The Use of Frailty Hazard Models for Unrecognized Heterogeneity That Interacts with Treatment: Considerations of Efficiency and Power
Bibliographic record
Abstract
Increasingly, genetic studies of tumors of the same histologic diagnosis are elucidating subtypes that are distinct with respect to clinical endpoints such as response to treatment and survival. This raises concerns about the efficiency of using the simple log-rank test for analysis of treatment effect on survival in studies of possibly heterogeneous tumors. Furthermore, such studies, designed under the assumption of homogeneity, may be severely underpowered. We derive analytic approximations for the asymptotic relative efficiency of the simple log-rank test relative to the optimally weighted log-rank test and for the power of the simple log-rank test when applied to subjects with unobserved heterogeneity, as reflected in a continuous frailty, that may interact with treatment. Numerical studies demonstrate that the simple log-rank test may be quite inefficient if the frailty interacts with treatment. Further, there may be a substantial loss of power in the presence of the frailty with or without an interaction with treatment.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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".