Widespread Incorrect Implementation of the Hoffmann Method, the Correct Approach, and Modern Alternatives
Bibliographic record
Abstract
Objectives: The Hoffmann method is a procedure for reference interval estimation using routine clinical results. Many authors incorrectly prepare Hoffmann plots on a linear rather than normal probability scale. We explore the consequences. Methods: This was investigated algebraically, by random number simulations (45 simulations, n = 100,000 each) and using clinical data sets. Strategies compared were: Hoffmann's method as originally and incorrectly implemented, Bhattacharya's method, and maximum likelihood (ML). All R source code and data sets are provided. Results: As the proportion of healthy individuals approaches 1, the incorrect approach generates reference interval estimates of approximately μH ± 1.19 σH delineating the central 77% of the healthy subpopulation, not the central 95%. Inappropriately narrow reference interval estimates were seen on random simulations and clinical data sets. ML methods performed best. Conclusions: The erroneous variant Hoffmann method should not be used. ML methods outperform others and are not restricted by Gaussian assumptions.
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| 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 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".