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

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 ( (Formula presented.) ), meaning that there are no quantitative data for these values, only the information that they are smaller than the (Formula presented.). Standard statistical methods for reference interval estimation are not designed to incorporate values below the (Formula presented.). 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 (Formula presented.). 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 (Formula presented.) contribute a substantial proportion to the data.