Properties of the Projected Length of the Curve (PLC) and Area Swept out by the Curve (ASC) Indices for the Receiver Operating Characteristic (SROC) Curve
Bibliographic record
Abstract
Several measures have been proposed to summarize the Receiver Operating Characteristic (ROC) curve, including the Projected Length of the Curve (PLC) and the Area Swept out by the Curve (ASC). These indices were first proposed by Lee (Epidemiology 1996; 7:605-611) to avoid certain deficiencies of the traditional Area Under the Curve (AUC) summary measure. More recently meta-analysis methods for assessing diagnostic test accuracy have been developed and the Summary Receiver Operating Characteristic (SROC) curve has been recommended to represent the performance of a diagnostic test. Some properties of the SROC curve were discussed by Walter (Statist. Med. 2002; 21:1237-1256). Here we extend that work to focus on properties of PLC and ASC in the context of SROC curve. Mathematical expressions for these two indices and their variances are derived in terms of the overall diagnostic odds ratio and the magnitude of inter-study heterogeneity in the odds ratio. Expressions for PLC and ASC and their variances are easily computed in homogeneous studies, and their values provide good approximations to the corresponding values for heterogeneous studies in most practical situations. General variances of PLC and ASC are derived by using delta methods, and are found to be smaller if the odds ratio is large. The methods are illustrated using data from two studies, the first being a meta-analysis on the detection of metastases in cervical cancer patients, and the second being a single study of HPV infection and pre-invasive cervical lesions.
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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 | 0.002 |
| 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".