VOLUME 19 NUMBER 1 (January to June 2026)

Robust biweight M-estimator-based simultaneous prediction intervals with applications in laboratory medicine

Reference intervals are among the most widely used tools in medical decision-making. Moreover, in diagnosing complex diseases based on multiple analytes, multivariate reference regions (MRRs) are indispensable. In such cases, MRRs are more appropriate than separate univariate reference intervals because the latter fail to account for the correlations among the analytes. The usual approach to construct MRRs is through an ellipsoidal reference region under multivariate normality. However, laboratory practitioners are reluctant to use ellipsoidal MRRs since such MRRs cannot detect component-wise outliers. To address this problem, this study proposes a methodology to construct rectangular MRRs by computing robust simultaneous prediction intervals through an approach that makes use of Tukey’s biweight estimator. Designed for symmetric multivariate distributions, the proposed procedure relaxes the multivariate normality assumption, which is a common assumption in computing reference regions. This study makes use of a nonparametric bootstrap solution to estimate a common prediction factor. The performance of the proposed procedure is evaluated through coverage probabilities and compared against a benchmark methodology. The results indicate that the proposed methodology shows consistently accurate performance regardless of the underlying data distribution, which suggests that it may be applied to data coming from any symmetric distribution.