Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine

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.

A Bayesian nonparametric meta-analysis model for estimating the reference interval

A reference interval represents the normative range for measurements from a healthy population. It plays an important role in laboratory testing, as well as in differentiating healthy from diseased patients. The reference interval based on a single study might not be applicable to a broader population. Meta-analysis can provide a more generalizable reference interval based on the combined population by synthesizing results from multiple studies. However, the assumptions of normally distributed underlying study-specific means and equal within-study variances, which are commonly used in existing methods, are strong and may not hold in practice. We propose a Bayesian nonparametric model with more flexible assumptions to extend random effects meta-analysis for estimating reference intervals. We illustrate through simulation studies and two real data examples the performance of our proposed approach when the assumptions of normally distributed study means and equal within-study variances do not hold.

Distribution-free hyperrectangular tolerance regions for setting multivariate reference regions in laboratory medicine

Reference regions are important in laboratory medicine to interpret the test results of patients, and usually given by tolerance regions. Tolerance regions ofp   ( ≥ 2 ) $$ p\;\left(\ge 2\right) $$ dimensions are highly desirable when the test results containsp $$ p $$ outcome measures. Nonparametric hyperrectangular tolerance regions are attractive in real problems due to their robustness with respect to the underlying distribution of the measurements and ease of intepretation, and methods to construct them have been recently provided by Young and Mathew [Stat Methods Med Res. 2020;29:3569-3585]. However, their validity is supported by a simulation study only. In this paper, nonparametric hyperrectangular tolerance regions are constructed by using Tukey's [Ann Math Stat. 1947;18:529-539; Ann Math Stat. 1948;19:30-39] elegant results of equivalence blocks. The validity of these new tolerance regions is proven mathematically in [Ann Math Stat. 1947;18:529-539; Ann Math Stat. 1948;19:30-39] under the only assumption that the underlying distribution of the measurements is continuous. The methodology is applied to analyze the kidney function problem considered in Young and Mathew [Stat Methods Med Res. 2020;29:3569-3585].