Sequential and Two-Stage Fixed-Width Confidence Interval Estimation in Response-Adaptive Designs

Abstract

Let be a sequence of consistent estimators of a parameter Δ in some response-adaptive design, where the data are not independent and identically distributed. A fixed-width confidence interval estimation involves determining a positive integer ν such that, for a given d (> 0) and α ∈ (0, 1), the coverage probability of the random interval for Δ is at least (1 − α). In this article, we first investigate such confidence intervals for a general structure of response-adaptive allocation design, for two-treatment allocation in clinical trials, in a complete sequential setup. We consider some examples in this context. We then carry out this exercise for a Stein-type two-stage procedure, where the parameters are estimated based on the first-stage data, which are then used for the allocation in the second stage. Fixed-width confidence intervals are obtained in this context. The procedures are evaluated by simulations. We then illustrate the proposed methodology using some real data set.

Keywords:

• Coverage probability
• Fixed-width confidence interval
• Risk difference
• Stopping time
• Two-stage design

Subject Classifications:

• 62L05
• 62L10

ACKNOWLEDGMENT

We are grateful to the editor for his interest in this article and for inviting this article for the Stein issue of the journal.

Notes

Recommended by Nitis Mukhopadhyay