Widespread Incorrect Implementation of the Hoffmann Method, the Correct Approach, and Modern Alternatives

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 sH 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.