Resumen
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.

Resumen
In a clinical trial comparing drug with placebo, where there are multiple primary endpoints, we consider testing problems where an efficacious drug effect can be claimed only if statistical significance is demonstrated at the nominal level for all endpoints. Under the assumption that the data are multivariate normal, the multiple endpoint-testing problem is formulated. The usual testing procedure involves testing each endpoint separately at the same significance level using two-sample t-tests, and claiming drug efficacy only if each t-statistic is significant. In this paper we investigate properties of this procedure. We show that it is identical to both an intersection union test and the likelihood ratio test. A simple expression for the p-value is given. The level and power function are studied; it is shown that the test may be conservative and that it is biased. Computable bounds for the power function are established.