BIVARIATE ESTIMATION WITH RIGHT-TRUNCATED DATA

Bivariate estimation with survival data has received considerable atte ntion recently; however, most of the work has focused on random censor ing models. Another common feature of survival data, random truncation , is considered in this study. Truncated data may arise if the time or igin of the events under study precedes the observation period. In a r andom right-truncation model, one observes the lid samples of (Y, T) o nly if (Y less than or equal to T), where Y is the variable of interes t and T is an independent variable that prevents the complete observat ion of Y. Suppose that (Y, X) is a bivariate vector of random variable s, where Y is subject to right truncation. In this study the bivariate reverse-hazard vector is introduced, and a nonparametric estimator is suggested. An estimator for the bivariate survival function is also p roposed. Weak convergence and strong consistency of this estimator are established via a representation by lid variables. An expression for the limiting covariance function is provided, and an estimator for the limiting variance is presented. Alternative methods for estimating th e bivariate distribution function are discussed. Obtaining large-sampl e results for the bivariate distribution functions present more techni cal difficulties, and thus their performances are compared via simulat ion results. Finally, an application of the suggested estimators is pr esented for transfusion-related AIDS (TR-AIDS) data on the incubation time.