[Quasi-distribution-free multivariate assessment of clinico-chemical patient data using of van der Waerden's...

A reference group (252 males, 436 females) and a group of patients with primary hyperparathyroidism (34 males, 67 females) and cirrhosis of the liver (33 males) were subjected to a multivariate data assessment; the analyses were performed on the Technicon autoanalyzer SMA 12/60 (sodium, potassium, chloride, total protein, albumin, inorganic phosphorus, cholesterol, urea nitrogen, calcium, creatinine, bilirubin, uric acid) and the SMA 6 plus (iron, copper, magnesium, alkaline phosphatase, acid phosphatase, glucose). A multivariate test statistic containing age as a regressor variable was used, thus correcting for age. Derivation of the test statistic required multivariate normality of the distributions of the clinical-chemical values, a condition which is generally not fulfilled in the data of patients. In order to arrive at the multivariate normality of the distributions, we applied the X-transformation of van der Waerden [1965) Mathematische Statistik, Springer Verlag, Berlin--Göttingen-Heidelberg) to the marginal values. We introduced the concept of group-conformity behaviour of the patient data. According to our definition, a patient behaves in conformity with a given group of patients with respect to a clinical-chemical value, if the patients' value deviates from the estimated age-specific expected value of the reference group and the deviation lies in the same direction as that of the mean value of the respective group of patients. Using this procedure, disease-specific deviation patterns were determined from the data, thus enabling us to make clear separations of the patient groups from the reference group and from each other. Furthermore, the computed deviation patterns throw light upon the pathobiochemical modifications of the parameters in the examined diseases.