Recalibrating single-study effect sizes using hierarchical Bayesian models
Bibliographic record
Abstract
Introduction There are growing concerns about commonly inflated effect sizes in small neuroimaging studies, yet no study has addressed recalibrating effect size estimates for small samples. To tackle this issue, we propose a hierarchical Bayesian model to adjust the magnitude of single-study effect sizes while incorporating a tailored estimation of sampling variance. Methods We estimated the effect sizes of case-control differences on brain structural features between individuals who were dependent on alcohol, nicotine, cocaine, methamphetamine, or cannabis and non-dependent participants for 21 individual studies (Total cases: 903; Total controls: 996). Then, the study-specific effect sizes were modeled using a hierarchical Bayesian approach in which the parameters of the study-specific effect size distributions were sampled from a higher-order overarching distribution. The posterior distribution of the overarching and study-specific parameters was approximated using the Gibbs sampling method. Results The results showed shrinkage of the posterior distribution of the study-specific estimates toward the overarching estimates given the original effect sizes observed in individual studies. Differences between the original effect sizes (i.e., Cohen's d) and the point estimate of the posterior distribution ranged from 0 to 0.97. The magnitude of adjustment was negatively correlated with the sample size (r = −0.27, p < 0.001) and positively correlated with empirically estimated sampling variance (r = 0.40, p < 0.001), suggesting studies with smaller samples and larger sampling variance tended to have greater adjustments. Discussion Our findings demonstrate the utility of the hierarchical Bayesian model in recalibrating single-study effect sizes using information from similar studies. This suggests that Bayesian utilization of existing knowledge can be an effective alternative approach to improve the effect size estimation in individual studies, particularly for those with smaller samples.
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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 | 0.061 | 0.021 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".