Confidence intervals for the common odds ratio based on the inverse sinh transformation

Abstract

ABSTRACT This paper proposes two new approximate confidence limit methods for the common odds ratio from multiple 2 × 2 tables. The two new procedures, based on the asymptotic distribution of Woolf estimator and Mantel-Haenszel estimator, associate with inverse sinh transformation. We employ three pseudo-frequency methods to calculate confidence intervals in order to avoid the interval failure caused by the presence of zero cells in multiple 2 × 2 tables. We develop the modified inverse sinh intervals for the common odds ratio which add one pseudo-frequency (c 1) to all the cells before computing the point estimate of common odds ratio and another pseudo-frequency (c 2) to all the cells before computing the standard error estimate. The simulation is to evaluate the 22 confidence intervals, including Woolf, Mantel-Haenszel, their inverse sinh intervals, and their pseudo-frequency modified inverse sinh intervals, in terms of their coverage probabilities and average log lengths. Simulation results demonstrate that the adjusted inverse sinh intervals by two different pseudo-frequencies perform quite well when c 2 is slightly greater than c 1 since the coverage probabilities of them are closer to confidence level of 95%. Larger values of c 2 lead to narrow intervals and low coverage probabilities. We also find that inverse sinh intervals are shorter than untransformed intervals based on Woolf estimator and Mantel-Haenszel estimator, respectively. These procedures were illustrated with two clinical trials.