Modeling Multistate Survival Illustrated in Bone Marrow Transplantation

In many applications of survival analysis techniques there are intermediate events whose occurrence may effect a patient's prognosis. The occurrence of these intermediate events can be modeled using a proportional hazards model with time dependent covariates or by a model using distinct hazards for each event that allows for non proportional hazard rates when other intermediate events occur. Of interest to clinical investigators are not the estimates of these transition intensities, but rather synthesized estimates of predictive probabilities of patient's final response given their current history of occurrence of these intermediate events. We show, using an example of bone marrow transplantation taken from the data base of the International Bone Marrow Transplant Registry, that these predictive probabilities are equivalent to certain transition probabilities in a multistate Markov model. We show how, by using a combination of proportional hazards regression and left truncated proportional hazards regression, one can estimate model parameters and the desired predictive probabilities. Asymptotic properties of the estimators are discussed. Finally, we show how these predictive probabilities can be used to study the effects of treatment strategies which alter the rate at which some intermediate events occur.