The Choice of a Noninformative Prior on Between-Study Variance Strongly Affects Predictions of Future Treatment Effect
Bibliographic record
Abstract
PURPOSE: Bayesian random-effects meta-analyses require the analyst to specify the prior distribution for between-study variance of the treatment effect. We assessed the sensitivity of prediction and other outputs of the meta-analysis to the choice of this prior. METHODS: We reanalyzed 7 published meta-analyses (5-14 trials) with rare (event rates <5%), moderate (15%-50%), and frequent binary outcomes (>50%). We examined 10 noninformative priors: inverse gamma on between-study variance (τ (2)), 2 uniforms on each of the between-study standard deviation (τ) and τ (2), uniform shrinkage on τ (2), DuMouchel shrinkage on τ, half-normal on τ (2), and half-normal priors on τ with large and small variances. For each analysis, we calculated the posterior distributions for τ, the population treatment effect in current studies, and the predicted treatment effect in a future study. We assessed goodness of fit using total residual deviance, the deviance information criterion, and predictive deviance (by cross-validations). RESULTS: According to total residual deviance, the best-fitting priors were uniform on τ (2). According to predictive deviance, half-normal on τ (2) and the shrinkage priors were optimal. Across analyses with the 10 priors, there were no important differences in the posteriors for the population treatment effect, but there were substantial differences in the posteriors for τ and predictions. The priors that fitted best according to predictive deviance resulted in less uncertainty around predictions of future treatment effect. CONCLUSIONS: In this sample of Bayesian meta-analyses with binary outcomes, the choice of noninformative prior for between-study variance affected model fit and the predictions of future treatment effect. When the predictive distribution is of interest, we highly recommend examination of multiple prior distributions for between-study variance, especially the half-normal on τ (2) and the shrinkage priors.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.076 | 0.068 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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; both teacher heads 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".