A Robust Parameterization for Unbounded Covariates Within the Cox Proportional Hazards Model
Bibliographic record
Abstract
The Cox proportional hazards model is widely used in the analysis of medical data either for survival or time to a particular event. Factors and continuous covariates can be easily incorporated into the model and hazard ratios calculated. The model can however be distorted when extreme value observations occur within a continuous covariate and the hazard ratio can become extremely large. To overcome this, transformations of the covariate are often made, which can be simple, e.g. log, or more sophisticated such as the fitting of a fractional polynomial. This paper takes a different approach and makes a transformation based on the logistic function that has the property that the hazard ratio is bounded. The models are introduced and discussed. Model diagnostics based on Schoenfeld residuals and the influence function are established and then data from a pancreatic cancer trial are used to illustrate the model.
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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 | 0.008 | 0.072 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".