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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.082 | 0.361 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".