reflimLOD: A Modified reflimR Approach for Estimating Reference Limits with Tolerance for Values Below the Lower Limit of Detection (LOD)

Frank Klawonn (), Georg Hoffmann, Stefan Holdenrieder and Inga Trulson
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Frank Klawonn: Institute for Information Engineering, Ostfalia University, 38302 Braunschweig, Germany
Georg Hoffmann: Medizinischer Fachverlag Trillium GmbH, 82284 Grafrath, Germany
Stefan Holdenrieder: Institute of Laboratory Medicine, German Heart Center Munich, 80636 München, Germany
Inga Trulson: Institute of Laboratory Medicine, German Heart Center Munich, 80636 München, Germany

Stats, 2024, vol. 7, issue 4, 1-19

Abstract: Reference intervals are indispensable for the interpretation of medical laboratory results to distinguish “normal” from “pathological” values. Recently, indirect methods have been published, which estimate reference intervals from a mixture of normal and pathological values based on certain statistical assumptions on the distribution of the values from the healthy population. Some analytes face the problem that a significant proportion of the measurements are below the limit of detection ( LOD ), meaning that there are no quantitative data for these values, only the information that they are smaller than the LOD . Standard statistical methods for reference interval estimation are not designed to incorporate values below the LOD . We propose two variants of the indirect method reflimR—a quantile- and maximum likelihood-based estimator—that are able to cope with values below the LOD . We show, based on theoretical analyses, simulation experiments, and real data, that our approach yields good estimates for the reference interval, even when the values below the LOD contribute a substantial proportion to the data.

Keywords: reference interval; limit of detection; Box–Cox transformation; maximum likelihood estimator (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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