Presmoothing the transition probabilities in the illness-death model

Ana Paula Amorim (1) , Jacobo de Uña-Álvarez (2) , Luís Meira-Machado (1)

1 Department of Mathematics and Applications
2 Department of Statistics and O.R.

One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, Meira-Machado, de Uña-Álvarez and Cadarso-Suárez (2006) introduce a substitute for the Aalen- Johansen estimator in the case of a non-Markov illness-death model. The idea behind their estimator is to weight the data by the Kaplan-Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of Meira-Machado et al (2006) estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes.

Mots clés: Kaplan-Meier; Markov condition; Multi-state models; Semiparametric censorship

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Ana Paula Amorim, Jacobo de Uña-Álvarez, Luís Meira-Machado. Presmoothing the transition probabilities in the illness-death model. Statistics and Probability Letters, 2011, 81 (7), pp.797. ⟨10.1016/j.spl.2011.02.017⟩. ⟨hal-00746100⟩