Confidence intervals for confirmatory adaptive two-stage designs with treatment selection

The construction of adequate confidence intervals for adaptive two-stage designs remains an area of ongoing research. We propose a conditional likelihood-based approach to construct a Wald confidence interval and two confidence intervals based on inverting the likelihood ratio test, one of them using first-order inference methods and the second one using higher order inference methods. The coverage probabilities of these confidence intervals, and also the average bias and mean square error of the corresponding point estimates, compare favorably with other available techniques. A small simulation study is used to evaluate the performance of the new methods. We investigate other extensions of practical interest for normal endpoints and illustrate them using real data, including the selection of more than one treatment for the second stage, selection rules based on both efficacy and safety endpoints, and the inclusion of a control/placebo arm. The new method also allows adjustment for covariates, and has been extended to deal with binomial data and other distributions from the exponential family. Although conceptually simple, the new methods have a much wider scope than the methods currently available.