Estimation and Asymptotic Theory for Transition Probabilities in Markov Renewal Multi-State Models

In this paper we discuss estimation of transition probabilities for semi-Markov multi-state models. Non-parametric and semi-parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta method and the use of resampling is proposed to derive confidence bands for the transition probabilities. The last part of the paper concerns the presentation of the main ideas of the R implementation of the proposed estimators, and data from a renal replacement study are used to illustrate the behavior of the estimators proposed.