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

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 (H) 1.19 sigma(H) 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.