600R03107
&ER&
United States
Environmental Protection
Agency
Acute-to-Chronic
Estimation (ACE v 2.0) with
Time-Concentration-Effect
Models
User Manual and Software
HIGH
ill
V)
o
Q.
LOW
v2.0
ACE
ACUTE
EFFECT
-^CHRONIC
-------
-------
EPA/600/R-03/107
December 2003
Acute-to-Chronic Estimation (ACE v 2.0)
with Time-Concentration-Effect Models
User Manual and Software
By
Mark R. Ellersieck, Amha Asfaw, Foster L. Mayer*, Gary F. Krause, Kai Sun, and Gunhee Lee
University of Missouri-Columbia
College of Agriculture, Food and Natural Resources
Agricultural Experiment Station-Statistics
Columbia, MO 65211
*U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research Laboratory
Gulf Ecology Division
Gulf Breeze, FL 32561-5299
U.S. Environmental Protection Agency
Office of Research Development
1200 Pennsylvania Avenue, NW
Washington, DC 20460
Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer fiber content
processed chlorine free.
-------
Notice
The U.S. Environmental Protection Agency through its Offices of Research and Development, Pesticide
Programs, Pollution Prevention and Toxics, and Water partially funded and collaborated in the research
described herein under EPA Project No. CR82827901 to University of Missouri-Columbia, College of
Agriculture, Food and Natural Resources, Agricultural Experiment Station-Statistics. It has been subjected
to the Agency's peer and administrative review and has been approved for publication as an EPA
document. Mention of trade names or commercial products does not constitute endorsement or
recommendation for use.
-------
Abstract
Predictive toxicological models, including estimates of uncertainty, are necessary to address probability-
based ecological risk assessments. Methods and software (ACE) were developed for estimating chronic
toxicity from raw acute toxicity data (all response observations at all times and exposures). Three methods
were developed - - Accelerated Life Testing (ALT), Multifactor Probit Analysis (MPA), and two-stage
Linear Regression Analysis (LRA). Of the three, the method of choice is ALT, in that time to failure
(death) of each experimental unit is independent. It requires three partial responses over the time period of
acute testing, but will function with one. The MPA is a two dimensional probit analysis using both time
and concentration to produce a multiple regression equation, however, each experimental unit is not
independent. Also, the MPA requires more partial responses than the ALT. The LRA calculates LC values
for each time period and then regresses the LC values as the Y axis and the reciprocal of time as the X axis.
The Y intercept is the chronic no-effect concentration. The LRA will function when ALT and MPA fail;
no partial responses are required. All methods provide confidence limits for the point estimates. The
methods have previously been shown to estimate chronic no-effect concentrations very well when validated
against actual paired acute and chronic test results with fishes.
111
-------
-------
Contents
Abstract iii
List of Figures vi
Acknowledgement vii
Introduction 1
Background 2
Software Language 2
Installing ACE 3
System Requirements 3
Using ACE in Windows 3
Menu Bar - Main Screen 4
Menu Bar - ALT, MPA, LRA 4
Data Entry 5
Format 5
Entering Data Directly 5
Entering Data from Outside Source 6
Obtaining Data from Outside Source 6
Data Correction 7
Model Selection. 7
ACE Application Windows 7
Data Analysis 7
Printing Output 8
ALT - Accelerated Life Testing Model 8
MPA - Multifactor Probit Analysis Model 10
LRA - Linear Regression Analysis Model 11
Options 13
Font 13
Alpha 13
Exposure Time 14
Zero Concentration 14
Title 15
Selecting MPA Models 15
Estimating Sublethal Effects 16
Additional Model Documentation 17
ALT 17
MPA 17
LRA 18
References 18
-------
List of Figures
Figure 1 Main ACE Screen 4
Figure 2 Accelerated Life Testing (ALT) Screen 8
Figures ALT Full Screen 9
Figure 4 Multifactor Probit Analysis (MPA) Screen 10
Figures MPAFull Screen 11
Figure 6 Linear Regression Analysis (LRA) Screen 12
Figure? LRA Full Screen 13
FigureS Options Screen 14
VI
-------
Acknowledgement
This project was sponsored in part by the U.S. Environmental Protection Agency's Offices of Research and
Development, Pesticide Programs, Pollution Prevention and Toxics, and Water under Cooperative
Agreement CR82827901. Thanks to Vic Camargo for technical support on graphics, and to Debbie
Scholes, Mary Adkinson, and Bonnie George for manual preparation. Peer review and beta testing were
contributed by M. Anderson, L. Burns, J. Faircloth, T. Linton, R. Pepin, D. Rodier, G. Smith, and W.
Waller.
vn
-------
-------
Introduction
Both understanding and evaluating chronic toxicity of chemicals are essential to assessing their ecological
hazards and making environmentally sound management decisions. Because of the large number and
variety of industrial, agricultural and home-use chemicals released in the U.S. annually and the high cost
and effort required for chronic tests, resources are often insufficient to obtain experimental information
about long-term environmental impacts for all potentially hazardous chemicals. In comparison, acute tests
are less costly and time consuming and, for these reasons, an abundance of acute toxicity data exists for
numerous chemicals and organisms. Also, procedures have been developed for extrapolating effects data
within classes of chemicals sharing similar chemical structures (Lipnick 1995). Thus, there is a strong
rationale to relate acute and chronic toxicities of chemicals and to develop statistical and mathematical
techniques to predict chronic toxicity based on data from acute experiments.
Use of short-term tests as a basis for linkage of exposure and time to response with chronic effects for
ecological risk assessments is significant. The ability to accurately and precisely associate chronic effects
from acute time-concentration-effect data is a powerful approach that integrates various aspects of
toxicokinetics and directly addresses a variety of uncertainties in terms of chronicity. Three models were
developed (Lee et al. 1995; Mayer et al. 1994, 2002; Sun et al. 1995b), tying together classical methods
(e.g., probit regression) (Finney 1978) and time to event methods (Newman 1994) to provide models that
predict chronic toxicity from acute toxicity data.
• Accelerated Life Testing (ALT) - A survival analysis and population-based approach (Weibull
distribution) using accelerated life testing theory (Mayer et al. 2002, Sun et al. 1995b). The
method was originally used for mechanical and electrical devices placed under short-term or
"acute" stress (e.g., generator running constantly at full power and high heat) to predict long-term
or "chronic" time to failure. In the ACE software, the model is applied to organisms placed under
acute stress (i.e., toxicant), and the variable measured is time to failure or death. The model
assumes that both exposure concentrations and duration affect survival probability, and hence, has
the ability to summarize the entire concentration-time-response data of a toxicity test. Actual
proportion responses are used; probit transformations are not applied. ALT also takes into account
the spontaneous survival probability and is suitable to describe both acute and chronic lethality
data. The survival function includes competing risks, with contaminant exposure being one.
• Multifactor Probit Analysis (MPA) - Multiple regression models that simultaneously evaluate the
relationship among exposure concentration, time, and probit % mortality to predict chronic
response (Mayer et al. 2002, Lee et al. 1995). This model is appropriate when different
experimental units are present for concentration-time combinations (i.e., one complete replicate is
removed at one or more time intervals for a measurement different than survival; only the
remaining replicates are used for the remainder of the toxicity test). ALT and LRA models are
more appropriate for predicting chronicity from standard acute toxicity data; however, multiple
regression models, such as MPA, are necessary when estimating chronicity under changing
conditions (e.g., varying exposure scenarios in effluents).
• Linear Regression Analysis (LRA) - A two-step linear regression analysis (Mayer et al. 1994,
Mayer et al. 2002). This model combines two linear regressions: 1) estimates low lethal
concentrations at each observation time period and 2) regresses those concentrations (dependent
variable) against the reciprocal of time (independent variable), with the intercept being the chronic
no-effect concentration. Probit transformations of percent response are used.
The software program, Acute-to-Chronic Estimation (ACE), described herein, allows the user to estimate
chronic toxicity for a species from raw acute toxicity data with accuracy and precision. ACE will,
therefore, greatly enhance the use of probability-based risk assessments for chemicals having minimal data
sets. However, if a chronic test is to be conducted, ACE can be used to more accurately identify the range
of exposure concentrations required. ACE is based on the Windows platform and is specifically designed
-------
-------
for estimating chronic toxicity and providing graphical and tabular presentation of results. ACE v 2.0 is an
upgrade of the former DOS version (Mayer et al. 1999).
Background
Using acute mortality data to estimate chronic toxicity (survival, growth, reproduction) to aquatic
organisms customarily involves deriving an application factor (Mount and Stephan 1967) or an acute-to-
chronic ratio (Kenaga 1982), both of which require acute and chronic toxicity testing. Kenaga (1979)
reviewed the principal measurements of the acute LC50, the maximum acceptable toxicant concentration
(MATC), and the application factor (AF) used in determining chronic NOECs (highest concentration
causing 0% or no statistically significant effect) for many chemicals. The AF is derived by dividing the
MATC for a compound, as determined in a chronic toxicity test with a given species, by the acute LC50 for
the same compound tested with the same species. The acute-to-chronic ratio (ACR) is the inverse of the
AF. The AF or ACR is then used to estimate chronic NOECs for other species for which only acute
toxicity data (EC or LCSOs) exist (Buikema et al. 1982). These approaches have limitations.
One limitation is that the biological endpoints and degrees of responses are often not comparable between
acute and chronic toxicity data. When either the AF or ACR is used, the acute median lethal concentration
(EC or LC50) is compared with the MATC, often derived from an endpoint other than mortality. Although
different degrees of response (acute 50% vs. chronic no-effect) could be used when response slopes are
similar, the slopes may be different. Additionally, use of the AF or ACR method does not take into
consideration the progression of mortality through time that is derived in acute toxicity tests. The
concentration-time-response interaction has been addressed by Shirazi and Lowrie (1988), but they directed
their efforts toward better defining the LC50. The acute toxicity value represents only one point in time
(e.g., 96-h LC50), and the relationship of degree of response with duration of exposure should be essential
when chronic toxicity is predicted from acute toxicity data.
Lethality and other toxic effects are dependent on both concentration of a chemical to which an organism is
exposed and length of exposure time. It is a common practice to investigate the toxicity of new and
existing chemicals and effluents using acute toxicity tests. This is done by observing mortality resulting
from exposure to a series of chemical concentrations, usually at 24, 48, 72, and 96 h. Time course
distinguishes acute from chronic toxicity and also relates them as an integrated and progressive process. A
time to response approach gives a better understanding of the progression of toxic effects over time, and
survival time modeling has shown great applicability in toxicological studies (Crane et al. 2002, Dixon and
Newman 1991, Newman and Aplin 1992).
The models included here are more comprehensive approaches to predicting chronicity, both
toxicologically and statistically. Simultaneous consideration is given to exposure concentration, degree of
response, and time course of effect, all of which are usually included in describing the results of an acute
toxicity test, but are seldom used in hazard assessment. A consistent endpoint (mortality) and degree of
response (~0%) are used to predict long-term (chronic) lethality from acute toxicity test data. These
calculations are based solely on raw acute toxicity test data and do not require conducting a chronic toxicity
test. Estimated long-term (chronic) lethality values have previously been validated for accuracy with actual
chronic no-effect values derived for 28 chemical-fish species combinations (Mayer et al. 2002).
Software Language
The ACE software is based on a Windows® platform and written in Visual Basic (Microsoft® Visual
Basic 6.0 1987-2000). Subroutines (Fortran programs) in Visual Basic and Visual Fortran are required to
call Fortran IMSL Routines necessary in certain calculations (Compaq Fortran 1999, Visual Numeric
1999).
-------
-------
Installing ACE
System Requirements
• Operates on Microsoft Windows 95, 98, 2000, NT and XP (Windows® 98 or later is suggested).
• Minimum 16 MB RAM (64 MB or greater is suggested).
• CPU speed of over 200 MHz is suggested; ACE will work with less, but is very slow.
• 6MB hard disk space.
• Mouse or pointing device.
• Printer (optional).
Remove any existing versions of ACE before installing the new one or malfunctions may occur.
To remove old ACE software:
1. Double click My Computer.
2. Double click Control Panel.
3. Double click Add/Remove Programs.
4. Click ACE.
5. Click Delete or Change/Remove.
To install new ACE software:
1. Place the ACE CD in the CD ROM drive.
2. Click Start button.
3. Select Run from the menu.
4. Select Browse from the Run window.
5. Select drive letter associated with the CD drive from Browse window (or ACE 2003 [D:]).
6. Double-click Setup file or D:\SETUP.EXE file.
7. Click OK.
8. Windows now walks you through the installation process. If a "Yes" or "No" question is encountered,
choose "Yes".
9. Following installation, the ACE program can be accessed by clicking Start, Programs, and then ACE.
You can create an icon on the Desktop screen by placing the mouse pointer on the ACE icon, holding
down on the control button, and dragging the icon to desired location on the screen.
Using ACE in Windows
Double click on the ACE icon in the Desktop screen and the main ACE screen will appear (Fig. 1).
There are three main sections to the screen. The first section (left) is for data entry or for including data
from other sources (e.g., Excel, Lotus 123, etc.). The second section (right center) represents the models
available in ACE (ALT, accelerated life testing; MPA, multifactor probit analysis; LRA, linear regression
analysis). The third section is the ACE logo, appearing in the background at right. Following data entry
and conversion to ASCII files (see below), click on the box for the model of choice (ALT, MPA, LRA),
and the analysis results and graphics will automatically be generated.
-------
-------
Figure 1 - Main ACE Screen
[9/24/2003 TT(H6AM
Menu Bar - Main Screen
File - Clicking on File provides the following drop down menu:
• New - Clears spreadsheet so new data can be entered.
• Open - Obtains a saved data set from an outside source (see Obtaining Data from an Outside
Source).
• Save - Saves any changes back to the same file name.
• Save As - Saves a data set for the first time or saves an existing data set to a new file name.
• Exit - Clicking on Exit will end the ACE program; clicking on X in the upper right-hand corner of the
main ACE window will perform the same function as Exit.
• Help - User manual.
Options - Option screen will appear; see OPTIONS for explanation.
Log - If the ACE program does not run, then an error list will appear; the screen will be empty if no
problems occur.
Sheet icon - This is the same as New under the File drop down menu.
File icon - This is the same as Open under the File drop down menu.
Floppy disk icon - This is the same as Save under the File drop down menu.
Menu Bar - ALT, MPA, LRA
• Print - Allows printing of selected output (statistical output, graph, or log).
• Save_on_file - Saves the statistical output to a file; this is the same as Save as described previously.
-------
-------
Log - Provides additional statistical output information.
Data Entry
Format
The following acute toxicity data set for Kepone (Buckler et al. 1981) is used to demonstrate data
formatting. The data must be entered in column format as follows, except that columns may be in any
order; each column is identified by column headers in the first window (Fig. 1). Data must be entered in
the following format for rows:
Concentration
0
10
16
22
27
40
56
73
0
10
16
22
27
40
56
73
0
10
16
22
27
40
56
73
0
10
16
22
27
40
56
73
24
24
24
24
24
24
24
24
48
48
48
48
48
48
48
48
72
72
72
72
72
72
72
72
96
96
96
96
96
96
96
96
Total (# of
Organisms Tested)
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
Response (# Dead)
0
0
3
5
8
20
20
20
0
1
7
12
20
20
20
20
0
5
12
13
20
20
20
20
0
5
12
13
20
20
20
20
Entering Data Directly
Acute toxicity data can be entered directly to ACE using the spreadsheet (Fig. 1) and keypad functions.
The following keypad functions are operational in the spreadsheet: arrow keys, Delete key, Enter key
-------
-------
(functions the same as the down arrow key), and number keys. Each column has to be identified for the
ACE program to function properly. Click on each of the column headers, click on arrow, and select
appropriate descriptor for that column.
• ID - This is not necessary if a single data set is entered. If more than one data set is to be entered, see
Entering Data from Outside Source below.
• Concentration - Exposure concentration or % effluent (for extremely large numbers, convert to next
higher unit [e.g., \ig to mg]).
• Time - Observation time in hours, usually 24, 48,72, and 96 hours (maximum times are 12).
• Total - Number of organisms exposed per concentration.
• Response - Number of organisms dead or affected.
The ACE default order of column designation is the same as above.
Next, enter the data, click on File and then Save as and enter a data set name in the file name box. The data
set will be saved as a tab delimited file unless an extension name of CSV is typed. An extension name of
CSV will results in a comma delimited file. The Tab or Comma delimited file types are preferred. The data
are brought back into ACE by clicking on the icon file, data set to be analyzed, and Open. Then click on
the model of preference (ALT, MPA, LRA), and the analysis is automatically conducted. If data are not
analyzed, recheck the column headers to make sure they are correct.
Entering Data from Outside Source
The software is not meant to be a sophisticated spreadsheet, and the best way to enter multiple data sets is
from an outside source using softwares capable of producing ASCII text files (e.g., Excel, Word, etc.). If
data sets are stacked, a fifth column (ID) must be added in order to identify the different acute data sets.
Once data have been entered, save them as an ASCII file. This is done by clicking on File in the upper left
corner and then clicking on Save as. The Save as screen will appear with two boxes at the bottom; File
name and Save as type:. Type in a name for the data set in the File name box. Click Save as type:, a list
of file types will appear. The following file types are appropriate for the ACE software: Space delimited,
Tab delimited and Comma delimited (CSV). The Tab delimited or CSV file types are preferred.
Obtaining Data from Outside Source
To obtain a data set from an outside source while in the ACE program, click on the File icon in the upper
left-hand corner and the following drop down menu will appear:
New Ctrl N
Open
Save
Save As
Exit
Click Open; if the data set is not listed in the Open screen, click Files of type:. Click arrow and then
All(*.*). If the file is still not present, click on Look in:. This will list all of the disk drives in your
computer. Once the data set has been found, double click on the data set and the data will be entered into
the ACE program. Again, data sets must be converted to Tab, Comma or Space delimited file types, with
Tab and CSV being preferred.
Once the data set is imported into the ACE program in the correct format, title or other descriptive lines
must be removed. Click on the line number in the spreadsheet for the line that is to be deleted (left side of
main ACE window) and press the Delete key on keyboard.
-------
-------
Each column needs to be identified by the ACE program. Check the column headers on the Main ACE
Screen. If they are correct, the program is ready to run. If not, click on each of the column headers and
correct (see Entering Data Directly).
Data Correction
If data need to be corrected, it can be done within ACE. Just click on the cell, delete the incorrect number
with the Delete key, and then correct the entry. If columns are too narrow to fully observe identifiers or
numbers, widen the columns by placing the cursor on the right border of the column header and, while
holding down the left mouse button, drag to the right until the desired width is achieved. Reverse this
process to narrow the columns. Changes are saved by clicking on File, selecting either Save or Save as,
entering a name for the data set in File name:, and clicking on Save.
Model Selection
Brief guidelines for using ACE and selecting the appropriate models are:
1. Exposure Type - Historically, three test exposure techniques have been used to determine acute
toxicity for aquatic organisms (static, static renewal, and flow-through). Acute toxicity data used in
ACE should be based on static renewal or flow-through techniques, since static exposure may give
erroneous results, except for chemicals that are water soluble (see fluridone, Mayer et al. 1994).
Further research is needed to determine at what octanol/water or solubility values static test data begin
resulting in erroneous chronic predictions.
2. Model Preference - ALT is the method of choice, followed by LRA and MPA, based on experimental
designs commonly used in acute toxicity testing. MPA is a special case application and is seldom
used.
3. Partial Responses - Dependability of chronicity estimates is generally enhanced with increasing
numbers of partial responses (% mortality >0<100%). Recommended partial responses are: ALT > 3,
MPA > 5, and LRA > 1. However, ALT will generally function with one partial response; LRA will
function with no partial responses as long as there is an exposure-response in time. It is not
uncommon to conduct acceptable acute toxicity tests where no partial responses occur, only 0 and
100%; under these conditions, the LRA is the model of choice.
4. Percent Effect for Chronicity - Recommended percent values to be selected for estimated chronic
toxicity are: ALT = 1.0%, MPA = 0.01%, and LRA = 0.01%. Use of 0.01% for the MPA and LRA
represents a very close approximation to zero on the probit scale (Mayer et al. 1994, Mayer et al.
2002). ALT differs in that 1.0% is presently considered the smallest detectable difference due to the
model being population-based (small numbers of organisms usually exposed in each concentration).
These percentages correspond well to statistically-based chronic no-effect concentrations for mortality
using hypothesis testing (i.e., analysis of variance; Mayer et al. 2002).
ACE Application Windows
Data Analysis
Download a data set to the main ACE screen and click on a model (ALT, MPA, or LRA); the data will
automatically be analyzed. Click on the X in the upper right hand corner to return to the main screen; a
different model can then be selected. When you click on a model on the main screen, a split screen will
appear; statistical output on the left and graphics on the right. Double click on either to fill screen; double
click again to return to split screen. Click on the X in the upper right-hand corner of the main screen to exit
ACE.
-------
-------
Printing Output
Printing of the statistical or graphics output is achieved by clicking Print, or the outputs can be saved by
clicking Save_on_file (upper left-hand corner of screen). Additional statistical output can be obtained by
clicking on Log. The output for Log includes the statistical output plus the additional information below
and can also be printed or saved.
• ALT - Data input, iterations required to solve function estimates, variance-covariance matrix for
function estimates to estimate confidence intervals, and data used in the analysis (the highest
concentration having 0% response and the lowest concentration having 100% response are used for
each observation time).
• MPA - Data used in the analysis as described in ALT.
• LRA - Statistical analyses for all six models including slope, estimated no-effect chronic
concentration, confidence intervals, r~, and data used in the analysis as described in ALT.
ALT- Accelerated Life Testing Model
Click on the box ALT (Accelerated Life Testing) in the main ACE screen, and analysis of the downloaded
acute toxicity data is performed (Fig. 2).
Figure 2 -Accelerated Life Testing (ALT) Screen
Print Save_on_File Log
Acute to Chronic Esti:
Accelerated Life Te
Parameter
Estimate
95.00% Lower
AA
B
C
A
C/B
16.9481841
3 .2795173
1.2104229
0.0000931
0.3690856
13.7574
1.90S4
0.9932
0.0000
0.2243
IHTEPRETATION: AA—measure of initial
of mode of concentration-response; C—:
A=(1/AA)**B; C/B—measure of dominatio
Haxiuum likelihood estim
Mortality Concentration
0.01%
0.05%
0.10%
0.50%
1.00%
0.49318
0.80568
0.99538
1.62700
2.01146
Standard
0.40
0.57
0.66
0.91
1.04
ALT Time-dependent LC curves
2.25
c
.Q
"GJ
"c
8
— 0.01 %
— 0.10%
•• 1.00 %
0.75
Time (days)
-------
-------
Double click on the statistical output screen (left side) in order to obtain the full screen (Fig. 3).
Figure 3 - ALT Full Screen
Print Savejjnjfe Log
Acute to Chronic Estimation
Accelerated Life Testing
Parameter
Estimate
95.00% Lower limit 95.00% Upper limit
AA
B
C
A
C/B
16.9481841
3.2795173
1. 2104229
0.0000931
0.3690856
13.7574889
1.9054583
0.9932257
0.0000000
0.2243269
20.1388793
4.6535763
1.4276201
0.0005032
0.5138444
IHTEPRETATION: AA—measure of initial toxic strength;B—measure
of mode of concentration-response; C—measure of mode of time-response;
A=(1/AA)**B; C/B—measure of domination between concentration and time.
Haxiuum likelihood estimates for 'No-effect' concentrations
30-DAYS
Mortality Concentration Standard Error 95.00% lower limit 95.00% upper limit
0.01%
0.05%
0 . 10%
0.50%
1.00%
0.49318
0.80568
0.99538
1.62700
2.01146
0.40204
0.57287
0.66316
0.91498
1.04130
0.14235
0.21427
0.25501
0.38003
0.45026
1.28118
1.92351
2.29517
3.42035
4.05238 X;!
There are two main parts to the statistical output. The first part contains statistical parameter estimates,
along with confidence limits. Interpretation of these parameters follows the estimates. C/B provides an
indication of the importance of exposure time (C) versus exposure concentration (B); if equal to one, both
are equally important.
The second part of the statistical output is the maximum likelihood estimates of chronic no-effect
concentrations. By default, analyses are performed for three different chronic times (30, 60 and 90 days).
Within each time period are percent level of chronic mortality (0.01 - 10.0%; 1.0% is recommended for
chronic survival with ALT), predicted toxicant concentration associated with each percentage, standard
error of the predicted toxicant concentration, and confidence limits (default is 95% confidence limits).
-------
-------
The ALT procedure will function even with a small number of partial responses in the raw acute toxicity
data. However, the confidence limits may be large; an error message will appear and the ALT will fail if
no partial responses are present in the data.
Additional chronic exposure times and the alpha level for confidence limits can be specified (see Options).
MPA - Multifactor Probit Analysis Model
Click on the box MPA (Multifactor Probit Analysis) in the main ACE screen, and analysis of the
downloaded acute toxicity data is performed (Fig. 4).
Figure 4 - Multifactor Probit Analysis (MPA) Screen
Acute co Chronic Estimation
1.29155
-0.64934
-1.13191
-1.18113
-1.18346
-1.18353
-1.18359
-1.13359
3.50730
5.26531
5.71547
5.76023
5.76218
5.76228
5.76229
5.76229
CONVERGENCE CRITERIA 13 MET AFTER 7 ITERATION(S)
CHI-SQUARE STATISTIC IS 27.01861
COMMON LOG (CONCENTRATION)
:RITICAL VALUE HITH DF - 14 ALPHA-
VARIANCE COVARIANCE HATRIX
INTERCEPT
0.44086
-0.35771
1.03961
CONCENTRATION
-0.35771
0.31024
-1.71380
INTERCEPT
CONCENTRATION
TIKE
SINCE CHI-SQUARE TEST FOR HETEROGENEITY OF DISCREPANCIES I.
ALL VARIANCES ARE MULTIPLIED BY A HETEROGENEITY FACTOR.
FIDUCIAL LIMIT HILL BE COMPUTED USING T-DISTRIBUTION INSTEl
ADJUSTED VARIANCE COVARIAIJCE HATRIX
INTERCEPT
0.85082
-0.69036
2.00635
CONCENTRATION
-0.69036
0.59874
-3.36536
INTERCEPT
CONCENTRATION
TIHE
I/TIME (COMPUTED USING TIME TJSTVER
HETEROGENEITY FACTOR
Double click on the statistical output screen (left side) in order to obtain the full screen (Fig. 5).
The output provides the number of iterations required to calculate factors for the MPA model, test statistics,
variance-covariance matrix, and the predicted chronic no-effect concentrations along with 95% confidence
limits.
The MPA includes four different models to choose from that may give different estimates of the MPA
functions (see Options). The default model is Model 3 in Options:
Probitp = a + ^(Concentration) + Y/Time
10
-------
-------
Chronic exposure time is specified and the assumption is that slopes change with a constant rate as
observation times increase.
mre 5 - MPA Full Screen
Acute to Chronic Estimation ^
ITERATION INTERCEPT
0 1.29155
1 -0.64934
2 -1.13191
3 -1.18118
4 -1.13346
; 5 -1.1S358
f 6 -1.13359
- 7 -1.13359
1
| CONVERGENCE CRITERIA 13 HET AFTER
F
I
1 CHI-SQUARE STATISTIC 15
I CRITICAL VALUE WITH DF " 14 ALPHA-
1
* VARIANCE COVARIANCE MATRIX
i INTERCEPT
INTERCEPT 0.440S6
CONCENTRATION -0.35771
TIM 1.03961
CONCENTRATION
3 .50730
5. 2 6531
5.71S47
5.76023
5.76218
5.76223
5.76229
5.76229
7 ITERATIONS)
27.01861
0.0500 IS
CONCENTRATION
-0.3S771
0.31024
-1.7433Q
j, SINCE CHI-SO.CARE TEST FOR HETEROGENEITY OF DISCREPANCIES
1 ALL VARIANCES AR.E MULTIPLIED BY A
HETEROGENEITY FACTOR.
TIKE
-38. 625S1
-44.78770
-47.70971
-47.93103
-47.93029
-47.93007
-47.93006
-47.93006
23.68442
TIME
1.03961
-1.74380
53.08837
IS SIGNIFICANT,
f FIDUCIAL LIHIT ¥ILL BE COHPUTED DSIHG T-DISTRIBUTIOH INSTEAD OF NORMAL.
ADJUSTED VARIANCE COVARIANCE MATRIX
INTERCEPT
CONCENTRATION
TIHE
INTERCEPT
0.35082
-0.69036
2.00635
CONCENTRATION
-0.69036
0.59874
-3.36536
TIHE
2.00635
-3.36536
102.4S530
NOTE : HETEROGENEITY FACTOR IS 1.92990091136951
By default, there is one chronic time period (infinity). Within each time period are percent level of
mortality (0.01 - 50%; 0.01% is recommended for MPA), predicted toxicant concentration associated with
each percentage, and confidence limits (default = 95%). The data fit the model if the chi-square statistic is
< the critical chi-square value.
The MPA is the most sensitive to lack of partial mortalities (responses); at least five partial responses
between 10 and 90% among all exposure concentrations and times are preferred. An error message will
appear and MPA will fail if inadequate partial responses or an insufficient range of partial responses exist.
Additional chronic exposure times and the alpha level for confidence limits can be specified (see Options).
LRA - Linear Regression Analysis Model
Click on the box LRA (Linear Regression Analysis) in the main ACE screen, and analysis of the
downloaded acute toxicity data is performed (Fig. 6).
11
-------
-------
Figure 6 - Linear Regression Analysis (LRA) Screen
Acute to Chronic Estimation
-------
-------
Figure 7 - LRA Full Screen
REGRESSION ANALYSIS OF Actual
value (CONCENTRATION) VERSUS
Actual value (Time)
HODEL IS: Actual value (CONCENTRATION) -INTERCEPT + SLOPE/Actual value(Tlne)
(LEAST SQUARE REGRESSION
Prob (PROSIT)
0.01 %
o.io •*
1.00 %
5.00 %
10.00 %
20.00 ••>
30.00 %
40.00 4
50.00 k
CONCENTRATION
(INFINITE HOURS)
2.86834
3.56836
4.62874
5.81439
6.5S702
7.57553
3.40027
9 . 17079
9.94960
REGRESSION ANALYSIS OF
HODEL
LOBER 95.00%
0.69411
1.40153
2.51690
3.76652
4.52230
5.49869
6.22329
6.84317
7.41591
AT EACH TIHE)
UPPER 95.00%
5.04258
5.73512
6.74058
7.86226
8.59124
9.65236
10.57724
11.49842
12.48330
LoglO (CONCENTRATION) VERSUS
IS: LoglO (CONCENTRATION) "INTE
(PROSIT ANALYSIS AT
Prob (PROBIT)
0.01
0.10
1.00
5.00
10.00
20.00
30.00
40.00
50.00
_.
CONCENTRATION
(INFINITE HOURS)
0.11511
0.20374
0.40770
0.75717
1.05334
1.S7123
2.09634
2.63156
3.37411
LOWER 95.00%
0.00122
0.00441
0.02072
0.08141
0.16719
0.39176
0.703 56
1.11437
1.60708
R-SQDARE
0.97577
0.97989
0.9S451
0.98781
0.98903
0.98973
0.98953
0.98875
0.98740
LoglO (Time)
RCEPT + SLOPE/LoglO (Time)
EACH TIHE)
UPPER 95.00%
10.79633
9.41304
8.02158
7.04214
6.63616
6.30167
6.24539
6.44985
7.08404
R-SQUARE
0.85106
0.86918
0.89494
0.92145
0.93660
0.95491
0.96639
0.97498
0.97913
Options
A number of options are available for controlling the output of each of the ACE models. The options screen
is obtained from the main ACE screen. Click Options located in the upper left-hand corner of the main
ACE window and the following screen will appear (Fig. 8). Once an alpha for confidence limits, chronic
exposure time, MPA model, and/or statistical output title are changed, click Save Options. These changes
will remain for present and future analyses. If Save Options is not selected, the changes will only remain
for the current analysis and then return to default values the next time ACE is used. Click Restore defaoul
options at the bottom right of the Options window to return to default values.
Font
Select Font (upper right-hand corner) to change font style of statistical output. Two font styles are
presented; fixed font styles should be selected in the left-hand box. The font size may also be changed to
fill the data output screen.
Alpha
To change alpha levels, click on the arrow associated with Alpha located on the upper right side of the
Options screen; choose the desired alpha percent. The alpha controls the t, T, or chi-square values for
producing confidence limits; the alpha default value is 57c.
13
-------
-------
Figure 8 - Options Screen
Transformations
Actual value Log 10 Natural log (e)
Concentration F" R !""
Time |7 F T
Fonts
Alpha |^ ^
C 2 Independent vatiable(concentration .time) with parallel slope ^~ g. Drocessjia
C I nteraction between concentration time with non parallel slope f .
\ Ignore response
(S Two independent variables with par aOel slope using reciprocal of time ^- .. ... .,, - .
f Two independent variables with non parallel slope using reciprocal of time f» I t H 'nH' iri II
Title lAcute to Chronic Estimation
Save Options
Input teoncentrafmTimeTptafResponse ,., - > , Fie ICAace\ACE\KEPQNE. Restore default options I
1"- -,,-> :..""»-,-•'•-., 1 I , , , , • I
Exposure Time
In order to change to a different time, go to options window as described previously. To the right is a white
box with the header Exposure Time. A time change can be accomplished in a number of ways. Type in a
number (in hours) in the white box. If a number already exists in the box, write over it or add a number
below the existing numbers. No time definition is needed if the number is in terms of hours. However, if
one wants to enter days, just type the number of days desired and type "days" after the number and days
will be converted to hours by the program. Weeks, months or years can be used as well, by typing in the
appropriate time description. Two of these time descriptions (eg., days and months) cannot appear together
on the same line. The default for the ALT is 30, 60 and 90 days. The default for MPA is infinite time if
the model is based on the reciprocal of time. It" the models are not based on the reciprocal of time, a number
has to be placed in the Exposure Time box in order for the program to calculate NOEC values. The LRA
procedure only calculates for infinite time.
Zero Concentration
This section applies only to the MPA and LRA. Abbott's formula (Finney 1978) is used to adjust data if
control mortality (zero concentration) exists when probit analysis is performed. The default is Let me
14
-------
-------
choose individually. If control mortality exists, the MPA or LRA will present a message box that allows
the user to choose Abbott"s correction. If only one control mortality is present, the message box will
appear only once. If control mortality appears more than once, the message box will appear for each one.
If Stop processing is selected, MPA and LRA will not run if control mortality is present. The Ignore
response option does not apply Abbott's correction. The Use Abbott's formula applies Abbott's
correction to all control mortalities.
Title
The title of the statistical output can be changed; click on Title and type in a new title. The default title is
"Acute to Chronic Estimation".
Selecting MPA Models
The basic Multifactor Probit Analysis equation has a general form in which LC% = Intercept + bt (Exposure
Concentration) + b2(Time) where b] and b2 are partial regressions for exposure concentration and time,
respectively. An additional b3 [interaction of (exposure concentration)(time)] is added if the slopes among
probits are not parallel (see Lee et al. 1995, Mayer et al. 2002).
A number of statistics require evaluation to determine the MPA model of choice. If the chi-square statistic
is < the critical chi-square value, the data fit the model adequately. Should the other models provide a
smaller chi-square statistic, that model is preferred.
To change to one of the other three basic MPA models, exit the MPA program by clicking the X in the
upper right corner, and then click on Options in the upper left-hand corner of the main ACE screen; select
Models and the four models listed below will appear. The model parameters can be changed to actual
values or log values of time and concentration within Data Transformation located in the upper left
portion of the Options screen. This procedure takes much more manipulation to determine the best model.
The combination of model choice and actual or log values of concentration and time that gives the lowest
chi-square statistics is the best model.
The four models are as follow (1.281 = probit value for 0.01%):
Model 1: Chronic exposure time is specified and equal slopes among observation times are assumed.
Exposure Concentration - Time - Response relationship is defined as:
Probitp = a + P(Concentration) + T(Time)
Chronic no-effect concentration (NOEC) at specified T hours is:
NQECr=l-™-a-r*T
Model 2: Chronic exposure time is unknown and equal slopes among observation times are assumed.
Exposure Concentration - Time - Response relationship is defined as:
Probitp = a + P(Concentration) + Y/Time
NOEC at infinite time is:
15
-------
-------
Model 3: Chronic exposure time is specified and it is assumed that the slope changes with constant rate as
observation times increase.
Exposure Concentration - Time - Response relationship is defined as:
Probitp = a + (i(Concentration) + Y(Time) + 8(Concentration)(Time)
NOEC at T hours is:
Note: This is the default model in ACE; actual value of time and the loglO of concentration.
Model 4: Chronic exposure time is unknown and and it is assumed that the slope changes with constant
rate as observation times increase.
Exposure Concentration - Time - Response relationship is defined as:
Probitp = a + P(Concentration) + Y/Time + 8 (Concentration)/(Time)
NOEC at infinite time is:
1.281 -a
NOEC =
Note: Chronic times are necessary for Models 1 and 2; default chronic time is infinity for
Models 3 and 4, but additional chronic times may be added.
Estimating Sublethal Effects
Raw data for sublethal endpoints are seldom available under acute exposure conditions for modeling
chronic no-effect concentrations. Sublethal endpoints are also difficult to estimate from chronic lethality
data. Conservative chronic no-effect concentrations for sublethal endpoints may be estimated by
multiplying the predicted NOEC for lethality by 0.2 for growth and other sublethal endpoints and 0.1 for
reproductive endpoints. This is based on the analysis of differences among endpoints in chronic toxicity
tests (Table 1). However, it must be understood that these estimates of chronic sublethal effects are
extremely conservative; note that the median values (that value where 50% of the observations are above or
below it) are approximately 1.0 for growth and reproduction and only slightly below 1.0 for "other"
sublethal endpoints. In addition, the NOECs for lethality were exactly the same or less than those for
weight, length, reproduction, and "other" endpoints 59, 58, 56, and 41% of the time, respectively. Based
on the extreme variation of ratios, and the fact that no central tendency exists within the distribution of
ratios, the authors do not recommend using factors to estimate sublethal endpoints at this time. The
data (see table below) are based on hypothesis testing, and using regression analysis to estimate no-effect
concentrations for lethal and sublethal endpoints might provide an improved comparison and deserves
further investigation.
16
-------
-------
Univariate analyses for the ratios of growth, reproduction, or other sublethal endpoint
chronic no-effect concentrations (NOEC) to that for survival (sublethal NOEC/survival
NOEC)1.
Univariate
parameter
n
Mean
Median
Range
95% CL
+1SD
95th percentile
Median
5th Percentile
Growth
Weight
46
0.96
1.0
0.10-4.4
0.7-1.2
0.2-1.8
2.3
1.0
0.1
Length
62
0.90
1.0
0.16-2.3
0.8-1.1
0.3-1.5
2.2
1.0
0.2
Reproduction
18
1.13
1.0
0.12-4.5
0.6-1.7
0.1-2.2
4.5
1.0
0.1
Other2
22
0.76
0.6
0.06-2.0
0.5-1.0
0.2-1.3
2.0
0.6
0.2
'Data are from Mayer et al. (1986) and the USEPA Gulf Ecology Division (ORD/NHEERL), Gulf Breeze,
FL.
2Sublethal endpoints deemed detrimental to survival and/or ability to contribute to population success were
cataracts, disease susceptibility, severe fin erosion, severe organ pathology, and spinal curvature.
Additional Model Documentation
Details regarding each model and validation of those models using paired acute and chronic toxicity data
are published (Lee et al. 1992, Lee et al. 1995, Mayer 1990, Mayer 1991, Mayer et al. 1992a, Mayer et al.
1992b, Mayer et al. 1994, Mayer et al. 1999, Mayer et al. 2002, Sun et al. 1992, Sun et al. 1994, Sun et al.
1995a, Sunetal. 1995b).
ALT
The ALT procedure uses a Quasi-Newton method to find the maximum likelihood estimates of parameters.
Confidence limits for parameters are based on Normal approximations to distributions of the maximum
likelihood estimates. The parameter estimates given in Fig. 3 are used in the following model to obtain
predicted chronic no-effect concentrations for a particular percent effect and exposure time in days.
No-effect concentration = Exp[(ln(-ln(l-p))-ln(A) - C*ln(days*0.24))/B]
A, B, and C are parameter estimates and p is the percent effect, ranging from 0.01 to 10% (see ALT -
Accelerated Life Testing Model).
MPA
The MPA method uses all time and concentration data simultaneously to produce a multiple regression
probit equation to predict chronic no-effect values for specified times.
17
-------
-------
If the chi-square statistic is < the critical chi-square value, a variance-covariance matrix is produced and is
necessary to calculate confidence limits. If the chi-square statistic is not < the critical chi-square value, the
variance-covariance matrix is adjusted by a heterogeneity factor to produce an adjusted variance-
covariance matrix. The heterogeneity factor (HF) is given in the statistical output and is equal to the chi-
square statistic divided by the degrees of freedom (n - 1 of data used; Finney 1978).
The assumptions of independence may be violated with typical acute toxicity data using MPA. The
procedure is appropriate if observations at one time are not the same experimental units at another time.
Regardless of the issue of independence, MPA does provide acceptable acute and predicted no-effect
chronic concentrations when adequate partial responses are present in the acute data.
LRA
Calculations are based on a two-stage regression analysis. Stage 1 performs two types of analyses. The
first type is a simple linear regression at each observation time in which the X axis is log 10 concentration
and the Y axis is the probit transformation of proportion responding (dead). The second type is a probit
analysis at each observation time (Finney 1978). Following these two types of analyses, no-effect
concentration values are estimated at different percent response levels. The concentrations are transferred
to the stage 2 simple linear regression in which the X axis is the reciprocal of time (1/t) and the Y axis is
the concentration at each observation time for a specific percentage value. The equation is:
c = a + b/t where c = chronic no-effect concentration
a = Y intercept
b = regression coefficient
t = time
There are three possible transformations that are made in the stage 2 regression: 1) actual values of
concentration and time, 2) loglO of concentration and actual value of time, and 3) loglO of both
concentration and time. Thus, six analyses occur due to two types of analyses in stage 1 and three
transformations of data in stage 2. As time goes to infinity, the term b/t goes to zero; thus, the
concentration at infinite time is the intercept (a), or the chronic no-effect concentration for lethality.
Acknowledgement
This project was sponsored in part by the U.S. Environmental Protection Agency's Offices of Research and
Development, Pesticide Programs, Pollution Prevention and Toxics, and Water under Cooperative
Agreement CR82827901. Thanks to Vic Camargo for technical support on graphics, and to Debbie
Scholes, Mary Adkinson, and Bonnie George for manual preparation. Peer review and beta testing were
contributed by M. Anderson, L. Burns, J. Faircloth, T. Linton, R. Pepin, D. Rodier, G. Smith, and W.
Waller.
References
Buckler, D.R., A. Witt, Jr.., F.L. Mayer and J. N. Huckins. 1981. Acute and chronic effects of Kepone and
Mirex on the fathead minnow. Trans. Am. Fish. Soc. 110:270-280.
Buikema, A.L., Jr., B.R. Nederlehner and J. Cairns, Jr. 1982. Biological monitoring. 4. Toxicity testing.
Water Res. 16:239-262.
Compaq Fortran. 1999. Compaq Computer Corporation, Houston, TX.
18
-------
-------
Crane, M., M.C. Newman, P.P. Chapman and J. Fenlon. 2002. Risk assessment with time to event models.
Lewis Publ., Boca Raton, FL. 175 p.
Dixon, P.M. and M.C. Newman. 1991. Analyzing toxicity data using statistical models for time-to-death:
An introduction. Pages 207-242, in M.C. Newman and A.W. Mclntosh, eds. Metal Ecotoxicology:
Concepts and Applications. Lewis Publ., Chelsea, MI.
Finney, D.J. 1978. Statistical methods in biological assay. Griffin, London.
Kenaga, E.E.. 1979. Aquatic test organisms and methods useful for assessment of chronic toxicity of
chemicals. Pages 101-111, in K.L. Dickson, A.W. Maki and J. Cairns, Jr., eds. Analyzing the Hazard
Evaluation Process. American Fisheries Society, Washington, DC.
Kenaga, E.E. 1982. Predictability of chronic toxicity from acute toxicity of chemicals in fish and aquatic
invertebrates. Environ. Toxicol. Chem. 1:347-358.
Lee, G., M. Ellersieck and G. Krause. 1992. Multifactor Probit Analysis. Pages 29-61, in F.L. Mayer et
al. Statistical Approach to Predicting Chronic Toxicity of Chemicals to Fishes from Acute Toxicity Test
Data. National Technical Information Service PB92-169655. U.S. Department of Commerce, Springfield,
VA.
Lee, G., M.R. Ellersieck, F.L. Mayer and G. Krause. 1995. Predicting chronic lethality of chemicals to
fishes from acute toxicity data: Multifactor probit analysis. Environ. Toxicol. Chem. 14:345-349.
Lipnick, R.L. 1995. Structure-activity relationships. Pages 609-655, in G.M. Rand, ed. Fundamentals of
Aquatic Toxicology, 2nd Ed. Taylor & Francis, Washington, DC.
Mayer, F.L., K.S. Mayer and M.R. Ellersieck. 1986. Relationship of survival to other endpoints in chronic
toxicity tests with fish. Environ. Toxicol. Chem. 5:737-748.
Mayer, F.L. 1990. Predicting chronic lethality of chemicals to fishes from acute toxicity test data.
EPA/600/X-90/147. U.S. Environmental Protection Agency, Gulf Breeze, FL. 15 p.
Mayer, F.L. 1991. Predicting chronic lethality of chemicals to fishes from acute toxicity test data. Pages
56-62 in L.A. Burns, ed. PIRANHA, Pesticide and Industrial Chemical Risk Analysis, Version 2.0. U.S.
Environmental Protection Agency, Athens, GA. 134 p. + Appendices.
Mayer, F.L., G.F. Krause, M.R. Ellersieck, and G. Lee. 1992a. Project summary: Statistical approach to
predicting chronic toxicity of chemicals to fishes from acute toxicity test data. EPA/600/SR-92/091. U.S.
Environmental Protection Agency, Gulf Breeze, FL. 5p.
Mayer, F.L. G.F. Krause, M.R. Ellersieck and G. Lee. 1992b. Statistical approach to predicting chronic
toxicity of chemicals to fishes from acute toxicity test data. National Technical Information Service PB92-
169644. U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22161, 94p. + software.
Mayer, F.L., G.F. Krause, D.R. Buckler, M.R. Ellersieck and G. Lee. 1994. Predicting chronic lethality of
chemicals to fishes from acute toxicity data: Concepts and linear regression. Envirol. Toxicol. Chem.
13:671-678.
Mayer, F.L., K. Sun, G. Lee, M.R. Ellersieck, and G.F. Krause. 1999. User guide: Acute to chronic
estimation. EPA/600/R-98/152. U.S. Environmental Protection Agency, Washington, DC. 19 p. +
software.
Mayer, F.L., M.R. Ellersieck, G.F. Krause, K. Sun, G. Lee, and D.R. Buckler. 2002. Time-concentration-
effect models in predicting chronic toxicity from acute toxicity data. Pages 39-67, in M. Crane, M.C.
19
-------
-------
Newman, P.P. Chapman, and J. Fenlon, eds. Risk Assessment with Time to Event Models. Lewis Publ.,
Boca Raton, FL.
Microsoft Visual Basic 6.0(SP5). 1987-2000. Microsoft Corporation, United States.
Mount, D.I. and C.E. Stephan. 1967. A method for establishing acceptable limits for fish-malathion and
the butoxyethanol ester of 2,4-D. Trans. Am. Fish. Soc. 96:185-193.
Newman, M.C. 1994. Quantitative methods in aquatic ecotoxicology. Lewis Publ., Boca Raton, FL.
Newman, M.C. and M.S. Alpin. 1992. Enhancing toxicity data interpretation and prediction of ecological
risk with survival time modeling: An illustration using sodium chloride toxicity to mosquitofish. Aquat.
Toxicol. 23:85-96..
Shirazi, M.A. and L. Lowrie. 1988. Comparative toxicity based on similar asymptotic endpoints. Arch.
Environ. Contam. Toxicol. 17:273-280.
Sun, K., G.F. Krause and F. Wright. 1992. Prediction of chemical chronicity using the theory of
accelerated life testing: A review. EPA/600/X-92/136. U.S. Environmental Protection Agency, Gulf
Breeze, FL. 27 p.
Sun, K., G.F. Krause, F.L. Mayer, M.R. Ellersieck and A.P. Basu. 1994. Predicting chronic toxicity based
on the theory of accelerated life testing. EPA/600/R94-058. U.S. Environmental Protection Agency, Gulf
Breeze, FL. 33p.
Sun, K., G.F. Krause, F.L. Mayer, M.R. Ellersieck and A.P. Basu. 1995a. Estimation of acute toxicity by
fitting a dose-time-response surface. Risk Anal. 15:247-252.
Sun, K., G.F. Krause, F.L. Mayer, M.R. Ellersieck and A.P. Basu. 1995b. Predicting chronic lethality of
chemicals to fishes from acute toxicity data: Theory of accelerated life testing. Environ. Toxicol. Chem.
14:1745-1752.
Visual Numeric. 1999. Visual Numerics IMSL Fortran 90 MP Library, Version 4.01 for Microsoft
Windows. Visual Numerics, Inc., Houston, TX.
20
-------
-------
-------
SERA
United States
Environmental Protection
Agency
Please make all necessary changes on the below label,
detach or copy, and return to the address in the upper
left-hand corner.
If you do not wish to receive these reports CHECK HERE l~):
detach, or copy this cover, and return to the address in the
upper left-hand corner.
PRESORTED STANDARD
POSTAGE & FEES PAID
EPA
PERMIT No. G-35
Office of Research and Development
National Health and Environmental
Effects Research Laboratory
Gulf Breeze, FL 32561
Official Business
Penalty for Private Use
$300
EPA/600/R-03/107
December 2003
www.epa.gov
Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer fiber content
processed chlorine free
------- |