On proportional reversed hazards frailty models

Frailty models are widely employed in bivariate survival data as they allow us to model the dependence through common random effect. The frailty models developed in literature are based on the assumption that the frailty random variables act multiplicatively on the baseline hazard rates and those models are useful for the analysis of right censored data. In the present paper, we introduce a class of semiparametric frailty models in terms of reversed hazard rates, which is useful for the analysis of left censored data. The shared gamma frailty reversed hazards model and correlated gamma frailty reversed hazards model are studied. The estimation of the parameters of the models by maximum likelihood method, using EM algorithm, is presented. The properties of the estimates are also discussed. The gamma frailty reversed hazards models in presence of observed covariates are also studied. Finally, we apply the models to a real data set.