Variance estimation of a survival function for interval‐censored survival data

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Abstract
Interval‐censored survival data often occur in medical studies, especially in clinical trials. In this case, many authors have considered estimation of a survival function. There is, however, relatively little discussion on estimating the variance of estimated survival functions. For right‐censored data, a special case of interval‐censored data, the most commonly used method for variance estimation is to use the Greenwood formula. In this paper we propose a generalization of the Greenwood formula for variance estimation of a survival function based on interval‐censored data. Also a simple bootstrap approach is presented. The two methods are evaluated and compared using simulation studies and a real data set. The simulation results suggest that the methods work well. Copyright © 2001 John Wiley & Sons, Ltd.