How Gaussian mixture modelling can help to verify reference intervals from laboratory data with a high proportion of pathological values

Abstract

Objectives Although there are several indirect methods that can be used to verify reference limits, they have a common weakness in that they assume a low proportion of pathological values. This paper investigates whether a Gaussian decomposition algorithm can identify the non-pathological fraction even if it is not the main subset of mixed data. Methods All investigations are carried out in the R programming environment. The mclust package is used for Gaussian mixture modelling via the expectation maximization (EM) algorithm. For right-skewed distributions, logarithms of the original values are taken to approximate the Gaussian model. We use the Bayesian information criterion (BIC) for evaluation of the results. The reflimR and refineR packages serve as comparison procedures. Results We generate synthetic data mixtures with known normal distributions to demonstrate the feasibility and reliability of our approach. Application of the algorithm to real data from a Nigerian and a German population produces results, which help to interpret reference intervals of reflimR and refineR that are obviously too wide. In the first example, the mclust analysis of hemoglobin in Nigerian women supports the medical hypothesis that an anemia rate of more than 50 % leads to falsely low reference limits. Our algorithm proposes various scenarios based on the BIC values, one of which suggests reference limits that are close to published data for Nigeria but significantly lower than those established for the Caucasian population. In the second example, the standard statistical analysis of creatine kinase in German patients with predominantly cardiac diseases yields a reference interval that is clearly too wide. With mclust we identify overlapping fractions that explain this false result. Conclusions Gaussian mixture modelling does not replace standard methods for reference interval estimation but is a valuable adjunct when these methods produce discrepant or implausible results.