Regression-based Rectangular Tolerance Regions as Reference Regions in Laboratory Medicine

Music City Center 

Reference ranges are essential tools in interpreting laboratory test results. In many situations, measurements on several analytes are needed by medical practitioners to diagnose complex conditions such as kidney function or liver function. In such situations, multivariate reference regions (MRRs), which account for the cross-correlations among the analytes, are preferred over univariate reference ranges. Traditionally, these MRRs have been constructed as ellipsoidal regions, with the disadvantage of not being able to detect component-wise outlying measurements. To address this problem, rectangular reference regions have recently been put forward in literature. This study develops methodologies to compute rectangular MRRs that incorporate covariate information, which are often vital in evaluating laboratory test results. We construct reference regions using tolerance-based criteria so that resulting regions possess the multiple use property. Results show that the proposed regions yield coverage probabilities that are accurate and robust to the sample size. These procedures are then applied to a real-life example for three components of the insulin-like growth factor system.

reference intervals

tolerance regions

multivariate reference region

parametric bootstrap

laboratory medicine 

Section on Statistical Computing