This paper develops a testing framework for comparing the predictive accuracy of competing multivariate density forecasts with different predictive copulas, focusing on specific parts of the copula support. The tests are framed in the context of the Kullback-Leibler Information Criterion, using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on the region of interest. Monte Carlo simulations document that the resulting test statistics have satisfactory size and power properties for realistic sample sizes. In an empirical application to daily changes of yields on government bonds of the G7 countries we obtain insights into why the Student-t and Clayton mixture copula outperforms the other copulas considered; mixing in the Clayton copula with the t-copula is of particular importance to obtain high forecast accuracy in periods of jointly falling yields.
Objectives: To develop a consensus framework that can guide the process of decision-making on continuing or limiting life-sustaining treatments in ICU patients, using evidence-based items, supported by caregivers, patients, and surrogate decision makers from multiple countries. Design: A three-round web-based international Delphi consensus study with a priori consensus definition was conducted with experts from 13 countries. Participants reviewed items of the decision-making process on a seven-point Likert scale or with open-ended questions. Questions concerned terminology, content, and timing of decision-making steps. The summarized results (including mean scores) and expert suggestions were presented in the subsequent round for review. Setting: Web-based surveys of international participants representing ICU physicians, nurses, former ICU patients, and surrogate decision makers. Patients: Not applicable. Interventions: Not applicable. Measurements and Main Results: In three rounds, respectively, 28, 28, and 27 (of 33 invited) physicians together with 12, 10, and seven (of 19 invited) nurses participated. Patients and surrogates were involved in round one and 12 of 27 responded. Caregivers were mostly working in university affiliated hospitals in Northern Europe. During the Delphi process, most items were modified in order to reach consensus. Seven items lacked consensus after three rounds. The final consensus framework comprises the content and timing of four elements; three elements focused on caregiver-surrogate communication (admission meeting, follow-up meeting, goals-of-care meeting); and one element (weekly time-out meeting) focused on assessing preferences, prognosis, and proportionality of ICU treatment among professionals. Conclusions: Physicians, nurses, patients, and surrogates generated a consensus-based framework to guide the process of decision-making on continuing or limiting life-sustaining treatments in the ICU. Early, frequent, and scheduled family meetings combined with a repeated multidisciplinary time-out meeting may support decisions in relation to patient preferences, prognosis, and proportionality.
