Confidence intervals for odds ratio and relative risk based on the inverse hyperbolic sine transformation

Abstract

The inverse hyperbolic sine transformation can be used to shorten the standard delta logit interval for the odds ratio and the delta log interval for the relative risk. As it stands, this transformation does not provide sufficient coverage. A pseudo-frequency modification is suggested and evaluated. The modification achieves an improvement in coverage for both the odds ratio and the relative risk and a further improvement in interval width for the odds ratio. We also find that another closed form interval, called MOVER-R Wilson, which is based on the method of variance estimates recovery, performs well. When the more complex and software demanding intervals, such as the asymptotic score, are unavailable, the adjusted inverse sinh intervals and MOVER-R Wilson provide two simple approaches to interval estimation of the odds ratio and the relative risk.