The Impact of Violation of the Proportional Hazards Assumption on the Calibration of the Cox Proportional Hazards Model
Bibliographic record
Abstract
The Cox proportional hazards regression model is frequently used to develop clinical prediction models for time-to-event outcomes, allowing clinicians to estimate an individual's risk of experiencing the outcome within specified time horizons (e.g., estimate an individual's 10-year risk of death). The Cox regression model models the association between covariates and the hazard of the outcome. A key assumption of the Cox model is the proportional hazards assumption: the ratio of the hazard function for any two individuals is constant over time, and the ratio is a function of only their covariates and the regression coefficients. Calibration is an important aspect of the validation of clinical prediction models. Calibration refers to the concordance between predicted and observed risk. The impact of the violation of the proportional hazards assumption on the calibration of clinical prediction models developed using the Cox model has not been examined. We conducted a set of Monte Carlo simulations to assess the impact of the magnitude of the violation of the proportional hazards assumption on the calibration of the Cox model. We compared the calibration of predictions obtained using a Cox regression model that ignored the violation of the proportional hazards assumption with those obtained using accelerated failure time (AFT) models, Royston and Parmar's spline-based parametric survival models, and generalized linear models using pseudo-observations. We found that violation of the proportional hazards assumption had negligible impact on the calibration of predictions obtained using a Cox 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 | 0.001 | 0.001 |
| 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 | 0.000 | 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".