Regression-based rectangular multivariate normal prediction regions for setting reference regions

Abstract

Reference intervals are among the most widely used decision-making tools in the medical field, and are invaluable in the interpretation of laboratory test results. Moreover, when several biochemical analytes are needed to diagnose the same condition, a multivariate reference region is necessary to take the correlations among the analytes into account. Traditionally, multivariate reference regions have been constructed as ellipsoidal in shape. Since such regions are difficult to interpret and cannot detect the outlyingness of a specific analyte, many authors prefer rectangular regions. Reference intervals and regions may also depend on covariates such as age and sex. The covariate values are often random quantities since they are typically not controlled in reference interval determination studies. In this study, we propose procedures to construct rectangular multivariate reference regions that incorporate random covariate information. The reference regions are computed in a multivariate normal setting, using a prediction region criterion. A parametric bootstrap approach is employed to compute the prediction factor. Numerical results show that the parametric bootstrap approach is quite accurate, with coverage probabilities close to the desired nominal value. Finally, we apply the proposed methods to real-life data from a study to compute covariate-dependent reference regions for insulin-like growth factors.