Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects
Bibliographic record
Abstract
BACKGROUND: A 2-stage randomized trial design, incorporating participant choice, provides unbiased estimates of the effects of the treatment or intervention (treatment effect), the difference between outcomes for participants who prefer one treatment compared with another (selection effect), and the interaction between participants' preferences for treatment and the treatment actually received (preference effect). It is important to ensure that such trials are adequately powered to estimate these effects. SAMPLE SIZE FORMULAS: This paper presents methods for determining the required sample sizes for estimating treatment, selection, and preference effects. We demonstrate the changes in sample size as various key parameters are changed. In general, approximately twice as many participants (in total) are needed to have equivalent power for detecting both treatment and selection/preference effects compared with a trial of the treatment effect alone. PRIMARY SCREENING EXAMPLE: We illustrate their application for the design of a primary screening trial comparing human papillomavirus DNA testing versus cervical screening (by Pap smear). Our example would require 520 participants to have 80% power to detect moderate-sized preference and selection effects and a small to moderate treatment effect. CONCLUSIONS: With the growing interest in understanding treatment choices and with the use of decision aids, well-designed and adequately powered 2-stage randomized trial designs offer the opportunity to determine the effects of participants' preferences. Our sample size formulas will help future studies ensure that they have adequate power to detect selection and preference effects.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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; a candidate call from one teacher head, 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".