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.