Model-based ROC (mROC) curve: examining the effect of case-mix and model calibration on the ROC plot
Bibliographic record
Abstract
The performance of risk prediction models is often characterized in terms of discrimination and calibration. The Receiver Operating Characteristic (ROC) curve is widely used for evaluating model discrimination. When evaluating the performance of a risk prediction model in a new sample, the shape of the ROC curve is affected by both case-mix and the postulated model. Further, compared to discrimination, evaluating calibration has not received the same level of attention. Commonly used methods for model calibration involve subjective specification of smoothing or grouping. Leveraging the familiar ROC framework, we introduce the model-based ROC (mROC) curve to assess the calibration of a pre-specified model in a new sample. mROC curve is the ROC curve that should be observed if a pre-specified model is calibrated in the sample. We show the empirical ROC and mROC curves for a sample converge asymptotically if the model is calibrated in that sample. As a consequence, the mROC curve can be used to assess visually the effect of case-mix and model mis-calibration. Further, we propose a novel statistical test for calibration that does not require any smoothing or grouping. Simulations support the adequacy of the test. A case study puts these developments in a practical context. We conclude that mROC can easily be constructed and used to evaluate the effect of case-mix and model calibration on the ROC plot, thus adding to the utility of ROC curve analysis in the evaluation of risk prediction models. R code for the proposed methodology is provided (https://github.com/msadatsafavi/mROC/).
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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 | 0.104 | 0.379 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.008 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".