Estimation of diagnostic test accuracy: A “Rule of Three” for data with repeated observations but without a gold standard
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
This article considers how to estimate the accuracy of a diagnostic test when there are repeated observations, but without the availability of a gold standard or reference test. We identify conditions under which the structure of the observed data is rich enough to provide sufficient degrees of freedom, such that a suitable latent class model can be fitted with identifiable accuracy parameters. We show that a Rule of Three applies, specifying that accuracy can be evaluated as long as there are at least three observations per individual with the given test. This rule also applies if the three observations arise from combinations of different test methods, or from a sequential design in which individuals are tested for a maximum number of times with the same test but stopping if a positive (or negative) result occurs. The rule pertains to tests having an arbitrary number of response categories. Accuracy is evaluated by parameters reflecting rates of misclassification among the response categories, and the model also provides estimates of the underlying distribution of the true disease state. These ideas are illustrated by data from two medical studies. Issues discussed include the advantages and disadvantages of analyzing the response variable as binary or multinomial, as well as the feasibility of testing goodness of fit when the model incorporates a large number of parameters. Comparisons are possible between models that do or do not assume equal accuracy rates for the observations, and between models where certain misclassification parameters are or are not assumed to be zero.
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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 | 0.001 | 0.282 |
| 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) | 0.000 | 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