Effects of Censoring on the Validity of Confidence Intervals

Abstract This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds asymptotically in the case of complete censoring, first conditions are found under which the exponential maximum likelihood estimate of a percentile is asymptotically normal uniformly in F, where F is an arbitrary survival distribution function. Then, the asymptotic coverage probability of the exponential-based interval is found for a percentile of a local alternative to the exponential distribution. If the censoring distribution converges weakly to point mass at 0, and if the departure from exponentiality is independent of the cens...