A Nonparametric Global Win Probability Approach to the Analysis and Sizing of Randomized Controlled Trials With Multiple Endpoints of Different Scales and Missing Data: Beyond O'Brien–Wei–Lachin
Bibliographic record
Abstract
Multiple primary endpoints are commonly used in randomized controlled trials to assess treatment effects. When the endpoints are measured on different scales, the O'Brien rank-sum test or the Wei-Lachin test for stochastic ordering may be used for hypothesis testing. However, the O'Brien-Wei-Lachin (OWL) approach is unable to handle missing data and adjust for baseline measurements. We present a nonparametric approach for data analysis that encompasses the OWL approach as a special case. Our approach is based on quantifying an endpoint-specific treatment effect using the probability that a participant in the treatment group has a better score than (or a win over) a participant in the control group. The average of the endpoint-specific win probabilities (WinPs), termed the global win probability (gWinP), is used to quantify the global treatment effect, with the null hypothesis gWinP = 0.50. Our approach involves converting the data for each endpoint to endpoint-specific win fractions, and modeling the win fractions using multivariate linear mixed models to obtain estimates of the endpoint-specific WinPs and the associated variance-covariance matrix. Focusing on confidence interval estimation for the gWinP, we derive sample size formulas for clinical trial design. Simulation results demonstrate that our approach performed well in terms of bias, interval coverage percentage, and assurance of achieving a pre-specified precision for the gWinP. Illustrative code for implementing the methods using SAS PROC RANK and PROC MIXED is provided.
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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 | 0.050 | 0.619 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.008 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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; 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".