A revisit on comparing the asymptotic interval estimators of odds ratio in a single 2 x 2 table

It is well known that CORNFIELD'S confidence interval of the odds ratio with the continuity correction can mimic the performance of the exact method. Furthermore, because the calculation procedure of using the former is much simpler than that of using the latter, CORNFIELD'S confidence interval with the continuity correction is highly recommended by many publications. However, all these papers that draw this conclusion are on the basis of examining the coverage probability exclusively. The efficiency of the resulting confidence intervals is completely ignored. This paper calculates and compares the coverage probability and the average length for WOOLF'S logit interval estimator, GART'S logit interval estimator of adding 0.50, CORNFIELD'S interval estimator with the continuity correction, and CORNFIELD'S interval estimator without the continuity correction in a variety of situations. This paper notes that CORNFIELD'S interval estimator with the continuity correction is too conservative, while CORNFIELD'S method without the continuity correction can improve efficiency without sacrificing the accuracy of the coverage probability. This paper further notes that when the sample size is small (say, 20 or 30 per group) and the probability of exposure in the control group is small (say, 0.10) or large (say, 0.90), using CORNFIELD'S method without the continuity correction is likely preferable to all the other estimators considered here. When the sample size is large (say, 100 per group) or when the probability of exposure in the control group is moderate (say, 0.50), GART'S logit interval estimator is probably the best.