A clarification on odds ratios as conditional risk ratios

Hoppe et  al. [1] propose a new interpretation of the odds ratio (OR) for situations where individuals are paired and then randomized to either the treatment or the control condition. They show that the OR is equivalent to the risk ratio (RR) conditionally on pairs having different outcomes and describe two cases, calling them “parallel groups” and “matched pairs,” respectively. In the former case (authors define it as unmatched case, given that pairs are matched randomly), the OR is called “common OR,” and it is equal to: p1*(1−p2)/p2*(1−p1) (defining p1 and p2 as the probability of e vent for treated and controls, respectively), and in the latter case (defined as matched case, given within-pair independence does not hold anymore), the OR is called “general OR” and is equal to: p10/p01 (defining p10 and p01 as the probability of discordant pairs, with event for the treated in the former case and for the control in the latter one).

Source: Journal of Clinical Epidemiology - October 30, 2017 Category: Epidemiology Authors: Federico Tedeschi Tags: Letter to the Editor Source Type: research