Graphical calibration curves and the integrated calibration index (ICI) for survival models
Why this work is in the frame
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Bibliographic record
Abstract
In the context of survival analysis, calibration refers to the agreement between predicted probabilities and observed event rates or frequencies of the outcome within a given duration of time. We aimed to describe and evaluate methods for graphically assessing the calibration of survival models. We focus on hazard regression models and restricted cubic splines in conjunction with a Cox proportional hazards model. We also describe modifications of the Integrated Calibration Index, of E50 and of E90. In this context, this is the average (respectively, median or 90th percentile) absolute difference between predicted survival probabilities and smoothed survival frequencies. We conducted a series of Monte Carlo simulations to evaluate the performance of these calibration measures when the underlying model has been correctly specified and under different types of model mis-specification. We illustrate the utility of calibration curves and the three calibration metrics by using them to compare the calibration of a Cox proportional hazards regression model with that of a random survival forest for predicting mortality in patients hospitalized with heart failure. Under a correctly specified regression model, differences between the two methods for constructing calibration curves were minimal, although the performance of the method based on restricted cubic splines tended to be slightly better. In contrast, under a mis-specified model, the smoothed calibration curved constructed using hazard regression tended to be closer to the true calibration curve. The use of calibration curves and of these numeric calibration metrics permits for a comprehensive comparison of the calibration of competing survival models.
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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 | 0.009 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it