Likelihood inference for a two-stage design with treatment selection.

A conditional likelihood-based approach is proposed to construct confidence intervals for the parameters of interest in a two-stage design with treatment selection after the first stage. Both a Wald confidence interval and a confidence interval based on inverting the likelihood ratio test are proposed. The operating characteristics of these confidence intervals: the coverage probabilities and average confidence interval lengths, as well as the average bias and mean-square error of the corresponding point estimates, compare favorably with other available techniques. Possible extensions and an alternative unconditional approach based on the likelihood with missing at random mechanism are also briefly described.