Sample size considerations for assessing treatment effect heterogeneity in randomized trials with heterogeneous intracluster correlations and variances
Bibliographic record
Abstract
An important consideration in the design and analysis of randomized trials is the need to account for outcome observations being positively correlated within groups or clusters. Two notable types of designs with this consideration are individually randomized group treatment trials and cluster randomized trials. While sample size methods for testing the average treatment effect are available for both types of designs, methods for detecting treatment effect modification are relatively limited. In this article, we present new sample size formulas for testing treatment effect modification based on either a univariate or multivariate effect modifier in both individually randomized group treatment and cluster randomized trials with a continuous outcome but any types of effect modifier, while accounting for differences across study arms in the outcome variance, outcome intracluster correlation coefficient (ICC) and the cluster size. We consider cases where the effect modifier can be measured at either the individual level or cluster level, and with a univariate effect modifier, our closed-form sample size expressions provide insights into the optimal allocation of groups or clusters to maximize design efficiency. Overall, our results show that the required sample size for testing treatment effect heterogeneity with an individual-level effect modifier can be affected by unequal ICCs and variances between arms, and accounting for such between-arm heterogeneity can lead to more accurate sample size determination. We use simulations to validate our sample size formulas and illustrate their application in the context of two real trials: an individually randomized group treatment trial (the AWARE study) and a cluster randomized trial (the K-DPP study).
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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 | 0.271 | 0.682 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.005 | 0.008 |
| Insufficient payload (model declined to judge) | 0.005 | 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; 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".