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.
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.
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