Testing for a Sweet Spot in Randomized Trials
Bibliographic record
Abstract
Introduction Randomized trials recruit diverse patients, including some individuals who may be unresponsive to the treatment. Here we follow up on prior conceptual advances and introduce a specific method that does not rely on stratification analysis and that tests whether patients in the intermediate range of disease severity experience more relative benefit than patients at the extremes of disease severity (sweet spot). Methods We contrast linear models to sigmoidal models when describing associations between disease severity and accumulating treatment benefit. The Gompertz curve is highlighted as a specific sigmoidal curve along with the Akaike information criterion (AIC) as a measure of goodness of fit. This approach is then applied to a matched analysis of a published landmark randomized trial evaluating whether implantable defibrillators reduce overall mortality in cardiac patients ( n = 2,521). Results The linear model suggested a significant survival advantage across the spectrum of increasing disease severity (β = 0.0847, P < 0.001, AIC = 2,491). Similarly, the sigmoidal model suggested a significant survival advantage across the spectrum of disease severity (α = 93, β = 4.939, γ = 0.00316, P < 0.001 for all, AIC = 1,660). The discrepancy between the 2 models indicated worse goodness of fit with a linear model compared to a sigmoidal model (AIC: 2,491 v. 1,660, P < 0.001), thereby suggesting a sweet spot in the midrange of disease severity. Model cross-validation using computational statistics also confirmed the superior goodness of fit of the sigmoidal curve with a concentration of survival benefits for patients in the midrange of disease severity. Conclusion Systematic methods are available beyond simple stratification for identifying a sweet spot according to disease severity. The approach can assess whether some patients experience more relative benefit than other patients in a randomized trial. [Box: see text]
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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 | 0.589 | 0.780 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.012 | 0.013 |
| Bibliometrics | 0.008 | 0.009 |
| Science and technology studies | 0.002 | 0.029 |
| Scholarly communication | 0.012 | 0.016 |
| Open science | 0.009 | 0.008 |
| Research integrity | 0.016 | 0.016 |
| Insufficient payload (model declined to judge) | 0.018 | 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".