Understanding and reporting odds ratios as rate-ratio estimates in case-control studies

Kerr, Steven and Greenland, Sander and Jeffrey, Karen and Millington, Tristan and Bedston, Stuart and Ritchie, Sir Lewis and Simpson, Colin R and Fagbamigbe, Adeniyi Francis and Kurdi, Amanj and Robertson, Chris and Sheikh, Sir Aziz and Rudan, Igor (2023) Understanding and reporting odds ratios as rate-ratio estimates in case-control studies. Journal of Global Health, 13. 04101. ISSN 2047-2978 (https://doi.org/10.7189/jogh.13.04101)

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Background: We noted that there remains some confusion in the health-science literature on reporting sample odds ratios as estimated rate ratios in case-control studies. Methods: We recap historical literature that definitively answered the question of when sample odds ratios (ORs) from a case-control study are consistent estimators for population rate ratios. We use numerical examples to illustrate the magnitude of the disparity between sample ORs in a case-control study and population rate ratios when sufficient conditions for them to be equal are not satisfied. Results: We stress that in a case-control study, sampling controls from those still at risk at the time of outcome event of the index case is not sufficient for a sample OR to be a consistent estimator for an intelligible rate ratio. In such studies, constancy of the exposure prevalence together with constancy of the hazard ratio (HR) (i.e., the instantaneous rate ratio) over time is sufficient for this result if sampling time is not controlled; if time is controlled, constancy of the HR will suffice. We present numerical examples to illustrate how failure to satisfy these conditions adds a small systematic error to sample ORs as estimates of population rate ratios. Conclusions: We recommend that researchers understand and critically evaluate all conditions used to interpret their estimates as consistent for a population parameter in case-control studies.