Semiparametric varying-coefficient study of mean residual life models

In this paper, we consider a flexible class of semiparametric varying-coefficient mean residual lifetime (MRL) models that depended on an exposure variable where some effects may be functions of the exposure variables and some may be constants. We develop three-step estimation procedures to estimate parametric and nonparametric parts in the semiparametric varying-coefficient MRL model under the right censoring. We first establish a local estimating equation with inverse probability of censoring weighting (IPCW) approach, and estimate parametric and nonparametric parts simultaneously. In the second step, substituting the nonparametric estimator into estimating equations, we can obtain the global parametric estimating equation to refine the estimators of the parametric part. The asymptotic normality of the parametric estimator is established, meanwhile it has been shown that the estimators achieve the n convergence rate under some smoothed conditions. In the third step, substituting the refined parametric estimator into the local estimating equations, we can obtain updated local nonparametric estimating equations to estimate the nonparametric part, and show that the asymptotic normality of nonparametric estimator is still true. Some numerical simulations are conducted to illustrate performance of the proposed methods.