Evaluation of univariate ranges with a multivariate standard

In medical decision making generally many test results are produced. Several authors have discussed the problems involved and concluded that a multivariate approach often has to be preferred. Because until now such an approach has not often been used in practice and qualitative arguments for a multivariate approach are seldom supported by quantitative results, in this paper the use of univariate reference ranges is evaluated with a multivariate range as the standard, taking into account correlation coefficients. Probabilities of false positive and false negative results and predictive values are computed and displayed for decision rules based on two separate test results with an elliptic region as the gold standard. The conclusion is that the quality of the univariate approach is dependent on the correlation coefficient and on the choice of the decision rule. In the most important cases, however, it falls short compared with a multivariate approach. For example, the probability that a univariate positive result is false is around 50% for all values of the correlation coefficient, which is unacceptably high.