Semiparametric Estimation For Shared-frailty Models With Doubly-censored Data

In this paper,we investigate frailty models for clustered survival data that are sub-ject to both left-and right-censuring,termed "doubly-censored data".This model ex-tends current survival literature bu brodening the application of frailty models from right-censoring to a more complicated situation with additional left-censoring.We adopt a likelihood approach to estimate unknown parameters.The key algorith-m in estimation process is EM algorithm.Based on properties of the proposed model which are constitutive of infinite-dimensional parameters and no explicit forms,non-parametric maximum likelihood approach and Newton-Raphson method are applied in the proposed algorithm to solve these issues.Besides we adopt the improved algorithm——MCEM algorithm to solve computational challenge.Asymptotic properties of the NPMLE are estimated along with semiparametric efficiency of the NPMLE for the finite-dimensional parameters.The consistency of bootstrap estimators for the standard errors of the NPMLE is also discussed.We con-ducted some simulations to illustrate the numerical performance and robustness of the proposed algorithm.