Statistical inference for proportional mean residual life model with continuous auxiliary covariate

Abstract

In many statistical studies involving failure data, the main covariate is only measured in a validation set due to financial and technical restriction, while some auxiliary information for the main covariate is collected for the full cohort. Making use of the auxiliary information will increase the efficiency of the study. In this paper, we consider statistical inference for the proportional mean residual life model when the primary covariate is measured only for a randomly chosen subcohort and some auxiliary variables are available for the whole study cohort. To further make use of the auxiliary information to improve the efficiency of the study, we propose anestimating equation based on the inverse probability of censoring weighting techniques. The resulting estimators are shown to be consistent and asymptotically normal. Extensive simulations are conducted to evaluate the finite sample performance of the proposed methods. We illustrate the proposed method with a real data set from the Mayo Clinic trial in primary biliary cirrhosis of the liver.