Applying a marginalized frailty model to competing risks
Bibliographic record
Abstract
The marginalized frailty model is often used for the analysis of correlated times in survival data. When only two correlated times are analyzed, this model is often referred to as the Clayton–Oakes model [7,22]. With time-to-event data, there may exist multiple end points (competing risks) suggesting that an analysis focusing on all available outcomes is of interest. The purpose of this work is to extend the single risk marginalized frailty model to the multiple risk setting via cause-specific hazards (CSH). The methods herein make use of the marginalized frailty model described by Pipper and Martinussen [24]. As such, this work uses the martingale theory to develop a likelihood based on estimating equations and observed histories. The proposed multivariate CSH model yields marginal regression parameter estimates while accommodating the clustering of outcomes. The multivariate CSH model can be fitted using a data augmentation algorithm described by Lunn and McNeil [21] or by fitting a series of single risk models for each of the competing risks. An example of the application of the multivariate CSH model is provided through the analysis of a family-based follow-up study of breast cancer with death in absence of breast cancer as a competing risk.
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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 | 0.014 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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; a candidate call from one source (direct Gemma or distilled Codex), 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".