Accurate confidence limits for quantiles under random censoring.

In survival analysis, estimates of median survival times in homogeneous samples are often based on the Kaplan-Meier estimator of the survivor function. Confidence intervals for quantiles, such as median survival, are typically constructed via large sample theory or the bootstrap. The former has suspect accuracy for small sample sizes under moderate censoring and the latter is computationally intensive. In this paper, improvements on so-called test-based intervals and reflected intervals (cf., Slud, Byar, and Green, 1984, Biometrics 40, 587-600) are sought. Using the Edgeworth expansion for the distribution of the studentized Nelson-Aalen estimator derived in Strawderman and Wells (1997, Journal of the American Statistical Association 92), we propose a method for producing more accurate confidence intervals for quantiles with randomly censored data. The intervals are very simple to compute, and numerical results using simulated data show that our new test-based interval outperforms commonly used methods for computing confidence intervals for small sample sizes and/or heavy censoring, especially with regard to maintaining specified coverage.