Testing Covariates Effects on Bivariate Reference Regions

Correlated clinical measurements are routinely interpreted via comparisons with univariate reference intervals examined side by side. Multivariate reference regions (MVRs), i.e., regions that characterize the distribution of multivariate results, have been proposed as a more adequate interpretation tool in such situations. However, MVR estimation methods have not yet been fully developed and are rarely used by physicians. The multivariate distribution of correlated measurements might change with certain patient characteristics (e.g., age or gender), and their effect on the shape of an MVR can be complex, involving interaction terms. For instance, the reference region shape for a given set of continuous covariates might vary across groups with respect to the value of a categorical variable. This paper examines the use of a bootstrap-based hypothesis test for examining the effect of covariates on bivariate reference regions, testing the effect of factor-by-region interactions. An estimation algorithm based on smoothing splines was used to construct the bivariate reference region for a pediatric anthropometric dataset, and the bootstrapping procedure was used to determine the effect of age and gender on the shape of the reference region. (Height, weight) bivariate distribution was shown to depend on the interaction between age and gender. The bootstrapping procedure confirmed that a bivariate growth chart is desirable over univariate age-gender body mass index (BMI) percentile curves. Whereas the well-known BMI criterion detects only two atypical situations (i.e., underweight, overweight), the bootstrap-tested bivariate reference region detected abnormally large or small body frames for different ages and genders.