Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

Abstract

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions and the conditional distribution of the second gap time given the first gap time. In this work we consider the estimation for the survival given the first gap time. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. Real data illustration based on a German breasts cancer study is included.