2011/11/21_Ana Moreira (University of Minho) and Jacobo de Uña (University of Vigo)

November 21st 2011

Faculty of Economic and Business Sciences | Salón de Grados

Premsoothing the Aalen-Johansen estimator in the illness-death model

2011/11/21 – 12:00 h | Ana Moreira, University of Minho.


One major goal in clinical applications of multi-state models is the estimation of transition probabilities. The usual nonparametric estimator of the transition matrix for non-homogeneous Markov processes is the Aalen-Johansen estimator (Aalen and Johansen 1978). In this paper we propose a modification of the Aalen-Johansen estimator in the illness-death model based on presmoothing. The consistency of the proposed estimators is formally established. Simulations show that the presmoothed estimators may be much more efficient than the Aalen-Johansen estimator. A real data illustration is included. This is joint work with Luis F Meria-Machado and Jacobo de Uña-Álvarez.

A nonparametric test for markovianity in the illness-death model

2011/11/21 – 12:45 h | Jacobo de Uña Álvarez, University of Vigo.


Multi-state models are useful tools for modeling disease progression when survival is the main outcome but several intermediate events of interest are observed during the follow-up time. The illness-death model is a special multi-state model with important applications in the biomedical literature. It provides a suitable representation of the individual’s history when an unique intermediate event can be experienced before the main event of interest. Nonparametric estimation of transition probabilities in this and other multi-state models is usually performed through the Aalen-Johansen estimator under a Markov assumption . The Markov assumption claims that given the present state, the future evolution of the illness is independent of the states previously visited and the transition times among them. However, this assumption fails in some applications, leading to inconsistent estimates. In this paper we provide a new approach for testing markovianity in the illness-death model. The new method is based on measuring the future-past association along time. This results in a deep inspection of the process which often reveals a non-markovian behaviour with different trends in the association measure. A test of significance for zero future-past association at each time point is introduced, and a significance trace is proposed accordingly. Besides, we propose a global test for markovianity based on a supremum-type test statistic. The finite sample performance of the test is investigated through simulations. We illustrate the new method through the analysis of two biomedical data sets. This is joint work with Mar Rodríguez-Girondo.