Explicit solutions for constrained maximum likelihood estimators in survival/sacrifice experiments

Abstract

SUMMARY Regulatory agencies routinely base conclusions regarding carcinogenicity of compounds tested in long-term animal studies on tests which are known to be biased under conditions of treatment lethality and tumour lethality. The recognition of these biases has led to a variety of proposed approaches which rely on survival and sacrifice data. Williams & Portier (1992) derived analytic expressions for maximum likelihood estimators of the tumour incidence rate and discrete death rates based on a discrete multistate model. A disadvantage of the proposed estimators was that they sometimes resulted in negative estimates of the tumour incidence rate. In this paper, explicit solutions for constrained estimators are derived under the imposition of boundary conditions for a study design with one or two interim sacrifices and a terminal sacrifice. For study designs with more than two interim sacrifices, alternative estimators of the tumour incidence rate and discrete death rates are developed heuristically by pooling data together from adjacent