The Odds Ratio is "portable" across baseline risk but not the Relative Risk: Time to do away with the log link in binomial regression

Abstract

Objectives: In a recent paper we suggest that the relative risk (RR) be replaced with the odds ratio (OR) as the effect measure of choice in clinical epidemiology. In response, Chu, and colleagues raise several points that argue for the status quo. In this paper, we respond to their response.

Study designs and settings: We use the same examples given by Chu and colleagues to recompute estimates of effect and demonstrate the problem with the RR.

Results: We reaffirm the following findings: a) the OR and RR measure different things and their numerical difference is only important if misinterpreted b) this potential misinterpretation is a trivial issue compared to the lack of portability of the RR c) the same examples reaffirm non-portability of the RR and demonstrate how misleading the results might be in contrast to the OR, which is independent of the baseline risk d) the concept of non-collapsibility for the OR should be expected in the presence of a non-confounding risk factor, and is not a bias e) the log link in regression models that generate RRs as well as the use of RRs in meta-analysis is shown to be problematic using the same examples.

Conclusion: The OR should replace the RR in clinical research and meta-analyses though there should be conversion of the end product into ratios or differences of risk, solely, for interpretation. To this end we provide a Stata module (logittorisk) for this purpose.

Keywords: Binary outcome; Binomial regression; Effect measure; Meta-analysis; Non-collapsibility; Odds ratio; Relative risk; Risk difference.