An Application of Imputation to an Estimation Problem in Grouped Lifetime Analysis

Abstract

Tanner and Wang (in press) have introduced the data augmentation algorithm for the analysis of parametric missing data problems. In this article, this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data. This algorithm makes use of the notions of cross-validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate. A procedure for estimating the variance of the estimator is also proposed. The nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study. The algorithm is illustrated with a numerical example.