Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and applied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand

PurposeWhether the quality of the ethical climate in the intensive care unit (ICU) improves the identification of patients receiving excessive care and affects patient outcomes is unknown.MethodsIn this prospective observational study, perceptions of excessive care (PECs) by clinicians working in 68 ICUs in Europe and the USA were collected daily during a 28-day period. The quality of the ethical climate in the ICUs was assessed via a validated questionnaire. We compared the combined endpoint (death, not at home or poor quality of life at 1 year) of patients with PECs and the time from PECs until written treatment-limitation decisions (TLDs) and death across the four climates defined via cluster analysis.ResultsOf the 4747 eligible clinicians, 2992 (63%) evaluated the ethical climate in their ICU. Of the 321 and 623 patients not admitted for monitoring only in ICUs with a good (n = 12, 18%) and poor (n = 24, 35%) climate, 36 (11%) and 74 (12%), respectively were identified with PECs by at least two clinicians. Of the 35 and 71 identified patients with an available combined endpoint, 100% (95% CI 90.0–1.00) and 85.9% (75.4–92.0) (P = 0.02) attained that endpoint. The risk of death (HR 1.88, 95% CI 1.20–2.92) or receiving a written TLD (HR 2.32, CI 1.11–4.85) in patients with PECs by at least two clinicians was higher in ICUs with a good climate than in those with a poor one. The differences between ICUs with an average climate, with (n = 12, 18%) or without (n = 20, 29%) nursing involvement at the end of life, and ICUs with a poor climate were less obvious but still in favour of the former.ConclusionEnhancing the quality of the ethical climate in the ICU may improve both the identification of patients receiving excessive care and the decision-making process at the end of life.Electronic supplementary materialThe online version of this article (10.1007/s00134-018-5231-8) contains supplementary material, which is available to authorized users.

The use of copulas as flexible tools for constructing marginal‐free distribution functions for multivariate phenomena, such as rainfall, recently enjoys substantial attention by researchers in hydrology. In this study, commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall, observed at Uccle, Belgium. In the analysis, various problems that can occur are highlighted, and opportunities for further research are outlined. After selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data, a detailed seasonal dependence analysis is provided, together with a study on tail dependence. Further, different existing parameter estimation techniques and goodness‐of‐fit methods for selecting the most appropriate bivariate copulas are applied and compared. Finally, attention is given to the presence of asymmetric dependence and nonexchangeability.

[1] Because of a lack of historical rainfall time series of considerable length, one often has to rely on simulated rainfall time series, e.g., in the design of hydraulic structures. One way to simulate such time series is by means of stochastic point process rainfall models, such as the Bartlett-Lewis type of model. For the evaluation of model performance, with a focus on the reproduction of extreme rainfall events, often a univariate extreme value analysis is performed. Recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models. In this study, a copula-based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms. First, this study performs an analysis of several storm variables, which indicates a problem with the modeling of the temporal structure of rainfall by the models. Thereafter, the bivariate frequency analysis of storms, defined by their duration and volume, illustrates the underestimation and overestimation of the return period of the storms simulated by the models, which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume, the difference in the degree of association between the latter, and a different mean storm interarrival time. The proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made.

In this article, we will present statistical methods to assess to what extent the effect of a randomised treatment (versus control) on a time‐to‐event endpoint might be explained by the effect of treatment on a mediator of interest, a variable that is measured longitudinally at planned visits throughout the trial. In particular, we will show how to identify and infer the path‐specific effect of treatment on the event time via the repeatedly measured mediator levels. The considered proposal addresses complications due to patients dying before the mediator is assessed, due to the mediator being repeatedly measured, and due to posttreatment confounding of the effect of the mediator by other mediators. We illustrate the method by an application to data from the LEADER cardiovascular outcomes trial.