Dose‐response models for time‐to‐response toxicity data

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Abstract
This paper concerns the modelling and analysis of toxicity data in which the time to some toxic response is recorded and of importance. The paper begins with a review of a variety of dose‐response models, including log‐linear, proportional hazards, multievent, and compartmental models, that have been suggested and used in this context. Models for competing risks are also reviewed and several possible approaches are considered and discussed in the context of dose response experiments. The formulation of a model for competing risks that utilizes cause‐specific hazards gives a natural basis for the modelling and analysis of certain experimental situations in which only partial information is available on the time to response. Such situations arise, for example, when the presence of tumour is not clinically detectable in carcinogenicity trials. Likelihood construction is discussed, and appropriate likelihood contributions are derived. The paper concludes with a discussion of measures of risk which take account of the time dependence of the toxic response under study.