Abstract
In some experimental studies such as clinical trials for new drug approvals, data may be obtained in multiple stages. In such cases, the sample sizes of later stages are often estimated based on the result of previous stages. In order to estimate required sample sizes we have to know relevant parameter values. For example, we need to know the parameter values of null and alternative hypothesis in order to calculate the power of testing to be performed. The power which is calculated based on the true parameter values will be called the "true power" in this paper. Such parameter value is generally unknown and should be estimated, in which the power calculated is an "estimated power".
In the present study, we will focus on testing of the difference of two binomial probabilities in two-stage sampling scheme. The test procedure considered here is Fisher's exact test. Sample sizes required to achieve statistical significance with pre-specified probability are estimated based on exact calculus of binomial probabilities except large sample sizes.
Power assessment is carried out under several conditions which are often encountered in practical clinical trials. The true power and the estimated power are compared numerically. It is observed in this paper that the "estimated power" often overestimates the corresponding "true power". This find-ing has practical implications. Since it is generally impossible to know the true parameter values, we have to estimate required sample sizes from the knowledge of estimated power. In such cases estimated sample sizes may be somewhat less than the size that would be needed. In order to make the estimated sample size closer to the true sample size we must have knowledge of the difference between the "true power" and the "estimated power" at least approximately.
