Estimation and Confidence Intervals for Two-Stage Sample-Size-Flexible Design with LSW Likelihood Approach

Adaptive sample size methods have been a popular topic in the field of clinical trials. There are a few basic requirements for the adaptive methods to be acceptable from the international regulatory viewpoint. All valid methods need to control the overall type-I error rate at the pre-specified level. The rule of the interim and final decisions needs to be explicit and clearly documentable. It is extremely desirable that the method employed also provides estimation of the treatment effect in addition to the significance test. In this paper we describe the point and confidence interval estimation for the likelihood approach of sample-size adaptive design proposed by Li et al. (Biostatistics 3:277–287, 2002, J. Biopharm. Stat. 15:707–718, 2005). We use the median unbiased estimator (Cox and Hinkley, Theoretical Statistics, p. 273, 1974) for estimating the treatment effect and demonstrate that the estimator has small mean squared error compared to the naive method, and that the confidence interval estimation has correct coverage probability.