Simple analysis of non-Markov models: A case study on heart transplant data

Abstract

In transplantation studies, often several response measurements are collected for patients while they are on the waiting list. In this settings it is often of primary interest to assess whether the available history of a patient can be used for predicting patient survival as well as further performance on the list. In this work, we use a multi-state model approach to analyze the performance of patients described by their urgency status that changes in time while waiting for a new organ. We use the pseudo-value approach introduced by Andersen et al. ( 2003 ) and apply it for the Aalen-Johansen estimator of the state occupation probabilities since the transition probabilities were found to depend on the history. This approach allows us to study the impact of baseline information on the occupation probabilities treating the dependence on the history as a nuisance. It was found that the previous state, the current state and time from the moment of entering the waiting list had an impact on the future performance of the patient. Depending on those, patients were more likely to come back to the particular status in which they were before, die or get a transplant. To address the problem of those competing events, a multinomial approach was used for the next state given the previous state observed.