Semiparametric Additive Frailty Hazard Model for Clustered Failure Time Data

In this paper, we propose 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 to semiparametric additive hazard model. Our method can deal with time-varying covariate effect and constant covariate effect simultaneously and the estimate of the covariate effects will not rely on the frailty distribution. The time-varying coefficient is estimated by utilizing the local linear technique, while $\sqrt{n}$-consistency convergence rate of constant coefficient estimate can be obtained by integration. Another advantage of the estimator is that it has a closed-form and can be easily implemented in practice. The large sample properties of the estimator have been established and simulation studies under various scenarios are conducted to demonstrate the performance of the proposed methods. A real data is applied for illustration purpose