Confidence Intervals for Survival Probabilities: A Comparison Study

The confidence interval of the Kaplan–Meier estimate of the survival probability at a fixed time point is often constructed by the Greenwood formula. This normal approximation-based method can be looked as a Wald type confidence interval for a binomial proportion, the survival probability, using the “effective” sample size defined by Cutler and Ederer. Wald-type binomial confidence interval has been shown to perform poorly comparing to other methods. We choose three methods of binomial confidence intervals for the construction of confidence interval for survival probability: Wilson's method, Agresti–Coull's method, and higher-order asymptotic likelihood method. The methods of “effective” sample size proposed by Peto et al. and Dorey and Korn are also considered. The Greenwood formula is far from satisfactory, while confidence intervals based on the three methods of binomial proportion using Cutler and Ederer's “effective” sample size have much better performance.