How big is a big hazard ratio in clinical trials?
Bibliographic record
Abstract
Background: The hazard ratio has been widely used as an index of effect size in clinical trials for time-to-event data. The use of the Cox proportional hazards models and other hazard centered models is ubiquitous in clinical trials for time-to-event data. The relativity of effect sizes (small, medium, large) has been widely discussed and accepted when comparing magnitude of association for continuous and categorical data, but not yet for time-to-event outcomes. Methods: We review published hazard ratios, investigate the relationships among HR, relative risk (RR), odds ratio (OR), and Cohen’s d, and calculate the corresponding HRs for given event rate in control group ( ) by adding standard normal deviation with 0.2 (small), 0.5 (medium) and 0.8 (large) to the event rate in the case group ( based on equation . Results: Our results indicate that HRs are from 1.68 to 1.16 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.2 (small). HRs are ranged between 3.43 and 1.43 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.5 (medium), HRs are valued between 6.52 and 1.73 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.8 (large). Conclusions: This study provides general guidelines in interpreting the magnitudes of HRs for time-to-event data in clinical trials.
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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 | 0.454 | 0.816 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.011 | 0.008 |
| Bibliometrics | 0.008 | 0.010 |
| Science and technology studies | 0.002 | 0.012 |
| Scholarly communication | 0.012 | 0.022 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.008 | 0.012 |
| Insufficient payload (model declined to judge) | 0.006 | 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".