A semiparametric shock model for a pair of event-related dependent censored failure times

Frédérique Letué (1)

1 SMS - Statistique et Modélisation Stochatisque

In this paper, we propose a semiparametric shock model for two dependent failure times where the risk indicator of one failure time plays the role of a time-varying covariate for the other one. Following Hougaard (2000), the dependence between the two failure times is therefore of event-related type. To derive our results, we define a joint distribution for the pair of failure times by means of a pair of parameters and a pair of baseline hazard rates. We then construct the associated counting processes and their compensators: in particular, we exhibit a special form of the risk indicators. We then propose a maximal partial likelihood estimator for the pair of parameters and Breslow estimators for the pair of baseline cumulative hazard rates. We establish the large sample properties of our estimators, following Andersen et al. (1992) and we illustrate our results by a short simulation study and an application to a real data set in demography.

Mots clés: Bivariate censored data; Bivariate survival analysis; Cox model

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

Frédérique Letué. A semiparametric shock model for a pair of event-related dependent censored failure times. Journal of Statistical Planning and Inference, 2008, 138 (12), pp.3869-3884. ⟨10.1016/j.jspi.2008.02.002⟩. ⟨hal-00160930⟩