Using James–Stein Estimators in Homogeneity Tests of the Risk Difference
Bibliographic record
Abstract
In multi-center clinical trials in which the success/failure of two treatments are measured, 2 × 2 × K contingency data are obtained, where K is the number of centers in the study. In this context, the risk difference may be preferred (over the odds ratio or relative risk) as a measure of the efficacy of the new treatment. To summarize the risk difference across centers, the estimated risk difference for each center must be comparable. Although several weighted least squares (WLS) tests of homogeneity of the risk difference have been proposed for the sparse data situation (1,2), none of these tests perform satisfactorily when each center has small samples. In the sparse data situation, the weights given to each center's risk difference estimate are imprecise and may be undefined. James–Stein estimates have been shown to be more precise (in terms of mean squared error) than their maximum likelihood counterparts. In this article, we investigate the use of James–Stein estimates for these weights. These estimates shrink the individual risk estimates towards the overall center mean and thus avoid problems encountered when risk estimates are zero or one. We use Monte Carlo simulations to show that using these estimates in the WLS test of homogeneity of risk differences improves their performance in terms of Type I error.
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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 | 0.162 | 0.513 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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; 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".