Estimating the Area under the ROC Curve with Modified Profile Likelihoods
Bibliographic record
Abstract
Receiver operating characteristic (ROC) curves are a frequent tool to study the discriminating ability of a certain characteristic. The area under the ROC curve (AUC) is a widely used measure of statistical accuracy of continuous markers for diagnostic tests, and has the advantage of providing a single summary index of overall performance of the test. Recent studies have shown some critical issues related to traditional point and interval estimates for the AUC, especially for small samples, more complex models, unbalanced samples or values near the boundary of the parameter space, i.e., when the AUC approaches the values 0.5 or 1.Parametric models for the AUC have shown to be powerful when the underlying distributional assumptions are not misspecified. However, in the above circumstances parametric inference may be not accurate, sometimes yielding misleading conclusions. The objective of the paper is to propose an alternative inferential approach based on modified profile likelihoods, which provides more accurate statistical results in any parametric settings, including the above circumstances. The proposed method is illustrated for the binormal model, but can potentially be used in any other complex model and for any other parametric distribution. We report simulation studies to show the improved performance of the proposed approach, when compared to classical first-order likelihood theory. An application to real-life data in a small sample setting is also discussed, to provide practical guidelines.
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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 | 0.000 |
| 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 | 0.000 |
| 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".