Importance and Uncertainty of λ -Estimation for Box–Cox Transformations to Compute and Verify Reference Intervals in Laboratory Medicine

Frank Klawonn (), Neele Riekeberg and Georg Hoffmann
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Frank Klawonn: Institute for Information Engineering, Ostfalia University, 38302 Braunschweig, Germany
Neele Riekeberg: Institute for Information Engineering, Ostfalia University, 38302 Braunschweig, Germany
Georg Hoffmann: Medizinischer Fachverlag Trillium GmbH, 82284 Grafrath, Germany

Stats, 2024, vol. 7, issue 1, 1-13

Abstract: Reference intervals play an important role in medicine, for instance, for the interpretation of blood test results. They are defined as the central 95% values of a healthy population and are often stratified by sex and age. In recent years, so-called indirect methods for the computation and validation of reference intervals have gained importance. Indirect methods use all values from a laboratory, including the pathological cases, and try to identify the healthy sub-population in the mixture of values. This is only possible under certain model assumptions, i.e., that the majority of the values represent non-pathological values and that the non-pathological values follow a normal distribution after a suitable transformation, commonly a Box–Cox transformation, rendering the parameter λ of the Box–Cox transformation as a nuisance parameter for the estimation of the reference interval. Although indirect methods put high effort on the estimation of λ , they come to very different estimates for λ , even though the estimated reference intervals are quite coherent. Our theoretical considerations and Monte-Carlo simulations show that overestimating λ can lead to intolerable deviations of the reference interval estimates, whereas λ = 0 produces usually acceptable estimates. For λ close to 1, its estimate has limited influence on the estimate for the reference interval, and with reasonable sample sizes, the uncertainty for the λ -estimate remains quite high.

Keywords: reference interval; Box–Cox transformation; Monte-Carlo simulation; nuisance parameter; confidence interval (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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