Nonparametric estimation of functions in a model of competing risks from incomplete longitudinal data

Abstract

Incomplete longitudinal data arise in many clinical trials and sample surveys conducted in connection with population research. The data are incomplete in the sense that only a time segment of each individual life is observed and measurements are grouped into intervals. Classical multiple decrement life table procedures, designed to handle transverse data used in studies of mortality, have been widely utilized to estimate the functions in a model of competing risks from incomplete longitudinal data. Although life table methods are well suited for handling transverse data, it is far from clear whether they make efficient use of incomplete longitudinal data. In this paper, two nonparametric procedures for estimating the functions in a model of competing risks, using a sampling framework with several cutoff points, are studied. One of these procedures is based on a linear unbiased estimator, and a second is based on the method of maximum likelihood. In large samples, it is shown that the method of maximum likelihood procedure is more efficient, because it has smaller variances. A generalization of the Cramér-Rao lower bound is used to demonstrate that the maximum likelihood estimators have smaller variances.