The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: A simulation study
Bibliographic record
Abstract
BACKGROUND: Meta-analysis of continuous outcomes traditionally uses mean difference (MD) or standardized mean difference (SMD; mean difference in pooled standard deviation (SD) units). We recently used an alternative ratio of mean values (RoM) method, calculating RoM for each study and estimating its variance by the delta method. SMD and RoM allow pooling of outcomes expressed in different units and comparisons of effect sizes across interventions, but RoM interpretation does not require knowledge of the pooled SD, a quantity generally unknown to clinicians. OBJECTIVES AND METHODS: To evaluate performance characteristics of MD, SMD and RoM using simulated data sets and representative parameters. RESULTS: MD was relatively bias-free. SMD exhibited bias (~5%) towards no effect in scenarios with few patients per trial (n = 10). RoM was bias-free except for some scenarios with broad distributions (SD 70% of mean value) and medium-to-large effect sizes (0.5-0.8 pooled SD units), for which bias ranged from -4 to 2% (negative sign denotes bias towards no effect). Coverage was as expected for all effect measures in all scenarios with minimal bias. RoM scenarios with bias towards no effect exceeding 1.5% demonstrated lower coverage of the 95% confidence interval than MD (89-92% vs. 92-94%). Statistical power was similar. Compared to MD, simulated heterogeneity estimates for SMD and RoM were lower in scenarios with bias because of decreased weighting of extreme values. Otherwise, heterogeneity was similar among methods. CONCLUSION: Simulation suggests that RoM exhibits comparable performance characteristics to MD and SMD. Favourable statistical properties and potentially simplified clinical interpretation justify the ratio of means method as an option for pooling continuous 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 | 0.124 | 0.263 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.006 | 0.015 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".