Estimating the prediction error in multistate models

Abstract

In medical research, the progress of a disease can be described with a multistate model. By estimating state occupation probabilities and transition probabilities, static and dynamic predictions can be made, based on individual patient covariates. The probabilities are estimated by the Aalen- Johansen estimator and a proportional hazards model is used to include time-?xed covariates. The thesis focuses on the study of the accuracy of the predictions. Measures for the prediction error, based on the Brier score and the Kullback-Leibler score, are introduced. We prove that these measures have the quality of properness. In order to estimate the prediction error with right-censored data, we propose two estimators: one using the method of inverse probability of censoring weights (IPCW) and one using pseudo-values. For both estimators we prove consistency. Finally, the estimation of the prediction error is implemented in the statistical software R, using data from bone marrow transplantation.