Robustness of a Sample Size Re-Estimation Procedure in Clinical Trials

One of the central questions that arise in clinical trials is, how many additional observations, if any, are needed beyond those originally planned. Consider a two treatment normal response double-blind clinical experiment. We wish to test the null hypothesis of equality of the means against one-sided alternative when the common variance σ² is unknown. We wish to determine the required total sample size when the error probabilities α and β are specified at a predetermined alternative. Shih (1992) provides a two-stage procedure which is an extension of Stein’s one-sample procedure. Assuming a preliminary guessed value of σ, he estimates σ ² by the method of maximum likelihood via the E − M algorithm. Since he introduces indicator variables which are treated as unknown parameters, the mie of σ ² may not be consistent. Here, we propose an estimator of σ ² that has a closed-form and derive expressions for the effective level of significance (α*) and the power of the test at the specified alternative. In particular, it is shown that α* − α is negligible and that the power exceeds 1 − β when the initial (total) sample size is large.