Survival models and health sequences

Medical investigations focusing on patient survival often generate not only a failure time for each patient but also a sequence of measurements on patient health at annual or semi-annual check-ups while the patient remains alive. Such a sequence of random length accompanied by a survival time is called a survival process. Ordinarily robust health is associated with longer survival, so the two parts of a survival process cannot be assumed independent. This paper is concerned with a general technique---time reversal---for constructing statistical models for survival processes. A revival model is a regression model in the sense that it incorporates covariate and treatment effects into both the distribution of survival times and the joint distribution of health outcomes. It also allows individual health outcomes to be used clinically for predicting the subsequent survival time.