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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.
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Gruttola et al. (1989) studied this question.
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