NONPARAMETRIC-ESTIMATION AND REGRESSION-ANALYSIS WITH LEFT-TRUNCATED AND RIGHT-CENSORED DATA

In many prospective and retrospective studies, survival data are subje ct to left truncation in addition to the usual right censoring. For le ft-truncated data without covariates, only the conditional distributio n of the survival time Y given Y greater than or equal to tau can be e stimated nonparametrically, where tau is the lower boundary of the sup port of the left-truncation variable T. Lf the data are also right cen sored, then the conditional distribution can be consistently estimated only at points not larger than tau, where tau* is the upper boundary of the support of the right-censoring variable C. In this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of Y, with the trimming inside the observable range between tau and tau. We then extend the approach to regression analysis and curve fitting in the presence of left truncation and rig ht censoring on the response variable Y. Asymptotic normality of M est imators of the regression parameters derived from this approach is est ablished, and the result is used to construct confidence regions for t he regression parameters. We also apply our methods of nonparametric e stimation, correlation analysis, and curve fitting for left-truncated and right-censored data to analyze transfusion-induced AIDS data, and present a simulation study comparing our approach with another kind of M estimators for regression analysis in the presence of left truncati on and right censoring.