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Understanding and reporting odds ratios as rate-ratio estimates in case-control studies
Steven Kerr1, Sander Greenland2, Karen Jeffrey1
1Centre for Medical Informatics, Usher Institute, The University of Edinburgh, Edinburgh, Scotland, UK.
Journal of Global Health
|September 15, 2023
Summary
In case-control studies, sample odds ratios (ORs) are not always consistent estimators for population rate ratios. Researchers must critically evaluate conditions ensuring ORs accurately represent rate ratios.
Area of Science:
- Epidemiology
- Biostatistics
Background:
- Confusion exists in health-science literature regarding the reporting of sample odds ratios (ORs) as estimated rate ratios in case-control studies.
- Historical literature provides definitive answers on when sample ORs consistently estimate population rate ratios.
Purpose of the Study:
- To clarify the conditions under which sample odds ratios (ORs) from case-control studies are consistent estimators for population rate ratios.
- To illustrate the disparities between sample ORs and population rate ratios when these conditions are not met.
Main Methods:
- Review of historical literature on the consistency of ORs as rate ratio estimators.
- Use of numerical examples to demonstrate the magnitude of disparity between sample ORs and population rate ratios.
- Analysis of conditions required for ORs to be consistent estimators, including sampling strategies and hazard ratio constancy.
Main Results:
- Sampling controls from those at risk is insufficient for ORs to consistently estimate rate ratios.
- Constancy of exposure prevalence and hazard ratio (HR) over time is sufficient if sampling time is uncontrolled; HR constancy suffices if time is controlled.
- Failure to meet these conditions introduces systematic error in ORs as estimates of population rate ratios.
Conclusions:
- Researchers must understand and critically evaluate the conditions for interpreting estimates from case-control studies as consistent population parameters.
- Accurate interpretation of ORs requires careful consideration of study design and statistical assumptions.
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