Computing the polytomous discrimination index
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Polytomous regression models generalize logistic models for the case of a categorical outcome variable with more than two distinct categories. These models are currently used in clinical research, and it is essential to measure their abilities to distinguish between the categories of the outcome. In 2012, van Calster et al proposed the polytomous discrimination index (PDI) as an extension of the binary discrimination c-statistic to unordered polytomous regression. The PDI is a summary of the simultaneous discrimination between all outcome categories. Previous implementations of the PDI are not capable of running on "big data." This article shows that the PDI formula can be manipulated to depend only on the distributions of the predicted probabilities evaluated for each outcome category and within each observed level of the outcome, which substantially improves the computation time. We present a SAS macro and R function that can rapidly evaluate the PDI and its components. The routines are evaluated on several simulated datasets after varying the number of categories of the outcome and size of the data and two real-world large administrative health datasets. We compare PDI with two other discrimination indices: M-index and hypervolume under the manifold (HUM) on simulated examples. We describe situations where the PDI and HUM, indices based on multiple comparisons, are superior to the M-index, an index based on pairwise comparisons, to detect predictions that are no different than random selection or erroneous due to incorrect ranking.
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.
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 | 0.004 | 0.211 |
| 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) | 0.001 | 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