On asymptotic normality in estimation after a group sequential trial

TL;DR

This paper demonstrates that the sample mean after a group sequential trial is asymptotically normal as the number of observations grows, supporting the use of standard confidence intervals.

Contribution

It provides a theoretical proof of asymptotic normality for the sample mean in group sequential trials, validating naive confidence interval use.

Findings

Asymptotic normality holds in many realistic scenarios.

Naive confidence intervals are often justified.

Simulation confirms theoretical results.

Abstract

We prove that in many realistic cases, the ordinary sample mean after a group sequential trial is asymptotically normal if the maximal number of observations increases. We derive that it is often safe to use naive confidence intervals for the mean of the collected observations, based on the ordinary sample mean. Our theoretical findings are confirmed by a simulation study.