Estimation of transition probabilities in a non-Markov model with successive survival times

Times between consecutive events are often of interest in medical studies. Usually the events represent different states of the disease process and are modeled using multi-state models. This paper introduces and studies a feasible estimation method for the transition probabilities in a progressive three-state model. We assume that the vector of gap times (T1,T2) satisfies a nonparametric location-scale regression model T2 = m(T1) + σ(T1)ε, where the functions m and σ are `smooth', and ε is independent of T1. Under this model, Van Keilegom, de Uña-Alvarez and Meira-Machado (2011) proposed estimators of the transition probabilities. In this paper, we study the performance of their estimator in practice, we propose some modifications and study practical issues related to the implementation of the estimator. In an extensive simulation study the good performance of the method is shown. Simulations also demonstrate that the proposed estimator compares favorably with alternative estimators. Furthermore, the proposed methodology is illustrated with a real database on breast cancer