Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model

One important goal in multi-state modeling is the estimation of transition probabilities. In longitudinal medical studies these quantities are particularly of interest since they allow for long-term predictions of the process. In recent years significant contributions have been made regarding this topic. However, most of the approaches assume independent censoring and do not account for the influence of covariates. The goal of the paper is to introduce feasible estimation methods for the transition probabilities in an illness-death model conditionally on current or past covariate measures. All approaches are evaluated through a simulation study, leading to a comparison of two different estimators. The proposed methods are illustrated using a real colon cancer data set.