Testing equality of risk ratios in multiple 2x2 tables with structural zero

This paper investigates the equality test of risk ratios in multiple 2x2 tables with structural zero, which is formed by a confounding factor such as age, gender, severity of disease, region or other variables of interest. Score statistic, Wald statistic and likelihood ratio statistic for testing equality of risk ratios in multiple 2x2 tables with structural zero are proposed. Three procedures for calculating p-values of the above three statistics based on the MaxT, MinP and Bonferroni methods are developed. An algorithm for determining sample size required for attaining the pre-specified power is presented. Empirical results show that (1) likelihood ratio statistic and score statistic via the MaxT and MinP methods behave satisfactorily in the sense that their type I error rates are close to the pre-given significance level; (2) the Wald-type statistic with logarithmic transformation behaves better than the Wald-type statistic. Simulation studies and a real example are used to illustrate the proposed methodologies.