How to Understand the 95% Confidence Interval Around the Relative Risk, Odds Ratio, and Hazard Ratio

Abstract

Statistics such as the mean difference (MD), standardized mean difference (SMD), relative risk (RR), odds ratio (OR), hazard ratio (HR), and others are meant to be examined along with their 95% confidence intervals (CIs), and their significance can be understood by viewing these CIs as compatibility intervals. The 95% CIs around the MD and SMD are easily understood because they are expressed along a linear scale. The 95% CIs around the RR, OR, and HR are harder to understand because they are expressed along an exponential scale; however, when the numbers are log-transformed, they are linearized, and understanding becomes easy. Another approach to understanding the CIs around the RR, OR, or HR is to examine the reciprocal of the lower limit of the CI; however, because the reciprocal also lies along an exponential scale, this method is inferior to the log-transformation method. These approaches may seem daunting, but the difficulty is an illusion because log transformation or reciprocal transformation takes only a few seconds when a statistical calculator is opened. All terms and concepts are explained with extreme simplification and with the help of examples.