One relative risk versus two odds ratios: implications for meta-analyses involving paired and unpaired binary data
Bibliographic record
Abstract
BACKGROUND: There are debates on whether the conditional odds ratio or marginal odds ratio should be used in meta-analysis involving both paired and unpaired binary data. Although statistically sound, both approaches result in overall odds ratios which are known to be less meaningful to consumers. PURPOSE: To show that while two odds ratios can be calculated in a pair-matched study, there is only one relative risk for such design, and to discuss the implications for meta-analysis involving both paired and unpaired binary data. METHODS: Algebra and an example, along with standard software for implementing relative risk regression models. RESULTS: The choice of relative risk as the effect measure in pair-matched design not only simplifies analysis and interpretation for individual studies, but makes mata-analysis involving both paired and unpaired studies straightforward. Pooling marginal odds ratios in a meta-analysis of diabetic retinopathy treatment resulted in a summarized odds ratio of 2.25 (95% CI 1.83-2.75), compared with that of 2.44 (95% CI 1.95-3.04) from pooling conditional odds ratios. In contrast, summarizing relative risks resulted in an overall effect measure of 1.09 (95% CI 1.06-1.11), implying the treatment reduces visual deterioration rate by 9%. CONCLUSION: Relative risk may be the first consideration in measuring effect for analyzing prospective studies with binary outcomes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.462 | 0.737 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.018 | 0.019 |
| Bibliometrics | 0.010 | 0.011 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.008 | 0.013 |
| Open science | 0.008 | 0.004 |
| Research integrity | 0.011 | 0.017 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".