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In this article we consider a pq-dimensional random vector x distributed normally with mean vector θ and the covariance matrix Λ, assumed to be positive definite. On the basis of N independent observations on the random vector x, we wish to estimate parameters and test the hypothesis H: Λ = Ψ ⊗Σ, where Ψ = (ψ ij ) : q × q and Σ = (σ ij ) : p × p, and Λ = (ψ ij Σ), the Kronecker product of Ψ and Σ. That is instead of

Maximum nocturnal serum melatonin level (MTmax) in relation to some clinical variables was studied in 32 patients with a major depressive episode and in 33 healthy subjects with reference to the outcome of the dexamethasone suppression test (DST). Significant regressions were found between MTmax levels and clinical rating scores in CPRS, interpreted as retardation symptoms. Four healthy subjects with disposition for dysthymic reactions had subnormal MTmax levels, which differed from MTmax levels in subjects without such disposition. Patients but not the healthy subjects, who reported parental loss before 17 years of age, had subnormal MTmax levels and differed from patients with no reported parental loss. Patients with no reported suicidal behaviour in clinical history had significantly lower MTmax levels than patients with reported suicide attempts. No relations were found between low MTmax levels and diagnoses, duration of illness, reported inheritance for depressive illness or sleep disturbances. A hypothetical low melatonin syndrome in depression is proposed: low nocturnal melatonin, abnormal dexamethasone suppression test, disturbed 24-h rhythm of cortisol, less pronounced daily and annual cyclic variation in depressive symptomatology.

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Risk assessment of chemical hazards is typically based on single critical health effects. This work aims to expand the current approach by characterizing the dose-related sequence of the development of multiple (lower- to higher-order) toxicological health effects caused by a chemical. To this end a “reference point profile” is defined as the relation between benchmark doses for considered health effects, and a standardized severity score determined for these effects. For a given dose of a chemical or mixture the probability for exceeding the reference point profile, thereby provoking lower- to higher-order effects, can be assessed. The overall impact at the same dose can also be derived by integrating contributions across all health effects following severity-weighting. In its generalized form the new impact metric relates to the probability of response for the most severe health effects. Reference points (points of departure) corresponding to defined levels of response can also be estimated. The proposed concept, which is evaluated for dioxin-like chemicals, provides an alternative for characterizing the low-dose region below the reference point for a severe effect like cancer. The shape and variability of the reference point profile add new dimensions to risk assessment, which for example extends the characterization of chemical potency, and the concept of acceptable effect sizes for individual health effects. Based on the present data the method shows high stability at low doses/responses, and is also robust to differences in severity categorization of effects. In conclusion, the novel method proposed enables risk-based integration of multiple dose-related health effects. It provides a first step towards a more comprehensive characterization of chemical toxicity, and suggests a potential for improved low-dose risk assessment.