Estimation of a k-monotone density: characterizations, consistency and minimax lower bounds

[Clinical-psychopathological aspects of therapeutic effects of agomelatine (valdoxan) and its place in perfection of methods of therapy of postschizophrenic depressive disorders]

AIM

To determine a therapeutic effect of agomelatine (valdoxan) on post-schizophrenic depression (PSD), taking into account its psychopathological structure.

MATERIAL AND METHODS

A total of 33 patients of both sexes (average age was 32.1 yrs) with symptoms of post-schizophrenic depression (F20.4 according to ICD-10) were examined by using clinical and psychometric methods in the dynamics of shift-like schizophrenia. HAMD-17, PANSS and CGI-S scales were applied. All the patients were subdivided into groups: mild, moderate and severe depressions. Valdoxan was used at a dose of 25-50 mg/day for 28 days along with preceding antipsychotic therapy at maintenance doses. Evaluation of the efficacy of treatment was carried out according to percentage reduction of average total score (ATS) in dynamics.

RESULTS

A significant effect of valdoxan, with 73.5% of PANSS score reduction and quicker response to treatment, was identified. Therapeutic effect of valdoxan on separate components of PSD was uneven. The decrease of depressive disorders per se assessed by HAМD-17 and PANSS G-subscale was equally high (78.4 and 78.2%, respectively). Therapeutic reduction of negative disorders according to PANSS N-subscale was the lowest, at the level of 'good' effect (53.6%). In 27.3%, negative disorders were irreversible and were assessed as schizophrenic defect; in 72.7% of patients they were diagnosed as 'secondary' negative symptoms in atypical depression. In the subgroups of mild, moderate, and severe depression, the reduction of negative disorders was 62.4; 44.2 and 60.8%, respectively, and that of total PANSS score were 81.5; 66.1, and 78.6%, i.e. there was no correlation between these variables.

CONCLUSION

Agomelatin (valdoxan) is an effective medication for optimization of methods of PSD treatment, providing the therapeutic effect at the level of significant or complete reduction of symptoms. The quality (depth) and rate of formation of response in the dynamics of course treatment are determined not by the severity of depressive disorders in PSD structure, but by the ratio between negative (deficit) symptoms and 'secondary' symptoms, reflecting the degree of progression of the main disease.

On the rate of convergence of the maximum like-lihood estimator of a k-monotone density

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.