1. Nonparametric Inference on Tumor Incidence with Partially Identified Cause-of-Death Data

The use of survival-sacrifice experiments with animals, primarily rodents, has long been an indispensable tool for gauging the possible carcinogenic effect of a new drug or pharmaceutical agent. Because the tumor induced in the animal is generally impalpable and non-lethal, the precise time to its occurrence is unobservable. The only information that can be gleaned is its presence or absence when the animal dies from tumor-related or accidental causes. Provided that the cause of death is ascertained by a pathologist, Gomes (Braz J Probab Stat 15:135–145, 2001) provides a computationally efficient approach to nonparametric estimation of the cumulative distribution function for tumor onset time. In this article, we develop an EM-type algorithm to extend this approach to the situation where the cause of death is unknown on a subset of the animals. Such a scenario often occurs in practice as certain cases of death may elude the expertise of the pathologist. We also propose a class of logrank-type tests to compare different treatment groups on tumor incidence. Simulation studies show that, by properly accounting for missing data, the proposed methods outperform the naive approaches of complete-case analysis and simple imputations. Real data from a large-scale study on pituitary tumor in rats are analyzed as an illustration.