Understanding Misunderstandings About the Relative Risk and Odds Ratio

Categorical outcome analyses in randomized controlled trials (RCTs) and observational studies are commonly presented as relative risks (RRs) and odds ratios (ORs). In some situations, these RRs and ORs may be misunderstood, resulting in wrong conclusions. How this may happen is explained in the context of a hypothetical RCT that compares potentially lifesaving drugs A and B with placebo. In this RCT, the RR for survival is 1.67 for A vs placebo and 1.42 for B vs placebo. Using these RR data, as a challenge, readers are invited to answer 2 questions either intuitively or by other means. First, by how much is A better than B? Second, if the absolute survival rate with B is 8.5%, using the answer obtained from the previous question, what is the absolute survival rate with A? In this same RCT, the OR for survival is 1.74 for A vs placebo and 1.46 for B vs placebo. Using the OR data instead of the RR data, readers are again invited to answer the 2 questions listed above. This article explains why it is easy for readers and even authors to arrive at wrong answers to the 2 questions and draw wrong conclusions about the results. This article also explains what the correct answers are and how they may be obtained. The explanations involve simple concepts and even simpler arithmetic.