Sample Size Requirements to Test Subgroup-Specific Treatment Effects in Cluster-Randomized Trials
Bibliographic record
Abstract
Cluster-randomized trials (CRTs) often allocate intact clusters of participants to treatment or control conditions and are increasingly used to evaluate healthcare delivery interventions. While previous studies have developed sample size methods for testing confirmatory hypotheses of treatment effect heterogeneity in CRTs (i.e., targeting the difference between subgroup-specific treatment effects), sample size methods for testing the subgroup-specific treatment effects themselves have not received adequate attention-despite a rising interest in health equity considerations in CRTs. In this article, we develop formal methods for sample size and power analyses for testing subgroup-specific treatment effects in parallel-arm CRTs with a continuous outcome and a binary subgroup variable. We point out that the variances of the subgroup-specific treatment effect estimators and their covariance are given by weighted averages of the variance of the overall average treatment effect estimator and the variance of the heterogeneous treatment effect estimator. This analytical insight facilitates an explicit characterization of the requirements for both the omnibus test and the intersection-union test to achieve the desired level of power. Generalizations to allow for subgroup-specific variance structures are also discussed. We report on a simulation study to validate the proposed sample size methods and demonstrate that the empirical power corresponds well with the predicted power for both tests. The design and setting of the Umea Dementia and Exercise (UMDEX) CRT in older adults are used to illustrate our sample size methods.
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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 | 0.434 | 0.772 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.007 | 0.006 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.007 | 0.006 |
| Research integrity | 0.008 | 0.009 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".