Statistical inference of risk ratio in a correlated $$2 \times 2$$ table with structural zero

Abstract

This paper studies a compound interval hypothesis about risk ratio in an incomplete correlated $$2\times 2$$ table. Asymptotic test statistics of the Wald-type and the logarithmic transformation are proposed, with methods of the sample estimation and the constrained maximum likelihood estimation (CMLE) being considered. Score test statistic is also considered for the interval hypothesis. The approximate sample size formulae required for a specific power for these tests are presented. Simulation results suggest that the logarithmic transformation test based on CMLE method outperforms the other tests in terms of true type I error rate. A real example is used to illustrate the proposed methods.