Regression-based rectangular tolerance regions as reference regions in laboratory medicine

Reference ranges are invaluable in laboratory medicine, as these are indispensable tools for the interpretation of laboratory test results. When assessing measurements on a single analyte, univariate reference intervals are required. In many cases, however, measurements on several analytes are needed by medical practitioners to diagnose more complicated conditions such as kidney function or liver function. For such cases, it is recommended to use multivariate reference regions, which account for the cross-correlations among the analytes. Traditionally, multivariate reference regions (MRRs) have been constructed as ellipsoidal regions. The disadvantage of such regions is that they are unable to detect component-wise outlying measurements. Because of this, rectangular reference regions have recently been put forward in the literature. In this study, we develop methodologies to compute rectangular MRRs that incorporate covariate information, which are often necessary in evaluating laboratory test results. We construct the reference region using tolerance-based criteria so that the resulting region possesses the multiple use property. Results show that the proposed regions yield coverage probabilities that are accurate and are robust to the sample size. Finally, we apply the proposed procedures to a real-life example on the computation of an MRR for three components of the insulin-like growth factor system.