Semiparametric additive frailty hazard model for clustered failure time data

This article proposes a flexible semiparametric additive frailty hazard model under clustered failure time data, where frailty is assumed to have an additive effect on the hazard function. When there is no frailty, this model degenerates into a semiparametric additive hazard model. Our method can deal simultaneously with both time‐varying and constant covariate effects. The estimate of the covariate effects does not rely on the frailty distribution. The time‐varying coefficient is estimated by utilizing the local linear technique, while we can obtain a ‐consistency convergence rate of the constant‐coefficient estimate by integration. Another advantage of the estimator is that it has a closed form. We establish large sample properties of the estimator and conduct simulation studies under various scenarios to demonstrate its performance. The proposed method is applied to real data for illustration.