Sample size determination for 2-step studies with dichotomous response

In this article, we consider problems with correlated data that can be summarized in a 2×2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2×2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.