US EPA

The multistage Weibull (MSW) time-to-tumor model and related documentation were developed principally (but not exclusively) for conducting time-to-tumor analyses to support risk assessments under the IRIS program. These programs and related documentation are made available publicly to insure that the methods and calculations used for such analyses are transparent and reproducible.

The multistage Weibull (MSW) time-to-tumor model describes the probability P(d,t) of a test subject exhibiting a specific carcinogenic response by observation time t when the subject is exposed to a carcinogen at dose d. As used here, "tumor" refers loosely to a cancer or a relevant precancerous lesion (e.g., an adenoma that can progress to a carcinoma). One specific cancer type (along with associated precancerous lesions) is modeled using the MSW model, specific to a particular tissue or organ in one sex and strain of animal (e.g., hepatocellular carcinomas and adenomas in female B6C3F1 mice). This model is usually applied to bioassay experiment data. Note that the model is usually called a “time-to-tumor” model but really models the time to an operationally defined event, herein a tumor-related response. Thus, users may find this program useful for modeling time to response with other toxicology data, if individual animal data are available and if the time to the censoring event (death or sacrifice) is not associated with the time to response (i.e., if censoring is uninformative).

Here we consider two forms of tumor-related response:

• Death of the subject, with death resulting from a cancer (“death from cancer”)
• Appearance of a carcinogenic lesion that is detectable by pathologic methods, generally upon examination following death. Time of appearance is primarily of interest when the tumor is considered non-fatal. “Appearance” is used as shorthand here for the time at which a carcinogenic lesion is first detectable by the methods used in the study providing the data, and should not be equated with onset of the carcinogenic process.

The MSW software module allows fitting two distinct multistage Weibull models corresponding to these two types of responses.

The “MSW” program described in this manual was developed by Battelle Memorial Institute1 for the U.S. Environmental Protection Agency2 (“EPA”) during 2006-2009 (under EPA contract EP-C-04-027). Minor changes may have been made by EPA subsequently (as noted in source code comments). The MSW program and associated documentation are available at EPA’s BMDS web site.3 MSW was compiled using the GNU GCC compiler provided with MinGW5.0.

Graphical goodness-of-fit for MSW: EPA is developing graphical programs in R that can be used to evaluate goodness-of-fit for models fitted using MSW.

U.S. EPA. MSW Time to Tumor Model and Supporting Documentation. U.S. Environmental Protection Agency, Washington, DC, 2009.