Modeling conditional reference regions: Application to glycemic markers

Abstract

Many clinical decisions are taken based on the results of continuous diagnostic tests. Usually, only the results of one single test is taken into consideration, the interpretation of which requires a reference range for the healthy population. However, the use of two different tests, can be necessary in the diagnosis of certain diseases. This obliges a bivariate reference region be available for their interpretation. It should also be remembered that reference regions may depend on patient variables (eg, age and sex) independent of the suspected disease. However, few proposals have been made regarding the statistical modeling of such reference regions, and those put forward have always assumed a Gaussian distribution, which can be rather restrictive. The present work describes a new statistical method that allows such reference regions to be estimated with no insistence on the results being normally distributed. The proposed method is based on a bivariate location‐scale model that provides probabilistic regions covering a specific percentage of the bivariate data, dependent on certain covariates. The reference region is estimated nonparametrically and the nonlinear effects of continuous covariates via polynomial kernel smoothers in additive models. The bivariate model is estimated using a backfitting algorithm, and the optimal smoothing parameters of the kernel smoothers selected by cross‐validation. The model performed satisfactorily in simulation studies under the assumption of non‐Gaussian conditions. Finally, the proposed methodology was found to be useful in estimating a reference region for two continuous diagnostic tests for diabetes (fasting plasma glucose and glycated hemoglobin), taking into account the age of the patient.

Multivariate reference and tolerance regions based on conditional transformation models: Application to glycemic markers

“…For the tolerance region, we considered 𝛼 = 0.95. Additionally, the MCTMs conditional probabilistic regions were compared, in terms of RMSE, with two previous models: the Young & Mathew (2020) proposal and the refreg model (Lado-Baleato et al, 2021). The former is based on estimating by multiple linear regression and the latter on a location-scale bivariate regression model plus the nonparametric estimation of the multivariate reference region.…”

“…Based on the structure of MCTMs, estimates were made for the probabilistic regions covering different percentages of the bivariate distribution of the responses depending on covariate values. The literature contains some recent proposals in this respect (Lado‐Baleato et al., 2021; Young & Mathew, 2020), but the first of these is valid only for homoscedastic data, and the latter assumes a linear correlation between responses. The conditional MVRs of MCTMs, however, aim to characterize which bivariate response values are more likely to be observed for each covariate value, with the advantage that they deal with nonlinear structures of dependence between the responses.…”

Refreg: An R Package for Estimating Conditional Reference Regions

“…This agrees with the non-linear effect of age on the expected means and variability of both markers. The conditional region coverage and the performance of the methodology have already been assessed (Lado-Baleato et al, 2021).…”