Present thesis deals with the multivariate extreme value theory. First, concepts of modelling block maxima and threshold excesses in the univariate case are reviewed. In the multivariate setting the point process approach is chosen to model dependence. The dependence structure of multivariate extremes is provided by a spectral measure or an exponent function. Models for asymptotically dependent variables are provided. A construction principle from Ballani and Schlather (2011) is discussed. Based on this discussion the pairwise beta model introduced by Cooley et al. (2010) is modified to provide higher flexibility. Models are applied to data from nine hydrological stations from northern Moravia previously analysed by Jarušková (2009). Usage of the new pairwise beta model is justified as it brought a substantial improvement of log-likelihood. Models are also compared with Bayesian model selection introduced by Sabourin et al. (2013). Powered by TCPDF (www.tcpdf.org)

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Background: Shifting the healthcare payment system from a volume-based to a value-based model has been a significant effort to improve the quality of care and reduce healthcare costs in the US. In 2018, Massachusetts Medicaid launched Accountable Care Organizations (ACOs) as part of the effort. Constructing, assessing, and risk-adjusting quality measures are integral parts of the reform process. Methods: Using data from the MassHealth Data Warehouse (2016-2019), we assessed the loss of community tenure (CTloss) as a potential quality measure for patients with bipolar, schizophrenia, or other psychotic disorders (BSP). We evaluated various statistical models for predicting CTloss using deviance, Akaike information criterion, Vuong test, squared correlation and observed vs. expected (O/E) ratios. We also used logistic regression to investigate risk factors that impacted medication nonadherence, another quality measure for patients with bipolar disorders (BD). Results: Mean CTloss was 12.1 (±31.0 SD) days in the study population; it varied greatly across ACOs. For risk adjustment modeling, we recommended the zero-inflated Poisson or doubly augmented beta model. The O/E ratio ranged from 0.4 to 1.2, suggesting variation in quality, after adjusting for differences in patient characteristics for which ACOs served as reflected in E. Almost half (47.7%) of BD patients were nonadherent to second-generation antipsychotics. Patient demographics, medical and mental comorbidities, receiving institutional services like those from the Department of Mental Health, homelessness, and neighborhood socioeconomic stress impacted medication nonadherence. Conclusions: Valid quality measures are essential to value-based payment. Heterogeneity implies the need for risk adjustment. The search for a model type is driven by the non-standard distribution of CTloss.