Semiparametric proportional mean residual life model with covariates missing at random

Abstract

In this paper, we consider statistical inference for the proportional mean residual life model when some covariates are missing at random. Simple and augmented inverse probability-weighted estimating equations are used to obtain the estimators of the regression coefficients and baseline mean residual life function. The unknown non-missingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. We show that the simple inverse probability-weighted estimator with estimated non-missingness probability is more efficient than that with the true non-missingness probability, while the augmented inverse probability-weighted estimator with estimated non-missingness probability and that with the true non-missingness probability have the same efficiency. The asymptotic properties of all the proposed estimators are established. Extensive simulation studies are conducted to examine the finite sample performance of the proposed estimator. At last, the proposed method is applied to the mouse leukaemia data.