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.
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Maller et al. (1992) studied this question.
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