Kudô and Tarumi (1978) proposed a conditional test for testing equivalence of two proportions in 2 × 2 tables by assuming the date collected by a negative binomial sampling. The test is undoubtedly a counterpart of the Fisher exact test, but no comparison has been made of the two tests. In this paper we obtain asymptotic power of the Kudô-Tarumi test and compare it with the Fisher exact test by means of the Pitman asymptotic efficiency. It will be shown that the Kudô-Tarumi test is the most powerful similar test for a risk ratio, whereas the Fisher exact test is, the most powerful similar test for a risk ratio, whereas the Fisher exact test is, as well known, the most powerful similar test for an odds ratio. It is also shown that the Kudô-Tarumi test has higher efficiency than the Fisher exact test in many cases.

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Determination of a sample size of a clinical study is one of the essential design factors. This paper focuses on a problem of sample size determination of a clinical trial in the clinical development phase. Sample size calculation can be performed using a formula or simulation, once a set of conditions is given pertaining treatment effect, variability of observations, significance level and power. Contrary to calculation, determination of sample size is not an easy task. For example, formal application of a formula may result in a very large sample size. In designing a study, however, sample size calculation is affected by constraints from various design factors, amount of information at hand and feasibility of the study. I first present a principle for sample size calculation and stress on importance of assessment of risks of a given sample size. Next, I propose two conservative approaches to sample size calculation; double confidence limits method and effect size confidence limit method, and compare properties of these methods with an ordinary method for a two treatment parallel group study. A few actual examples of a conservative approach are presented and discussed. Further issues in and points to consider for sample size determination are also discussed. Several examples of approaches to sample size calculation in exploratory studies and dose-response studies are also presented.

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