SEfW
EPA/600/B-23/044
July 2023
Producing Plots to Assess
Goodness-of-Fit for the
Multistage Weibull (MSW)
Time-To-Tumor Model
\gofplot_mswQ]
USER MANUAL
Chemical & Pollutant Assessment Division
Center for Public Health and Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency

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Table of Contents
1.0 Introduction	3
1.1	Acknowledgements	3
1.2	Disclaimer	3
2.0 Installing and Using the gofp/ot_msw() Plotting Functions	4
2.1	Installing gofplot_msw()	4
2.2	Using gofplot_msw()	4
3.0 Types of Plots Incorporated in MSW Module	6
3 1 Probability vs. Time Plot (type="pr")	6
3.2	Dose-Response Plot (type="dr")	6
3.3	Hazard Plot (type="hz")	6
3.4	Quantile-Quantile Plot (type="qq")	7
3.5	Probability-Probability Plot (type="pp")	7
4.0 Generating the Plots	8
4.1	Usage	8
4.2	Arguments	8
4.3	Example Data Sets	9
5.0 Probability Models Used by gofp/ot_msw()	10
5.1	Fatal Risk	10
5.2	Incidental Risk	10
6.0 Goodness-of-Fit and Diagnostic Plots	12
7.0 References	14
8.0 Example Plots	15
Table of Figures
Figure 1: Generating probability vs. time (type="pr") plots for the Non-Fatal tumor model	15
Figure 2: Generating probability vs. time (type="pr") plots for the Non-Fatal and Fatal tumor models	16
Figure 3: Generating a Dose-Response (type="dr") plot for the Non-Fatal tumor model	17
Figure 4: Generating a cumulative hazard (type="hz") plot for the Non-Fatal tumor model	18
Figure 5: Generating a cumulative hazard (type="hz") plot for the Fatal tumor model	19
Figure 6: Generating a quantile-quantile (type="qq") plot for the Non-Fatal tumor model	20
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1.0 Introduction
This user manual describes installation and use of plotting functions developed for use
with output files produced by the "MSW" (multistage Weibull) program for time-to-tumor
(time-to- event) analysis. These functions are described in aggregate as "gofplot_msw()",
the name of the main function, the only one invoked by the user.
The functions were developed in the R language (R Core Team 2012). These R
functions are intended for comparing the fitted, parametric MSW model to an empirical,
nonparametric time-to-event model that is fitted to the same data. Comparisons between
the parametric and nonparametric models provide a subjective assessment for
goodness-of-fit of the multistage Weibull model to the data. This document describes the
use and interpretation of various types of plots which gofplot_msw() can generate.
A separate user manual describes the MSW program. Users of gofplot_msw() must be
familiar with the MSW user manual in order to understand, interpret, and report results
from MSW and gofplot_msw(). A user also should be familiar with the basics of R.
Users of these programs are expected to be familiar with basic methods of survival
analysis including graphical diagnostic methods (Collett 1994; Klein and Moeschberger
2003; Lawless 2003) and with the R package 'survival'.
1.1 Acknowledgements
The R programs in gofplot_msw (and the MSW programs in C) were originally developed
by Battelle Memorial Institute for the U.S.E.P.A. during 2006-2009 (contract EP-C-04-
027). EPA staff subsequently modified the plotting programs in R and wrote new
modules for dose- response plotting and hazard plotting.
The MSW program uses the C version (donlp2-intv) of the optimizer donlp2, copyright
dated June 21, 2004 by Peter Spellucci. A condition of use specified by the author is:
"The use of donlp2 must be acknowledged, in any publication which contains results
obtained with it or parts of it. Citation of the author's name and netlib-source is suitable."
Note that this may apply to plotting the results from MSW by using gofplot_msw.
1.2 Disclaimer
The views expressed in this manual are those of the author(s) and do not necessarily
represent the views or the policies of the U.S. Environmental Protection Agency.
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2.0	Installing and Using the gofplot_msw() Plotting
Functions
2.1	Installing gofplot_msw()
The following instruction assumes very little experience with R. An experienced user may
also want to review this section before setting up gofplot_msw. User is assumed to have
installed MSW (msw.exe) and know how to use it.
To install the R plotting functions in gofplot_msw.
1.	Ensure that R is installed on the user's computer, and note the folder in which it is
installed. R is available for download free-of-charge from the websites http://www.r-
proiect.org or at http://cran.r-proiect.org/.
2.	Create a Windows folder (subdirectory). Download and unzip(extract) contents of the
zip file gofplot_msw.zip into this folder.
For this example, we will assume that gofplot_msw is installed in folder "C:\
gofplot_msw\". Make sure there is a copy of msw.exe in the same folder for
convenience.
3.	Make a Windows shortcut to R, place it in the folder, and install the R plotting
function.
4.	Right click on the R icon and click on "Create Shortcut". Move the shortcut to "C:\
gofplot_msw\". Double click to test the shortcut. An R console window should open.
5.	Entering the R command > getwdQ, the response should be:
[1] "C:/gofplot_msw"
6.	If the response is different, change the work directory by typing
>	setwd ("C:/gofplot_msw/")
Note: The forward slash is an R convention.
7.	Install the R functions by entering the command
>	source("gofplot_msw.R")
8.	Typing > ls() will display the names of the R functions.
2.2	Using gofplot_msw()
This section describes a step-by-step procedure for using gofplot_msw().
1.	Create a folder for new data (e.g., "C:\timetotumor_1 \").
2.	For this demonstration, copy the data files (with file extensions '.(d)') and output files
(with file extensions '.out') from the folder where gofplot_msw is installed to this new
folder.
3.	Return to the folder "C:\gofplot_msw\" and open an R console.
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4.	Change the working directory by typing the command
>	setwd ("C:/timetotumor_l")
Note the forward slash!
5.	We will use the files EX1_C+F+l_Grouped_lrisk.(d) and
EX1_C+F+l_Grouped_lrisk.out.
6.	Type the command
>	gofplot_msw(dname="EXl_C+F+I_Grouped_Irisk.(d)", oname =
"EXl_C+F+I_Grouped_Irisk.out", type = "pr")
This should produce a plot in the R window. Right-clicking in the plot will list options
for saving the plot or printing it. To save it as a PDF or PNG file in R, read the R
documentation by typing
>	?pdf
or
>	?png
Details about plotting options and command arguments are described in Section 4.0 on
page 8.
Here is an example of commands for writing the figure to a png file:
>	png (filename="plotl.png"j width=7, height=7, units="in", res=200)
Be sure to use file extension . png in the file name.
>	gofplot_msw(dname="EXl_C+F+I_Grouped_Irisk.(d)", oname =
"EXl_C+F+I_Grouped_Irisk.out", type = "pr")
>	dev. of f () # closes the png 'device' & writes the new file
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3.0 Types of Plots Incorporated in MSW Module
The general objective of the MSW plotting tool is to assess the goodness-of-fit of the
(parametric) MSW model by comparing it to a nonparametric model fitted to the same
data. The nonparametric model imposes only the most necessary restrictions (esp.
monotonicity) on the relationship between time, dose, and probability of tumor onset or
death, with no assumption made on the specific distributional form of the data. By
minimizing the restrictions on the structure of the model, the empirical nonparametric
model fits the data as "closely" as possible.
The MSW plotting tool includes several plot types found useful for evaluating goodness-
of-fit of survival functions (Collett 1994, 2003; Klein and Moeschberger2003). It allows
the user to plot the following types of graphs, by specifying the type-"' argument in
gofplot_msw()\
3.1 Probability vs. Time Plot (type="pr")
In this plot (Figures 1 and 2), which is the default plot for gofplot_msw(), the fitted
distribution function is plotted against time, separately for each dose level specified in the
input (*.d) file. The MSW model is plotted as a smooth curve and the nonparametric
model is displayed as a series of points (representing a right-continuous step function). If
both Fatal and Incidental contexts occur in the data, two smooth curves and two series
of points are plotted, a solid curve and filled points for the Fatal tumor response, and a
dashed line and unfilled points for the Incidental tumor response.
3.2 Dose-Response Plot (type="dr")
This plot (Figure 3) shows response probability in relation to dose for a fixed time (usually
104 weeks for rodent bioassays) and also shows the BMD and BMDL values from the
output file. In fitting the MSW model, the user will have specified either the Fatal or
Incidental risk response at a specific time as a basis for calculating the benchmark dose
(BMD). The predicted probability values from the distribution functions of both the MSW
and nonparametric models for the specified risk response at the specified time are
plotted against the range of dose values occurring within the data. The parametric MSW
model is plotted as a smooth curve across the range of doses. The nonparametric
probability estimates are plotted as points at the distinct dose values that occur within
the data. The BMD and its lower confidence limit are also plotted and their values are
printed in the plot legend.
3.3 Hazard Plot (type="hz")
This option (Figures 4 and 5) plots the log (base e) of the cumulative hazard function
against event time for the parametric (MSW) model and for a nonparametric estimate.
The log cumulative hazard plot is linear for a Weibull hazard function; thus, the
parametric estimate is necessarily linear. If the nonparametric estimate is not
approximately linear, the MSW model may not be suitable. A plot is also produced
showing the nonparametric estimates for the dose groups in a single figure.
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3.4 Quantile-Quantile Plot (type="qq")
Using the fitted nonparametric model, predicted probability values from the distribution
function are calculated at distinct observation times that represent quantiles of the
predicted probabilities based on this model (Figure 6). Subsequently, the quantiles (in
time units) for those predicted probabilities are calculated using the fitted MSW model,
using the inverse of the estimated density function. The quantiles from the MSW model
are then plotted against quantiles from the nonparametric model, with each plot point
representing the quantiles at the given (predicted) probabilities. The graph also includes
a straight line with unit gradient slope through the origin. The goodness-of-fit for the
MSW model can be assessed by how well the plotted values follow this straight line.
Quantile plots are generated for each dose level specified in the input (*.d) file.
3.5 Probability-Probability Plot (type="pp")
The predicted probability values from the distribution functions of both the MSW and
nonparametric models are calculated for distinct observation time values that occur within
the data. The probabilities from the MSW model are then plotted against the probabilities
from the nonparametric model, with each plot point representing the two probabilities at a
given observation time. The graph also includes a straight line with unit gradient (i.e.,
1:1) slope through the origin. The goodness-of-fit for the MSW model can be assessed by
how well the plotted values follow this straight line. Probability plots are generated for
each dose level specified in the input (*.d) file (this plot is not illustrated).
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4.0 Generating the Plots
The R function gofplot_msw() serves as the primary user interface to the MSW plotting
routines. The gofplot_msw() function is called by specifying gofplot_msw on the R
command line, followed by specifying the following five parameters (function arguments)
in parentheses. It is recommended that the value of each parameter be specified by
name (e.g.,' type="dr"') and in the order given below. The user must have first executed
the MSW program and generated the output file before calling the plotting functions.
Figures 1-6 show how to call the function gofplot_msw to generate certain types of plots,
and how the plots appear upon executing these function calls.
4.1 Usage
gofplot_msw(dname="Filename.(d)", oname="Filename.out", type="dr",
title = NULL, digit = 4, mult = TRUE, Prange01="TRUE")
4.2 Arguments
dname
This required parameter specifies the name of the file containing the time-to-tumor
data used by the MSW.exe module to fit the MSW model. The filename 'dname' may
be written with or without the extension '.(d)'. If the files is not in the R working
directory, one may use the full path, e.g., C: \\mydata\\fname. (d). Wndows path
references should work, e.g., for data in a subdirectory data of the working directory,
use gofplot_msw(".\\data\\ fm_alvbr_lstage_auto").
Recall that in R, one must use either the double backslash or a single forward slash
in a pathname, but never the single backslash that is used by Windows. If the
filename plus extension exceeds 4 characters, the data file need not have extension
'.(d)' - whatever path and filename were typed will be used. However, we
recommend using the standard MSW file extension '.(d)'.
oname
This optional parameter specifies the name of the output file (*.out) generated by the
MSW module - this contains information on the MSW model fitted to the data
specified by dname. The parameter must be specified when the file names of dname
and oname differ (not a good practice!). If oname is not given, the output file (*.out)
must reside in the same directory as dname; the path and filename specified for
dname will be used, with file extension '.out' rather than '.(d)'.
type
This optional parameter specifies the type of plots to be generated for each dose
level. If no value is specified by the user, the parameter value defaults to "pr".
Possible values are:
•	"pr" -plots the parametric (MSW) and nonparametric probability functions
•	"dr" - generates a dose-response plot
•	"hz" - generates a cumulative hazard plot
•	"qq' - to generate Quantile-Quantile plots
•	"pp" - to generate Probability-Probability plots.
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title
This optional parameter is used to specify a title for figures where multiple plots
appear on one page (when parameter Mult=TRUE). The title will appear at the top of
the figure and thus will apply to all the plots on the page.
digit
This optional parameter is used to specify the number of significant digits used to
display Dose values in the plots. If no value is specified by the user, the default is 4
significant digits.
mult
This optional parameter equals TRUE if multiple plots are to be placed on a single
page (the default), and FALSE if a page is to hold a single plot. If this parameter
equals TRUE, then up to four plots (2x2) will be displayed on a single page.
save. Plot
Setting this argument to "TRUE" will cause a plot to be exported to the file type
specified by argument save.Plot.type. To see the valid types, type ?savePlot or
help(savePlot) in the R console. The types best suited for importing graphics into
your documents are likely to be "pdf, "png" "tiff' and "jpeg".
haz.npar.type
Specifies the type of nonparametric estimate to use in the hazard plot (type="hz").
Valid choices are "fh" (the default), "iso", and "km". These correspond to Fleming-
Harrington, isotonic regression, and Kaplan_Meier (Product-Limit) estimates.
PrangeOI
Logical argument. If TRUE, set range of probabilities in plot axis to [0,1], Default is
FALSE (use observed range of probabilities to determine plot axis range using style
"r" as in par(yaxs="r")).
A plot can also be copied from the R console by right-clicking inside the plot and
selecting from the pop-up menu, then pasting the graphic into an open document.
Function gofplot_msw invisibly returns a list containing the fitted models, named
par_resultl, par_resultF, npar_fh, nparjso, and npar_km. These represent the MSW
models ("par") and the nonparametric models ("npar") for Incidental (I) and Fatal (F) risk.
The parametric fits contain risk probabilities at equally spaced times ranging from the
lowest to highest observed times. The nonparametric fits contain risk probabilities at the
observed times. The object npar_fh is null unless a hazard plot was requested
(type="hz").
4.3 Example Data Sets
A number of example MSW input and output data sets are provided with the
gofplot_msw() download package. These serve to illustrate different types of data and
risk responses, and will assist users in becoming familiar with use of gofplot_msw and
with MSW and time-to-tumor data.
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5.0 Probability Models Used by gofplot_msw()
Animal observations from a carcinogenicity bioassay may be classified (see the user
manual for program MSW) as: Fatal (F), meaning that the animal death is attributed to
the tumor; Incidental (I), meaning that the animal died from another cause (including a
planned sacrifice) and the tumor was found to be present during necropsy; right
Censored (C), meaning that no tumor (of the sort under consideration) was present, and
Unknown (U), meaning that the animal was not necropsied (usually these are uncommon
and occur because of decomposition or cannibalism).
5.1 Fatal Risk
Multistage Weibull parametric model (plotted as a smooth curve):
object "par_resultF"
The distribution function for Fatal Risk is:
F(t.d) = F(tJj0,c	= 1-exp \-(j
I <=o J
where the maximum likelihood estimates from MSW are substituted for the model
parameters.
Nonparametric model (plotted as points representing a step function):
object "npar_km"
The censoring indicator for Fatal Risk is 1 for "F" observations and is 0 if death from
tumor has not occurred (context or class C, I, and U). Data are thus right-censored. The
nonparametric maximum likelihood estimator in this case is the Kaplan-Meier (Product-
Limit) estimator. The R function survfitQ is used to compute the KM estimate of the
survival function S(t) for death from tumor. The plotted function is 1 - S(t) = F(t).
5.2 Incidental Risk
Multistage Weibull parametric model (plotted as a smooth curve):
object "par_resultl"
The distribution function for Incidental Risk (non-fatal tumors) is:
f k	1
i, f=o j
where the maximum likelihood estimates from MSW are substituted for the model
parameters.
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Nonparametric model (plotted as points representing a step function):
object "nparjso"
The censoring indicators for Incidental Risk is 1 for'T' and "F" observations (i.e., if
growth of a tumor has already begun) and is 0 if a tumor has not yet occurred (context
"C"). These observations represent current-status data (e.g., Lawless 2003): if X® is the
time when a tumor just becomes detectable and T® is the observation time, either X® <
T(i> orX(i) > T(i> (the subscript indicates that the data are sorted in ascending order of the
T(i>, i = 1, 2, ..., n). The nonparametric maximum likelihood estimator (NPMLE) for such
data is the isotonic regression for the cumulative sum of indicators on the index I
(Groeneboom and Wellner 1992). This estimator is equivalent to that of Ayer et al.
(1955). The R function isoregQ is used for computing the NPMLE of the distribution
function (F(t) = 1 - S(t)) for the appearance of detectable tumors. The NPMLE based on
isoregQ is used for all plot types except the cumulative hazard plot, for which the
nonparametric estimate is based on Turnbull's EM approach.1
1 See comments in function 'hazardplot_msw()'. Also see documentation for package survival, functions SurvQ
and survfitQ, R Core Team 2012. The two nonparametric estimates appeared similar or indistinguishable for all
data sets so far tested.
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6.0 Goodness-of-Fit and Diagnostic Plots
The MSW software does not report a chi-square goodness-of-fit table. Methods similar to
the chi-square goodness-of-fit test that is applied to BMDS quantal models do not apply
to the MSW model with censored data. Development of a suitable goodness-of-fit test,
especially for heavily censored and current-status data, is difficult.2
Recent work3 explores new approaches for goodness-of-fit and confidence intervals on
the nonparametric survivor function for current-status and interval-censored data, but we
have not attempted implementation.
This leaves us with graphical comparison of the MSW parametric model and the
nonparametric model forjudging goodness-of-fit.4 This software provides several types of
diagnostic plots as described above. More detailed advice on use of these plots may be
found in textbooks on survival analysis (Anderson et al. 1993; Collett 1994, 2003; Klein
and Moeschberger2003; Lawless 2003).
Carcinogenicity data are heavily censored and events (Incidental and Fatal observations)
may be sparse in some dose groups. This limits ability to evaluate model fit and
distinguish between alternative models. The best one should expect from these plots,
applied to such data, is to occasionally identify cases of poor fit that do not strongly
support reliance on the BMD/BMDL inference.
The cumulative probability plot (type="pr") and dose-response plot (type="dr") will show
how well the model agrees with the data. Also, agreement of the model with data is
indicated by a linear pattern for hazard (type="hz"), probability-probability (type="pp") and
quantile-quantile (type="qq") plots.
We have found it useful to check the cumulative probability plot (type="pr"), dose-
response (type="dr"), and hazard (type="hz") plots. The 'qq' and 'pp' plots have specific
uses when considering models other than Weibull, for example loglogistic, and evaluating
an accelerated failure time model (ibid.). The hazard plot may indicate when an
alternative to the Weibull model needs to be considered.
When the multistage Weibull model is used to infer a benchmark dose (BMD), one should
be concerned about the goodness-of-fit at the corresponding time and dose level. Usually
the BMD is estimated for a nominal rodent lifetime, say 104 weeks (2 years). Often the
BMD falls near or below the lowest dose. In such a case, we desire a good fit at longer
times and lower doses. That does not imply that the fit at earlier times or higher doses
should be ignored.
The hazard plot (type="hz") is helpful in evaluating reasonableness of the multistage
Weibull model and alternative models (ibid.). The hazard plot option (type="hz") will
produce plots of the parametric (MSW) and nonparametric estimates separately for each
dose group (Figure 4), and a final plot showing the nonparametric estimates for all dose
groups in one figure. The log cumulative hazard for the nonparametric estimate will be
linear with time if the data agree with a Weibull model (for the estimated parametric
model, it is necessarily linear), with a slope determined by the Weibull shape parameter.
Increasing log cumulative hazard plots, parallel (with the same slope) and with different
intercepts for different dose groups, are consistent with the Weibull model. If the slope of
2	In principle, it should be possible to implement a bootstrap goodness-of-fit test (Lawless 2003, ibid.).
3	See References Section: Ren 2003, 2008; Banerjee & Wellner 2005; Koul & Yi 2006; Sun et al. 2007; Koul
& Aggarwal 2008; Maathuis & Hudgens 2011.
4	In fact, Klein and Moeschberger (2003, Ch. 12.5) favor graphical examination over formal significance tests,
and demonstrate how graphical diagnostics can inform alternative modeling choices and yield other insights.
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the nonparametric hazard function increases or decreases systematically with dose, a
different model may be appropriate or competing risks may need to be considered.
Even when interest lies in the Incidental risk, it can be useful to examine the cumulative
hazard for the Fatal risk function, which is identical to the Incidental risk function shifted to
the right by t0. There are more points of support for the nonparametric estimate and so it
is easier to judge agreement with the parametric estimate. One way to generate this plot
is to run MSWto estimate the Fatal Risk model (Figure 5), and to use those data and
output files as arguments to gofplot_msw(). Note that the cumulative hazard function for
Fatal risk is curved, not linear, in the plot (Figure 5). Alternatively, one can generate the
same plot using the MSWdata and output files for Incidental risk by using a special
argument to gofplot_msw(). This avoids re-running MSWjust to obtain the fatal risk
model. If the argument haz.npar.type is set to haz.npar.type="km" the hazard plot
appropriate for Fatal risk is printed, albeit with a subtitle "Incidental Risk" - read from the
output file - so it would be best to use the title argument of gofplot_msw() to remind you
that the Fatal risk function is plotted. Two cautions: (1) normally a user should not
specify the argument haz.npar.type. (2) the BMD and BMDL in the output file for the
Incidental risk model are still appropriate for Incidental risk, not Fatal risk, as is the dose-
response plot (type="dr
One final caution: When occurrence of tumor contexts (I, F, and C) is highly confounded
with dosage (d) or observation time (/), estimates can be unreliable6. Model diagnostic
plots, parameter confidence limits, and the table of response categories by dose groups
in the output file can help to identify such cases.
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7.0 References
Anderson,P.K., 0.Borgan, R.D.Gill and N.Keiding. 1993. Statistical Models Based on
Counting Processes, New York:Springer.
Ayer, M., H.D. Brunk, G.M. Ewing, W.T. Reid and E. Silverman. 1955. An empirical
distribution function for sampling with incomplete information. Annals of Mathematical
Statistics 26: 641-647.
Banerjee, M. and J.A. Wellner. 2005. Confidence intervals for current status data,
Scandinavian J. Stat. 32: 405-424
Collett,D. 1994. Modelling Survival Data in Medical Research. Chapman & Hall, (and 2nd
ed. 2003)
Groeneboom, P. and J.A. Wellner. 1992. Information Bounds and Nonparametric
Maximum Likelihood Estimation. Basel: Birkhauser.
Klein, J.P., and M.L. Moeschberger. 2003. Survival Analysis. 2nd ed. Springer.
Koul, K.L. and T. Yi. 2006. Goodness-of-fit testing in interval censoring case 1, Statistics
& Probability Letters 76: 709-718
Koul, K.L. and D. Aggarwal. 2008. Minimum empirical distance goodness-of-fit tests for
current status data, J. Indian Statistical Association 46: 79-125
Lawless, J.F. 2003. Statistical Models and Methods for Lifetime Data. 2nd ed. Hoboken:
Wiley- Interscience.
Maathuis, M. and Hudgens, M. 2011. Nonparametric inference for competing risks
current status data with continuous, discrete or grouped observation times, Biometrika
98:325-340
R Core Team. 2012. R: A Language and Environment for Statistical
Ren, J.-J. 2003. "Goodness of fit tests with interval censored data. Scandinavian Journal
of Statistics 30: 211-226
Ren, J-J. 2008. Smoothed weighted empirical likelihood ratio confidence intervals for
quantiles, Bernoulli 14: 725-748
Sun, J., L. Sun and C. Zhu. 2007. Testing the proportional odds model for interval-
censored data, Lifetime Data Analysis 13: 37-50
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8.0 Example Plots
Figure 1: Generating probability vs. time (type="pr") plots for the Non-Fatal tumor model
gofplot_msw("NTP273rat.Marshall.M.testis.appl.dose.TTT.Is")
Incidental Risk: NTP273rat.Marshall.M.testis.appl.dose.TTT.1s
Dose= 0.00	Dose= 357.00
Time	Time
Dose = 714.00
0 20 40 60 80 100
Time
Legend: The solid line represents probabilities as determined from the fitted MSW model, and
the filled points represent probabilities as determined from the nonparametric model.
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Figure 2: Generating probability vs. time (type="pr") plots for the Non-Fatal and Fatal tumor
models
gofplot_rnsw("EXAMPLE 1_Irisk", type="pr")
Incidental Risk: EXAMPLE1 Jrisk.
Points show nonparam. est. for Incidental (unfilled) and Fatal (filled).
Dose = 0.00	Dose = 350.00
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0 20 40 60 80 100
Time
Legend: The solid line represents probabilities as determined from the fitted MSW model for fatal
tumor risk, and the filled points represent probabilities as determined from the nonparametric
model. The dashed line represents probabilities as determined from the fitted MSW model for
incidental tumor risk, and the unfilled symbols represent probabilities as determined from the
corresponding nonparametric model. The title "Incidental Risk" refers to the user-specified risk
reported in the output file " EXAMPLE1 Jrisk.out", for which a BMD and BMDL were calculated
(these are not shown in this type of plot).
Page 16 of 20

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gofplot_msw() User Manual
	July 2023
Figure 3: Generating a Dose-Response (type="dr") plot for the Non-Fatal tumor model
gofplot_msw(fffm_alvbr_lstage_auto", type="dr")
BMD for Incidental Risk atT = 104, Extra Risk level = 0.1, conf. level = 0.9 points
show nonparametric estimate for nearest times at obsvd. doses
fm_alvbr_1 stage_auto
MSW Model for Incidental Risk
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Dose
Legend: The solid line represents the fitted MSW model, and the filled points represent
probabilities as determined from the nonparametric model. The latter must fall on observed times;
the high dose group has no nonparametric estimate at 104 weeks, so the probability estimate at
the time nearest 104 weeks (91 weeks) is plotted.
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gofplot_msw() User Manual
	July 2023
Figure 4: Generating a cumulative hazard (type="hz") plot for the Non-Fatal tumor model
gofplot_msw("siml.aug08.2s", type="hz")
Incidental Risk: sim1 ,aug08.2s.
Parametric (line) and nonparametric (th: points) estimates
Dose = 0
Dose = 0.2
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Log Event Time
Legend: The solid line represents the MSW model (for which the log cumulative hazard is
necessarily iinear). The unfilled points represent log cumulative hazard values determined from
the nonparametric model.
Page 18 of 20

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gofplot_msw() User Manual
	July 2023
Figure 5: Generating a cumulative hazard (type="hz") plot for the Fatal tumor model
gofplot_msw('r'TCP_Fmouse_ASCT_grp_rnd_FI_2s", type="hz")
Fatal Risk: TCP_Fmouse_ASCT_grp_rnd_FI_2s
Parametric (line) and nonparametric (km: points)
estimates parametric shifted by t0 (dashed line).
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npar: insufficient data
MSW: insufficient data
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Log Event Time	Log Event Time
Legend: Cumulative hazard plot for Fatal Risk. There were many more Fatal (F) observations and
the estimate of t0 was 27 weeks. Because t0 >0, the MSW model for Fatal Risk was plotted at t+t0
as a dashed line, which is non-linear in this log plot. The solid line represents the MSW model
without the time shift. On the log-log scale, the MSW model for fatal risk is not linear and it is not
parallel to the model for Incidental Risk (solid line), which is necessarily linear in a (Weibull)
cumulative hazard plot. The unfilled points represent log cumulative hazard values determined
from the nonparametric Kaplan-Meier (Product-Limit) estimates. There is reasonably good
agreement with the nonparametric estimates.
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gofplot_msw() User Manual
	July 2023
Figure 6: Generating a quantile-quantile (type="qq") plot for the Non-Fatal tumor model
gofplot_msw(';rEXAMPLEl_Irisk"J type="qq")
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Incidental Risk: EXAMPLE"! Jrisk.
Dose = 0.00
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Time (Nonparametric)
Time (Nonparametric)
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Dose = 700.00
20 40
Time (Nonparametric)
Legend: The solid line represents an ideal 1:1 relation between parametric and nonparametric
quantiles. The filled symbols represent the nonparametric estimates and the corresponding
parametric estimates. The title "Incidental Risk" refers to the user-specified risk reported in the
output file " EXAMPLE1 Jrisk.out."
Page 20 of 20

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