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The conditional lifetime expectancy function (LEF) is the expected lifetime of a subject given survival past a certain time point and the values of a set of explanatory variables. This function is attractive to researchers because it summarizes the entire residual life distribution and has an easy interpretation compared with the popularly used hazard function. In this paper, we propose a general framework of backward multiple imputation for estimating the conditional LEF and the variance of the estimator in the right-censoring setting. Simulation studies are conducted to investigate the empirical properties of the proposed estimator and the corresponding variance estimator. We demonstrate the method on the Beaver Dam Eye Study data, where the expected human lifetime is modeled with smoothing-spline ANOVA given the covariates information including sex, lifestyle factors, and disease variables.

Backward multiple imputation estimation of the conditional lifetime expectancy function with application to censored human longevity data