Sample Size for Testing a Proportion in Clinical Trials

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Abstract
In addition to the power of the statistical test, sample size calculations should consider the precision of the effect estimate. The expected width of the “exact” confidence interval, based on inverting the binomial test, is an appropriate measure of the latter together with the probability of obtaining, under the alternative hypothesis, confidence intervals with a width less than the expected one. In testing a proportion against a reference value, we devised a “two-step” procedure. At the first step the required sample size for the binomial testing is obtained; then, at the second step, this sample size is iteratively increased until the probability of obtaining “exact” confidence intervals with a width less than the expected one exceeds a required threshold.