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

Area of Science:

• Clinical Laboratory Science
• Biostatistics
• Medical Diagnostics

Background:

• Reference intervals are crucial for interpreting clinical laboratory results.
• The Hoffmann method is a common, though sometimes incorrectly applied, procedure for estimating these intervals.
• Accurate reference interval estimation impacts patient diagnosis and treatment.

Purpose of the Study:

• To investigate the consequences of incorrectly applying the Hoffmann method for reference interval estimation.
• To compare the performance of the incorrect Hoffmann method with other established methods, including Bhattacharya's method and maximum likelihood (ML).
• To evaluate these methods using both simulated and real-world clinical data.

Main Methods:

• Algebraic investigation of the Hoffmann method's assumptions.
• Extensive random number simulations (45 simulations, n = 100,000 each).
• Analysis of clinical data sets to compare estimation strategies.

Main Results:

• Incorrect Hoffmann method application yields reference intervals that capture only ~77% of the healthy subpopulation, not the desired 95%.
• Both simulations and clinical data demonstrated inappropriately narrow reference interval estimates with the erroneous Hoffmann method.
• Maximum likelihood (ML) methods demonstrated superior performance in reference interval estimation.

Conclusions:

• The variant Hoffmann method, when incorrectly implemented, should be avoided due to inaccurate reference interval generation.
• Maximum likelihood (ML) methods offer superior performance and are not limited by assumptions of data normality.
• Accurate reference interval estimation is vital, and ML methods provide a robust solution.