Stochastic Survival Models with Competing Risks and Covariates

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Abstract
In survival analysis, information of covariates was used to evaluate their importance in predicting the survival probability of a given individual. A stochastic survival model is developed which incorporates covaraites and allows 2 states of health and several competing risks of death. The transition intensity functions can have an exponential or Weibull form but depend upon the covariates. Other generalizations of the model are presented. The model of Lagakos (1976) is a special case of the models proposed here. The asymptotic theory of the maximum likelihood estimates and a goodness-of-fit procedure is discussed along with the estimation of the survival, transition and competing risks probabilities. These models are applicable to data collected in a clinical trial or prospective study and can distinguish between end-of-study and loss-to-follow-up censoring. An application is given which analyzes the survival of [human] patients in a heart transplant program.