The multivariate reference range: an alternative interpretation of multi-test profiles.

To test the utility of multivariate interpretation of laboratory data, we developed a multivariate reference range based of the Mahalonobis distance (D2) measure. Results for 20 commonly measured clinical chemistry analytes were collated for two sophomore medical-school classes (118 and 143 individuals in 1979 and 1980, respectively). The data for each test were examined for fit to a gaussian (normal) distribution by using a Kolmogorov--Smirnov test. Those results discovered to have a non-normal distribution were "normalized" by used the of a two-stage log-exponential transform. After this transformation, the D2 distance for each student group followed the expected chi-square distribution with 20 degrees of freedom. For each student's D2 distance an associated chi-square percentile was derived, and a cutoff percentile (95%) was selected to differentiate multivariately the "normal" from "abnormal" test results. Whereas more than two-thirds of the students had univariate test abnormalities, fewer than 7% had abnormal multivariate D2 scores. Analysis showed that the multivariate reference range could sensitively detect minor variations of multiple analytes but could also be quite insensitive to highly abnormal results for a single analtye. The multivariate approach has promise as a tool to avoid unnecessary followup of falsely abnormal test results, but further study and validation in a clinical setting are required.