Prevalence threshold (ϕe) and the geometry of screening curves
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
The relationship between a screening tests' positive predictive value, ρ, and its target prevalence, ϕ, is proportional-though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity a and specificity b beyond which the rate of change of a test's ρ drops precipitously relative to ϕ. Herein, we show the mathematical model exploring this phenomenon and define the prevalence threshold (ϕe) point where this change occurs as: [Formula: see text] where ε = a + b. From the prevalence threshold we deduce a more generalized relationship between prevalence and positive predictive value as a function of ε, which represents a fundamental theorem of screening, herein defined as: [Formula: see text] Understanding the concepts described in this work can help contextualize the validity of screening tests in real time, and help guide the interpretation of different clinical scenarios in which screening is undertaken.
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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 | 0.000 | 0.006 |
| 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 | 0.000 | 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 it