Theoretical and practical aspects of Birge ratio method for adjusting uncertainty in multivariate measurements

In the paper, we present the multivariate location-scale model connected to the multivariate Birge ratio method, a new approach to model the dark uncertainty which is usually present when the results of individual studies are pooled together. In the empirical illustration, the approach is applied to the measurement results used to study the presence of the effectiveness of the hypertension treatment. The findings are compared to the ones obtained when the multivariate random effects model is used. Both models confirm that the hypertension treatments can lower systolic blood pressure and diastolic blood pressure as well as lead to considerable reduction of the risks of cardiovascular disease and stroke. Furthermore, the multivariate Birge ratio method produces more precise estimators of the overall mean vector by resulting in considerably smaller standard errors and narrower confidence intervals.