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.

Keywords:

• Anscombe's CLT
• Bias correction
• Bootstrap
• Clinical trials
• Confidence interval
• Coverage probability
• Following SPRT
• MLE
• Random CLT
• Simulations

Subject Classifications:

• 62L10
• 62L12
• 62H15

ACKNOWLEDGMENTS

A preliminary version was presented by the first author (DB) as an invited paper at the 7th International Workshop in Applied Probability (IWAP) held in Antalya, Turkey, June 16–19, 2014. We remain grateful for a number of comments received during the IWAP 2014. We also thank an Associate Editor and the reviewers for their helpful feedback.