Analytic expressions for maximum likelihood estimators in a nonparametric model of tumor incidence and death

Abstract

This research focuses on the estimation of tumor incidence rates from long-term animal studies which incorporate interim sacrifices. A nonparametric stochastic model is described with transition rates between states corresponding to the tumor incidence rate, the overall death rate, and the death rate for tumor-free animals. Exact analytic solutions for the maximum likelihood estimators of the hazard rates are presented, and their application to data from a long-term animal study is illustrated by an example. Unlike many common methods for estimation and comparison of tumor incidence rates among treatment groups, the estimators derived in this paper require no assumptions regarding tumor lethality or treatment lethality. The small sample operating characteristics of these estimators are evaluated using Monte Carlo simulation studies.