
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= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[10] Restrict power >= 1
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[11] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[12] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[13] Smooth Option
= 0 if Unique
= 1 if C-Spline
[14] BMRType
= 0 if Absolute Dev.
= 1 ifStd. Dev.
= 2 if Relative Dev.(Default)
= 3 if Point
= 4 if Extra
[15] BMR (BMR Level)
= User input value (or default of 1.000)
[16] Constant Variance
= 0 if not (the variance is to be modeled as Var(i) = alpha*mean(i)Arho)
= 1 if box is checked (rho is set to 0 in the above equation)
[17] Confidence Level
= User input value (or default of .950)
[18] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Rho Parameter
= 0 if Constant Variance box is checked
If Constant Variance box not checked,
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] Control Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] Slope Parameter
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= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] Power Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[24] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[25] Rho Parameter
= 0 if Constant Variance box is checked
If Constant Variance box not checked,
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[26] Control Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] Power Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29]-[32] IN THIS ORDER, by checking the column assignment
pull down menus, these fields should contain:
If Group data is entered:
29 30 31 32
Dose name N name Mean Name ..
Name
If data is entered:
29 30
Dose name Response name
etc.
In the same column order as above, this should just be a data listing.
Format Example
[1] Power
[2] BMDS MODEL RUN
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[3] Power.SET
[4] Power
[5]
1
[8a]
250
[14]
1
[18]
-9999
[23] 0
[24]
-9999
[29]
DOSE
0
8
20
30
40
50
[6]
6
[8b]
[8c]
[7]
1
[9] [10] [11] [12] [13]
2.22045e-16 1.49012e-8 1011 0
[15]
1.00
[19]
-9999
[25]
-9999
[30]
Nl
4
5
4
4
4
5
[16]
1
[20]
-9999
[26]
-9999
[31]
MEAN
38.45
39.56
40.9
41.95
42.725
43.42
[17]
0.95
[21] [22]
-9999 -9999
[27] [28]
-9999 -9999
[32]
STD
1.1683
1.28218
1.303
1.418203
1.438
1 .45932
Probit and Log-Probit Dichotomous Model Input File Format
[1] Model name, in this case, the string Probit
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence
= Default of 1.49012e-8 if user does not input a value
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= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Log transformation
= 1 if Log transformation is to be used
= 0 otherwise
[9] Restrict Slope
= 1 if Restrict Slope >= 1 box is checked
= 0 otherwise
[10] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value or if Log transformation not selected
[17] Slope Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Intercept Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
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[20] Background Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected or if Log transformation not selected
[21] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22] Intercept Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[23] Dose Name
[24] Response Name
[25] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] Probit
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
[4] EXAMPLE
[5] 4
[6a] [6b]
250 2.22045e-
[13]
0.10
[16]
-9999
[19]0
[20]
-9999
[23]
Dose
0
50
100
150
i-16
[14]
0
[17]
-9999
[21]
-9999
[24]
Resp
3
6
10
19
[6c] [7] [8]
1.49012e-8 1 0
[15]
0.95
[18]
-9999
[22]
-9999
[25]
NEGATIVE,
47
44
40
31
[9] [10] [
0 1
RESPONSE
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Quanta! Linear Dichotomous Model Input File Format
[1] Model name, in this case, the string QuantalLinear
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] This parameter is set to 0 by the user interface, but is ignored when running the Quantal Linear
model.
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface andean only be changed by
manually editing the .(d) file!!!!
[11] Smooth Option
= 0 if Unique
= 1 if C-Spline
[12] BMR (BMR level)
= User input value (or default of .100)
[13] Risk Type
= 0 if Extra
= 1 if Added
[14] Confidence Level
= User input value (or default of .950)
[15] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
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enter a value
[16] Slope Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[1 7] Power parameter - for the Quantal Linear model, Power is set to a constant value of 1 , regardless
of what appears here in the input file.
[18] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[19] Background Parameter.
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[20] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[21] Power Parameter - Constant value -9999 for Quantal Linear model.
[22] Dose Name
[23] Response Name
[24] Constant String: NEGATIVE_RESPONSE
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1] QuantalLinear
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
[4] EXAMPLE
[5] 4
[6a] [6b] [6c] [7] [8] [9] [10] [11]
? 99045
250 o . 1 1110
[12]
0.10
[15]
-9999
[13]
0
[16]
-9999
[14]
0.95
[17]
1
[18]0
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[19]
-9999
[22]
Dose
0
50
100
150
User's Manual
[20]
-9999
[23]
Resp
3
6
10
19
[21]
-9999
[24]
NEGATIVE_RESPONSE
47
44
40
31
Rai and Van Ryzin Nested Model Input File Format
[1] Model name, here constant string RaiVR
[2] User notes
[3] Input file name
[4] Output file name
[5] Number of Observations
[5a] Number of Dose groups
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Restrict Power >= 1 (Note: Power = Rho parameter in model)
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Fixed Size
= 1 if Ctrl Group Mean selected
= 0 if overall mean selected
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
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NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMR (BMR level)
= User input value (or default of .100)
[14] Risk Type
= 0 if Extra
= 1 if Added
[15] Confidence Level
= User input value (or default of .950)
[16] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Rho Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Beta Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] Thetal Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] Theta2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] Phil Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] Phi2 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Phi3 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
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[24] Phi4 Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[24+] Phi5 through PhMO if necessary (as many Phi parameters as dose groups)
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[25] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[26] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] Rho Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] Beta Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29] Thetal Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[30] Theta2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[31] Phil Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[32] Phi2 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[33] Phi3 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34] Phi4 Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[34+] Phi5 through PhMO if necessary (as many Phi parameters as dose groups)
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[35] Dose Name
[36] Response Name
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[37] Constant String: NEGATIVE_RESPONSE
[38] Litter Size
Data:
Dose in first column
Response in Second
Total (Litter Size) minus Response in third column
Litter Size
Example Format
[1] RaiVR
[2] BMDS MODEL RUN
[3] NCTR31 .SET
[4] NCTR31
[5] [5a]
40 4
[6a] [6b] [6c] [7] [8] [9]
2.22 1.49
250 045 012 1 0 1
e-16 e-8
[10]
[11]
[12]
[21]
-9999
[25] 0
[26]
-9999
[31]
-9999
[35]
Dose
0
0
0
0
[14] [15]
0
[17]
-9999
[22]
-9999
[27]
-9999
[32]
-9999
[36]
resp
0
4
1
2
0.95
[18] [19]
-9999 -9999
[23]
-9999
[28] [29]
-9999 -9999
[33]
-9999
[37]
nega_resp
13
10
12
10
[20]
-9999
[24+]
-9999
[30]
-9999
[34+]
-9999
[38]
Liter
13
14
13
12
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0
0
0
0
0
0
25
25
25
25
25
25
25
25
25
25
50
50
50
50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
User's
2
2
2
0
2
0
4
4
3
7
5
3
1
5
3
5
3
10
10
3
5
7
5
3
8
6
10
2
13
3
10
9
9
6
5
7
Manual
10
9
5
12
10
9
9
8
11
3
6
9
11
8
8
11
6
6
3
5
4
4
3
9
3
3
4
1
1
3
1
1
1
3
4
2
12
11
7
12
12
9
13
12
14
10
11
12
12
13
11
16
9
16
13
8
9
11
8
12
11
9
14
3
14
6
11
10
10
9
9
9
Weibull Dichotomous Model Input File Format
[1] Model name, in this case, the string Weibull
[2] User notes
[3] Input file name
[4] Output file name
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[5] Number of Observations
[6a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[6b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[6c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[7] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[8] Restrict power >= 1
= 1 if Restrict Power >= 1 box is checked
= 0 otherwise
[9] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[10] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[11] Smooth Option
= 0 if Unique
= 1 if C-Spline
[12] BMR (BMR level)
= User input value (or default of .100)
[13] Risk Type
= 0 if Extra
= 1 if Added
[14] Confidence Level
= User input value (or default of .950)
[15] Background Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[16] Slope Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[17] Power parameter
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= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Initialize Parameters
= 1 if one or more parameters are set to initialized
= 0 otherwise
[19] Background Parameter.
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[20] Slope Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[21] Power Parameter
= user specified initial value if "initialized" is selected for this parameter
= -9999 if "initialized" is not selected
[22] Dose Name
[23] Response Name
[24] Constant String: NEGATIVE_RESPONSE
etc.
Data:
Dose in first column
Response in Second
Total minus Response in third column
Example Format
[1]Weibull
[2] BMDS MODEL RUN
[3] EXAMPLE.SET
[4] EXAMPLE
[5] 4
[6a] [6b] [6c] [7] [8] [9] [10] [11]
250 2.22045e-16 1.49012e-8 11110
[12] [13] [14]
0.10 0 0.95
[15] [16] [17]
-9999 -9999 -9999
[18]0
[19] [20] [21]
-9999 -9999 -9999
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[22]
Dose
0
50
100
150
User's Manual
[23]
Resp
3
6
10
19
[24]
NEGATIVE_RESPONSE
47
44
40
31
Exponential Continuous Models Input Format
[1] Model Name, in this case, the constant string Exponential_beta
[2] User Notes
[3] Input file name
[4] Output data file name
[5] In put Type
= 1 if entered as group data (e.g., Dose, N, Mean, Std.)
= 0 if individual animal data (e.g., Dose, Response) are entered
[6] A count of the number of observations
[7] Adverse Direction
= 0 if Automatic (adverse direction with increasing dose estimated by model)
= 1 if Up (dose-response curve trends up with increasing dose)
= -1 if Down (dose-response curve trends down with increasing dose)
OTHER PARAMETERS CONTROLLING WHICH MODELS ARE RUN
[8a] Maximum # of iterations
= Default of 250 if user does not input a value
= User input value otherwise
[8b] Rel Function Convergence
= Default of 2.22045e-16 if user does not input a value
= User input value otherwise
[8c] Parameter Convergence.
= Default of 1.49012e-8 if user does not input a value
= User input value otherwise
[9] BMDL Curve Calculation
= 1 if BMDL Curve Calculation box is checked
= 0 otherwise
[10] BMD Calculation
= 1 if BMD calculation box is checked
= 0 otherwise
[11] Append or Overwrite Output File
= 1 if Append is selected
= 0 if Overwrite is selected
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NOTE: This parameter is automatically set to 0 by the user interface and can only be changed by
manually editing the .(d) file!!!!
[12] Smooth Option
= 0 if Unique
= 1 if C-Spline
[13] BMRType
= 0 if Absolute Dev.
= 1 if Std. Dev.
= 2 if Relative Dev.
= 3 if Point
= 4 if Extra
[14] BMRF (BMR Level)
= User input value (or default of 1.000)
[15] Constant Variance
= 0 if not (the variance is to be modeled as Var(i) = alpha*mean(i)Arho)
= 1 if box is checked (rho is set to 0 in the above equation)
[16] Confidence Level
= User input value (or default of .950)
[17] Alpha Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[18] Rho Parameter
= 0 if Constant Variance box is checked
If Constant Variance box not checked,
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[19] a Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[20] b Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[21] c Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[22] d Parameter
= User input value if Specified Option is selected
= -9999 if Specified is not selected or when the user selects the Specified option, but does not
enter a value
[23] Initialize Parameters
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= 1 if one or more parameters are set to initialized
= 0 otherwise
[24] Alpha Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[25] Rho Parameter
= 0 if Constant Variance box is checked
If Constant Variance box not checked,
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[26] a Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[27] b Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[28] c Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
[29] d Parameter
= User specified initial value if "initialized" is selected for this parameter
= -9999 if not checked
Note: In the Exponential Beta software, no initial values may be specified by the user. Leave all
these entries as is (with "-9999").
[30]-[33] IN THIS ORDER, by checking the column assignment
pull down menus, these fields should contain:
If Group data are entered:
[29] [30] [31] [32]
Dose name N name Mean Name Std Name
If data are entered:
[29] [30]
Dose name Response name
[etc.]
In the same column order as above, this should just
be a data listing.
Format Example
[1] PROAST
[2] BMDS MODEL RUN
[3] Exponential.dax
[4] Exponential
[5] [6] [7]
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1
1
[8a] [8b]
250 2.22045e-16
[8c] [9] [10] [11] [12]
1.49012e-8 0110
[13]
1
[17]
-9999
[23] 0
[24]
-9999
[14]
1.00
[15]
1
[16]
0.95
[18] [19] [20] [21] [22]
-9999 -9999 -9999 -9999 -9999
[25] [26] [27] [28] [29]
-9999 -9999 -9999 -9999 -9999
[30] [31] [32]
DOSE Nl MEAN
[etc.]
0 4 38.45
8 5 39.56
20 4 40.9
30 4 41.95
[33]
STD
1.1683
1 28218
1.303
1.418203
40 4 42.725 1.438
50
43.42
1.45932
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