Non-Parametric Inference of Transition Probabilities Based on Aalen-Johansen Integral Estimators for Acyclic Multi-State Models: Application to LTC Insurance

Quentin Guibert (1, 2) , Frédéric Planchet (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 ACPR - Autorité de Contrôle Prudentiel et de Résolution

Studying Long Term Care (LTC) insurance requires to model the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. In this paper, we analyze this situation with a multi-state approach and we exhibit non-parametric estimators of transition probabilities considering the Markov assumption does not hold. The proposed estimators can be seen as Aalen-Johansen integrals for competing risks data, which are obtained by re-setting the system with two competing risks blocks. As little attention has been given to this issue, we derive asymptotic results for this type of estimator under non-dependent random right-censorship in presence of covariates and discuss their possible outlooks. We also develop a methodology to investigate time dependence association measures between cause-specific failure times. For key transition probabilities, we conduct simulations to analyze the performance of our estimators versus the classical Aalen-Johansen estimators. Finally, we propose a numerical application with LTC insurance data, which is traditionally analyzed with semi-Markov model.

Mots clés: Multi-state model; Aalen-Johansen integral; non-parametric estimator; non-Markov process; time-dependence association measure; LTC insurance

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Quentin Guibert, Frédéric Planchet. Non-Parametric Inference of Transition Probabilities Based on Aalen-Johansen Integral Estimators for Acyclic Multi-State Models: Application to LTC Insurance. 2015. ⟨hal-01183542v1⟩