Abstract. Despite the abundance of available global climate model (GCM) and regional climate model (RCM) outputs, their use for evaluation of past and future climate change is often complicated by substantial differences between individual simulations and the resulting uncertainties. In this study, we present a methodological framework for the analysis of multi-model ensembles based on a functional data analysis approach. A set of two metrics that generalize the concept of similarity based on the behavior of entire simulated climatic time series, encompassing both past and future periods, is introduced. To our knowledge, our method is the first to quantitatively assess similarities between model simulations based on the temporal evolution of simulated values. To evaluate mutual distances of the time series, we used two semimetrics based on Euclidean distances between the simulated trajectories and based on differences in their first derivatives. Further, we introduce an innovative way of visualizing climate model similarities based on a network spatialization algorithm. Using the layout graphs, the data are ordered on a two-dimensional plane which enables an unambiguous interpretation of the results. The method is demonstrated using two illustrative cases of air temperature over the British Isles (BI) and precipitation in central Europe, simulated by an ensemble of EURO-CORDEX RCMs and their driving GCMs over the 1971–2098 period. In addition to the sample results, interpretational aspects of the applied methodology and its possible extensions are also discussed.

No abstract

No abstract

PurposeWe reviewed the survival time for patients with primary brain tumors undergoing treatment with stereotactic radiation methods at the Masaryk Memorial Cancer Institute Brno. We also identified risk factors and characteristics, and described their influence on survival time.MethodsIn summarizing survival data, there are two functions of principal interest, namely, the survival function and the hazard function. In practice, both of them can depend on some characteristics. We focused on nonparametric methods, propose a method based on kernel smoothing, and compared our estimates with the results of the Cox regression model. The hazard function is conditional to age and gross tumor volume and visualized as a color-coded surface. A multivariate Cox model was also designed.ResultsThere were 88 patients with primary brain cancer, treated with stereotactic radiation. The median survival of our patient cohort was 47.8 months. The estimate of the hazard function has two peaks (about 10 months and about 40 months). The survival time of patients was significantly different for various diagnoses (p≪0.001), KI (p = 0.047) and stereotactic methods (p = 0.033). Patients with a greater GTV had higher risk of death. The suitable threshold for GTV is 20 cm3. Younger patients with a survival time of about 50 months had a higher risk of death. In the multivariate Cox regression model, the selected variables were age, GTV, sex, diagnosis, KI, location, and some of their interactions.ConclusionKernel methods give us the possibility to evaluate continuous risk variables and based on the results offer risk-prone patients a different treatment, and can be useful for verifying assumptions of the Cox model or for finding thresholds of continuous variables.

No abstract

Abstract. Despite the abundance of available global and regional climate model outputs, their use for evaluation of past and future climate changes is often complicated by substantial differences between individual simulations, and the resulting uncertainties. In this study, we present a methodology framework for the analysis of multi-model ensembles based on functional data analysis approach. A set of two metrics that generalize the concept of similarity based on the behaviour of 15 entire simulated climatic time series, encompassing both past and future periods, is introduced. As far as our knowledge, our method is the first to quantitatively assess similarities between model simulations based on the temporal evolution of simulated values. To evaluate mutual distances of the time series we used two semimetrics based on Euclidean distances between the simulated trajectories and on differences in their first derivatives. Further, we introduce an innovative way of visualizing climate model similarities based on a network spatialization algorithm. Using the layout graphs the data are 20 ordered on a 2-dimensional plane which enables an unambiguous interpretation of the results. The method is demonstrated using two illustrative cases of air temperature over the British Isles and precipitation in central Europe, simulated by an ensemble of EURO-CORDEX regional climate models and their driving global climate models over the 1971-2098 period.In addition to the sample results, interpretational aspects of the applied methodology and its possible extensions are also discussed. 25

The modelling of censored survival data is based on different estimations of the conditional hazard function. When survival time follows a known distribution, parametric models are useful. This strong assumption is replaced by a weaker in the case of semiparametric models. For instance, the frequently used model suggested by Cox is based on the proportionality of hazards. These models use non-parametric methods to estimate some baseline hazard and parametric methods to estimate the influence of a covariate. An alternative approach is to use smoothing that is more flexible. In this paper, two types of kernel smoothing and some bandwidth selection techniques are introduced. Application to real data shows different interpretations for each approach. The extensive simulation study is aimed at comparing different approaches and assessing their benefits. Kernel estimation is demonstrated to be very helpful for verifying assumptions of parametric or semiparametric models and is able to capture changes in the hazard function in both time and covariate directions.

SUMMARYNonparametric density estimates attempt to reconstruct the probability density from which a random sample has come, using the sample values and as few assumptions as possible about the density. These methods are smoothing operations on the sample distribution. Methods of kernel estimates represent one of the most effective nonparametric methods. These methods are simple to understand, easy to implement and they have very good mathematical properties. We employed the automatic procedure for the selection of the bandwidth, the kernel and the order of the kernel. This procedure is used for analysis of air temperature fluctuations for series of Central England and Prague-Klementinum in the periods 1661-2000 and 1771-2000, respectively. Graphical representation of the family of estimated densities in three dimensional space provide a better explanation of the long-term trends in temperature distribution of both series.