Robustness of a Sample Size Reestimation Procedure in Clinical Trials

Z. Govindarajulu

Abstract:

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 $\sigma ^{2}$ is unknown. We wish to determine the required total sample size when the error probabilities $\alpha $ and $\beta $ 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 $\sigma $, he estimates $\sigma ^{2}$ by the method of maximum likelihood via the $E-M$ algorithm. Since he introduces indicator variables which are treated as unknown parameters, the $m\ell e$ of $\sigma ^{2}$ may not be consistent. Here, we propose an estimator of $\sigma ^{2}$ that has a closed-form and derive expressions for the effective level of significance $% \left( \alpha ^{*}\right) $ and the power of the test at the specified alternative. In particular, it is shown that $\alpha ^{*}-\alpha $ is negligible and that the power exceeds $1-\beta $ when the initial (total) sample size is large.

Keywords: Robustness, clinical trials, double-blind experiment, sample size re-estimation.