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Confidence Interval Estimation Following SPRT in a Normal Distribution with Equal Mean and Variance

Abstract Confidence interval estimation following a sequential probability ratio test (SPRT) is an important and difficult problem with applications in clinical trials. Difficulties arise because following termination of SPRT, a customary estimator of an unknown parameter of interest obtained from the randomly stopped data is often biased. As a result, coverage probability of a naïve confidence interval based on the randomly stopped version of the customary estimator often falls below the target confidence level. We address this problem for a normal distribution having mean and variance unknown but equal and propose a methodology based on random central limit theorem that is remarkably easy to implement with bias-corrected estimators. We have also explored limited bootstrapped versions of our parametric resolutions. With the help of extensive sets of simulations, we have concluded that our data-driven bias-corrected parametric confidence intervals with a slight variance inflation perform remarkably well to uphold the target coverage probability.