Modeling time-to-tumor data: analysis of the ED01 study.

The ED01 study is an experiment conducted by the National Center for Toxicological Research (NCTR) of the FDA in which over 24,000 mice were exposed to the known carcinogen 2-acetylaminofluorene. The details of the experiment and analysis of the results by NCTR are documented in Staffa and Mehlman (1979). The analysis by the ED01 task force of the Society of Toxicology is in disagreement with NCTR on several issues, and is reported in Fundam. Appl. Toxicol. 1:26-128. The results given in this paper are from a separate analysis aimed at adequately and parsimoniously representing the functional relationship of dose and time to the carcinogenic response. A very general non-parametric approach is applied to the data on sacrificed animals, which eliminates any complications due to a change in protocol and avoids the difficulties in combining sacrifice and non-sacrifice data. It is shown that for either liver neoplasms or bladder neoplasms as the toxicological endpoint, any model which has a factorable hazard function (one that can be factored into the product of a function of dose exclusively and a function of time exclusively) is too simplistic to accurately describe the response over the entire experimental range of dose and time. The lack of fit of the liver neoplasm data to a time-dose product model is due to data at the highest time (month 33). If these data are excluded then a factorable hazard function fits the data well, with the function of dose following a J-shaped curve and the function of time being either a simple power of time or a polynomial in time. For a power of time, the resultant probability distribution is Weibull over time with dose affecting the scale parameter, and this result is consistent with the empirical equation of Druckrey (1967). Both of the functional forms described fit the data significantly better than the previously suggested Hartley-Sielken model which utilized polynomials in both dose and time. The lack of fit of bladder neoplasms to a model with a factorable hazard function is not due to just the data at month 33 or the data at months 24 and 33 combined. Unfortunately, from the viewpoint of model fitting, the response of bladder neoplasms is fairly insensitive to changes in time and dose, except at the high extremes. This leaves only a small number of observations which are actually very useful in model validation and comparison, which means that one could only hope to discriminate between gross differences of fit.(ABSTRACT TRUNCATED AT 400 WORDS)