STOCHASTIC NETWORK MODELS FOR SURVIVAL ANALYSIS

We present methodology giving highly accurate approximations for Bayes ian predictive densities and distribution functions of first passage t imes between states of a semi-Markov process with a finite number of s tates. When the states describe a degenerative disorder with an absorb ing end state, such predictive distributions are the survival distribu tions of a patient. We illustrate these methods with a variety of exam ples, including data from the San Francisco AIDS study. We achieve our approximations using a three-step sequence. First, we introduce advan ced concepts of flowgraph theory, which allow us to compute the moment generating function of the first passage time given the model paramet ers. Next, we use saddlepoint approximations to convert this into a de nsity or distribution function conditional on the model parameter. Fin ally, we use Monte Carlo methods to remove dependence on the model par ameter. These methods apply quite generally to all finite-state semi-M arkov models in discrete or continuous time. Currently, there are no c ompeting alternative methods that can achieve the saddlepoint accuracy of these computations.