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Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation. (English) Zbl 1209.62049

Summary: We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV-1 subtypes B and E.

MSC:

62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis
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