Confidence intervals for the common odds ratio based on the inverse sinh transformation
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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 (<i>c</i><sub>1</sub>) to all the cells before computing the point estimate of common odds ratio and another pseudo-frequency (<i>c</i><sub>2</sub>) 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 <i>c</i><sub>2</sub> is slightly greater than <i>c</i><sub>1</sub> since the coverage probabilities of them are closer to confidence level of 95%. Larger values of <i>c</i><sub>2</sub> 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.
