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Estimating the proportion of immunes in a censored sample. (English) Zbl 0764.62094

Summary: An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune proportion is not too close to zero. A simple nonparametric statistic is proposed to test whether the assumptions of the analysis are likely to be valid.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
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