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

Steven Kerr^#¹, Sander Greenland^#², Karen Jeffrey¹, Tristan Millington¹, Stuart Bedston³, Lewis Ritchie⁴, Colin R Simpson⁵, Adeniyi Francis Fagbamigbe⁶, Amanj Kurdi^{7

8

9

10}, Chris Robertson^{11

12}, Aziz Sheikh¹, Igor Rudan^{13

14}

Affiliations

¹ Centre for Medical Informatics, Usher Institute, The University of Edinburgh, Edinburgh, Scotland, UK.
² Department of Epidemiology and Department of Statistics, University of California, Los Angeles, California, USA.
³ Population Data Science, Swansea University Medical School, Swansea, Wales, UK.
⁴ Academic Primary Care, University of Aberdeen School of Medicine and Dentistry, Aberdeen, Scotland, UK.
⁵ Wellington Faculty of Health, Victoria University of Wellington, Wellington, NZ.
⁶ Institute of Applied Health Sciences, University of Aberdeen School of Medicine and Dentistry, Aberdeen, Scotland, UK.
⁷ Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, Scotland, UK.
⁸ Department of Clinical Pharmacy, College of Pharmacy, Hawler Medical University, Erbil, Iraq.
⁹ College of Pharmacy, Al-Kitab University, Kirkuk, Iraq.
¹⁰ School of Pharmacy, Sefako Makgatho Health Sciences University, Pretoria, South Africa.
¹¹ Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland.
¹² Public Health Scotland, Glasgow, Scotland, UK.
¹³ Centre for Global Health, Usher Institute, The University of Edinburgh, Edinburgh, Scotland, UK.
¹⁴ University College Algebra, Zagreb, Croatia.

^# Contributed equally.

PMID: 37712381
PMCID: PMC10502767
DOI: 10.7189/jogh.13.04101

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

Steven Kerr et al. J Glob Health. 2023.

. 2023 Sep 15:13:04101.

doi: 10.7189/jogh.13.04101.

Authors

Affiliations

¹ Centre for Medical Informatics, Usher Institute, The University of Edinburgh, Edinburgh, Scotland, UK.
² Department of Epidemiology and Department of Statistics, University of California, Los Angeles, California, USA.
³ Population Data Science, Swansea University Medical School, Swansea, Wales, UK.
⁴ Academic Primary Care, University of Aberdeen School of Medicine and Dentistry, Aberdeen, Scotland, UK.
⁵ Wellington Faculty of Health, Victoria University of Wellington, Wellington, NZ.
⁶ Institute of Applied Health Sciences, University of Aberdeen School of Medicine and Dentistry, Aberdeen, Scotland, UK.
⁷ Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, Scotland, UK.
⁸ Department of Clinical Pharmacy, College of Pharmacy, Hawler Medical University, Erbil, Iraq.
⁹ College of Pharmacy, Al-Kitab University, Kirkuk, Iraq.
¹⁰ School of Pharmacy, Sefako Makgatho Health Sciences University, Pretoria, South Africa.
¹¹ Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland.
¹² Public Health Scotland, Glasgow, Scotland, UK.
¹³ Centre for Global Health, Usher Institute, The University of Edinburgh, Edinburgh, Scotland, UK.
¹⁴ University College Algebra, Zagreb, Croatia.

^# Contributed equally.

PMID: 37712381
PMCID: PMC10502767
DOI: 10.7189/jogh.13.04101

Abstract

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.

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Conflict of interest statement

Disclosure of interest: The authors completed the ICMJE Disclosure of Interest Form (available upon request from the corresponding author) and declare the following activities and relationships: AS and CR are members of the Scottish Government’s CMO COVID-19 Advisory Group. IR is a member of the Croatian Government’s Scientific Committee on COVID-19 and co-Editor-in-Chief of the Journal of Global Health. AS and CR are members of NERVTAG’s risk stratification subgroup. CR is a member of SPI-M. AS is a member of AstraZeneca’s Thrombotic Thrombocytopenic Advisory Group and the Scottish Government’s Standing Committee on Pandemics. All roles are unremunerated. All other co-authors report no conflict of interests.

References

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

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

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Conflict of interest statement

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