Assessing a vector of clinical observations

The periodic monitoring of drug treatments often involves the collection of biological specimens (e.g. blood, urine, synovial fluid) for the purpose of clinical laboratory assessment. The analysis of a particular specimen yields a vector of measurements from which judgments are made concerning the status of a subject and the effect of the drug. Typically, an observation vector is compared to “normal values” which may be conditioned on covariates such as age, gender, or other relevant characteristics. Under an assumption of multivariate normality of the data available, a method is presented for deciding whether a particular observed vector looks “normal”. The method, based on a predictive approach, is compared to other proposals and is shown to have optimality properties not possessed by standard procedures. Three different approaches are used in the discussion of optimality within the class of invariant methods. The first involves tolerance regions with smallest normalized expected volume, the second involves a decision theoretic comparison of predictive distributions, while the third involves the foundational notions of incoherence (Dutch book) and strong inconsistency.