Finite sample pointwise confidence intervals for a survival distribution with right‐censored data

We review and develop pointwise confidence intervals for a survival distribution with right-censored data for small samples, assuming only independence of censoring and survival. When there is no censoring, at each fixed time point, the problem reduces to making inferences about a binomial parameter. In this case, the recently developed beta product confidence procedure (BPCP) gives the standard exact central binomial confidence intervals of Clopper and Pearson. Additionally, the BPCP has been shown to be exact (gives guaranteed coverage at the nominal level) for progressive type II censoring and has been shown by simulation to be exact for general independent right censoring. In this paper, we modify the BPCP to create a 'mid-p' version, which reduces to the mid-p confidence interval for a binomial parameter when there is no censoring. We perform extensive simulations on both the standard and mid-p BPCP using a method of moments implementation that enforces monotonicity over time. All simulated scenarios suggest that the standard BPCP is exact. The mid-p BPCP, like other mid-p confidence intervals, has simulated coverage closer to the nominal level but may not be exact for all survival times, especially in very low censoring scenarios. In contrast, the two asymptotically-based approximations have lower than nominal coverage in many scenarios. This poor coverage is due to the extreme inflation of the lower error rates, although the upper limits are very conservative. Both the standard and the mid-p BPCP methods are available in our bpcp R package. Published 2016. This article is US Government work and is in the public domain in the USA.