A stochastic model for censored-survival data in the presence of an auxiliary variable

In clinical trials and other investigations of survival time, information is often available on a time-dependent event other than survival. An example of such an auxiliary event in cancer studies is objective progression of disease. While some patients expire without experiencing objective disease progression, others die after progression is observed. This paper proposes a stochastic model which utilizes this type of information in the evaluation of survival time. Our intentions in presenting this model are to provide a means of relating survival and another time-dependent event to one another (each of which may be used in the evaluation of a patient's condition), and to obtain more precise estimates of survival time by exploiting its relationship with this other event. The intrinsic aspects of the model are related to the semi-Markov model proposed by Weiss and Zelen [1965]. An important difference is that the present model incorporates incomplete (censored) observations as well as covariante variables. Analysis of the model via the method of maximum likelihood and its testability are discussed. The methods are applied to the results of a recent lung cancer study.