Statistical inference for the two‐sample problem under likelihood ratio ordering, with application to the ROC curve estimation
Bibliographic record
Abstract
The receiver operating characteristic (ROC) curve is a powerful statistical tool and has been widely applied in medical research. In the ROC curve estimation, a commonly used assumption is that larger the biomarker value, greater severity the disease. In this article, we mathematically interpret "greater severity of the disease" as "larger probability of being diseased." This in turn is equivalent to assume the likelihood ratio ordering of the biomarker between the diseased and healthy individuals. With this assumption, we first propose a Bernstein polynomial method to model the distributions of both samples; we then estimate the distributions by the maximum empirical likelihood principle. The ROC curve estimate and the associated summary statistics are obtained subsequently. Theoretically, we establish the asymptotic consistency of our estimators. Via extensive numerical studies, we compare the performance of our method with competitive methods. The application of our method is illustrated by a real-data example.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.052 | 0.236 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".