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

• Published in: Sequential analysis Vol. 34; no. 4; pp. 504 - 531
• Main Authors: Bhattacharjee, Debanjan, Mukhopadhyay, Nitis
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.10.2015; Taylor & Francis Ltd
• Subjects: Anscombe's CLT; Bias correction; Bootstrap; Bootstrap method; Clinical trials; Confidence interval; Confidence intervals; Coverage probability; Following SPRT; MLE; Normal distribution; Probability; Random CLT; Simulations
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2015.1099948

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.