Corrected confidence intervals after sequential testing with application to survival analysis

Abstract

Corrected confidence intervals are developed for an unknown parameter for data from a sequential experiment. The corrections are obtained from asymptotic expansions for the distribution of the signed root transformation and they have a simple form. The model does not require independent and identically distributed random variables, or smooth stopping boundaries. Inference about the failure rate of an exponential distribution when data are subject to random censoring, censoring by real time, and optional stopping is used to illustrate the main results. The accuracy of the method is confirmed through simulation studies.