Randomised trials with provision for early stopping for benefit (or harm): The impact on the estimated treatment effect
Bibliographic record
Abstract
Stopping rules for clinical trials are primarily intended to control Type I error rates if interim analyses are planned, but less is known about the impact that potential stopping has on estimating treatment benefit. In this paper, we derive analytic expressions for (1) the over-estimation of benefit in studies that stop early, (2) the under-estimation of benefit in completed studies, and (3) the overall bias in studies with a stopping rule. We also examine the probability of stopping early and the situation in meta-analyses. Numerical evaluations show that the greatest concern is with over-estimation of benefit in stopped studies, especially if the probability of stopping early is small. The overall bias is usually less than 10% of the true benefit, and under-estimation in completed studies is also typically small. The probability of stopping depends on the true treatment effect and sample size. The magnitude of these effects depends on the particular rule adopted, but we show that the maximum overall bias is the same for all stopping rules. We also show that an essentially unbiased meta-analysis estimate of benefit can be recovered, even if some component studies have stopping rules. We illustrate these methods using data from three clinical trials. The results confirm our earlier empirical work on clinical trials. Investigators may consult our numerical results for guidance on potential mis-estimation and bias in the treatment effect if a stopping rule is adopted. Particular concern is warranted in studies that actually stop early, where interim results may be quite misleading.
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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 | 0.302 | 0.720 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.009 | 0.009 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.009 | 0.013 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.013 | 0.013 |
| 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".