Comparing multivariate and univariate subject-specific reference regions for blood constituents in healthy persons

We examined the comparative behavior of subject-specific multivariate and univariate reference regions, using both computer-generated data and serial (semi-annual) measurements of selected analytes in subjects from a large health-maintenance program. Univariate studies under both homeostatic and random-walk time-series models were helpful in defining expected results, but only the homeostatic model was used in multivariate as well as univariate forms. Analysis of the computer-generated data and the real biochemical series produced similar findings, which showed the multivariate subject-specific reference region to be much more conservative than corresponding univariate intervals. That is, a multidimensional point of p correlated observations is quite likely to lie within the individual's multivariate reference region (based on past observation vectors), even when one or more of the observations lie outside their separate reference intervals for that individual. One consequence of this high specificity against univariate false positives in a large surveillance program is a higher than expected proportion of positive multivariate vectors in which none of the values lie outside their univariate ranges. Thus, although the development of multivariate reference regions should be encouraged, they should be used in conjunction with, not instead of, univariate ranges.