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clinicaltrials.gov Identifier: NCT00197587.

This paper proposes nonparametric and weakly structured parametric methods for analyzing survival data in which both the time origin and the failure event can be right- or interval-censored. Such data arise in clinical investigations of the human immunodeficiency virus (HIV) when the infection and clinical status of patients are observed only at several time points. The proposed methods generalize the self-consistency algorithm proposed by Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) for singly-censored univariate data, and are illustrated with the results from a study of hemophiliacs who were infected with HIV by contaminated blood factor.

In this paper we derive and investigate nonparametric estimators of the distributions of lifetime and time until onset associated with an irreversible disease that is detectable only at death. The nonparametric maximum likelihood solution requires an iterative algorithm. An alternative though closely related pair of estimators for the lifetime and onset distributions exists in closed form. These estimators are the familiar Kaplan-Meier estimator and an isotonic regression estimator, respectively. First-order approximations provide variance estimators. The proposed methods generalize and shed additional light on the constrained estimators presented by Kodell, Shaw and Johnson (1982, Biometrics 38, 43-58). Data from an animal experiment illustrate the techniques.