Using total correlation to discover related clusters of clinical chemistry parameters

Clinical chemistry tests are widely used in medical diagnosis. Physicians typically interpret them in a univariate sense, by comparing each parameter to a reference interval, however, their correlation structure may also be interesting, as it can shed light on common physiologic or pathological mechanisms. The correlation analysis of such parameters is hindered by two problems: the relationships between the variables are sometimes non-linear and of unknown functional form, and the number of such variables is high, making the use of classical tools infeasible. This paper presents a novel approach to address both problems. It uses an information theory-based measure called total correlation to quantify the dependence between clinical chemistry variables, as total correlation can detect any dependence between the variables, non-linear or even non-monotone ones as well, hence it is completely insensitive to the actual nature of the relationship. Another advantage is that is can quantify dependence not only between pairs of variables, but between larger groups of variables as well. By the virtue of this fact, a novel approach is presented that can handle the high dimensionality of clinical chemistry parameters. The approach is implemented and illustrated on a real-life database from the representative US public health survey NHANES.