Ivanka Horová

Treatment of uterine sarcoma

Purpose: Surgery, radiotherapy and chemotherapy are employed in the treatment of uterine sarcoma. We claim to evaluate the role of radiotherapy in the treatment of uterine sarcoma. Patients and methods: We report a retrospective study of 49 patients with uterine sarcoma treated from 1990–1999 at Masaryk Memorial Cancer Institute in Brno. All 49 patients had surgery, 19 (38.7%) had adjuvant radiotherapy and 25 (51%) had chemotherapy. Using the FIGO classification: 71.4% had stage I, 6.1% stage II, 16.3%, stage III and 6.1% stage IVa disease. 42.9% of tumors were mixed Müllerian tumors, 34.7% leiomyosarcomas and 22.4% endometrial stromal sarcomas. 12 cases (24.5%) had a local recurrence, 7 (14.3%) had hematogenous dissemination. There was an increased disease free interval (DFI) for patients treated with adjuvant radiotherapy (p=0.005). The DFI was favourably influenced by the stage of the disease. Of 12 patients with a local recurrence only one had postoperative radiotherapy. Radiotherapy had an impact on overall survival (OS). The five-year OS probability was 51.6% without radiotherapy and 88.9% with radiotherapy (p=0.0066). Conclusion: We conclude that postoperative radiotherapy in our series of patients diagnosed with uterine sarcoma has an impact on locoregional and disease-free progression intervals (LRFI, DFI) and overall survival (OS). The most important prognostic factor is the extend of the disease (stage). Stage I patients have a significantly better survival.

Kernel smoothing in MATLAB : theory and practice of kernel smoothing

Methods of kernel estimates represent one of the most effective nonparametric smoothing techniques. These methods are simple to understand and they possess very good statistical properties. The book provides a brief comprehensive overview of statistical theory and moreover, the emphasis is given to implementation of presented methods in Matlab. All created programs are included into a special toolbox which is an integral part of the book. This toolbox contains many Matlab scripts useful for kernel smoothing of density, cumulative distribution function, regression function, hazard function, indices of quality and bivariate density. Especially, methods for a choice of the optimal bandwidth and a special procedure for simultaneous choice of the bandwidth, the kernel and its order are implemented. The toolbox is divided into six parts according to chapters of the book. All scripts are included in a user interface and it is easy to manipulate with this interface. Each chapter of the book contains a detailed help for the related part of the toolbox, too. The book is intended for newcomers to the field of smoothing techniques and would be also appropriate for a wide audience: students and researches from both the statistical science and interface disciplines.

Full bandwidth matrix selectors for gradient kernel density estimate

The most important factor in multivariate kernel density estimation is a choice of a bandwidth matrix. This choice is particularly important, because of its role in controlling both the amount and the direction of multivariate smoothing. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or a pre-transformation of the data. A general multivariate kernel density derivative estimator has been investigated. Data-driven selectors of full bandwidth matrices for a density and its gradient are considered. The proposed method is based on an optimally balanced relation between the integrated variance and the integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. In order to compare this method with cross-validation and plug-in methods the relative rate of convergence is determined. The utility of the method is illustrated through a simulation study and real data applications.

Optimal Choice Of Nonparametric Estimates Of A Density And Of Its Derivatives

Kernel smoothers are one of the most popular nonparametric functional estimates. These smoothers depend on three parameters: the bandwidth which controls the smoothness of the estimate, the form of the kernel weight function and the order of the kernel which is related to the number of derivatives assumed to exist in the nonparametric model. Because these three problems are closely related one to each other it is necessary to address them all together. In this paper we concentrate on the estimation of a density function and of its derivatives. We propose to use polynomial kernels and we construct data-driven choices for the bandwidth and the order of the kernel. We show a~theorem stating that this method for solving simultaneously the three selection problems mentioned before is asymptotically optimal in terms of Mean Integrated Squared Errors. As a by-product of our result we show an asymptotic optimality property for a~new bandwidth selector for density derivative which is quite appealing because of the simplicity of its implementation.

Visualization and Bandwidth Matrix Choice

Kernel smoothers are among the most popular nonparametric functional estimates. These estimates depend on a bandwidth that controls the smoothness of the estimate. While the literature for a bandwidth choice in a univariate density estimate is quite extensive, the progress in the multivariate case is slower. The authors focus on a bandwidth matrix selection for a bivariate kernel density estimate provided that the bandwidth matrix is diagonal. A common task is to find entries of the bandwidth matrix which minimizes the Mean Integrated Square Error (MISE). It is known that in this case there exists explicit solution of an asymptotic approximation of MISE (Wand and Jones, 1995). In the present paper we pay attention to the visualization and optimizers are presented as intersection of bivariate functional surfaces derived from this explicit solution and we develop the method based on this visualization. A simulation study compares the least square cross-validation method and the proposed method. Theoretical results are applied to real data.

Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches

Purpose We 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. Methods In 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. Results There 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. Conclusion Kernel 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.

Kernel Density Gradient Estimate

The aim of this contribution is to develop a method for a bandwidthmatrix choice for kernel estimate of the first partial derivatives of the unknown density.

Kernel Estimates of Hazard Functions for Biomedical Data Sets

The purpose of this chapter is to present a method of kernel estimates in modelling survival data. Within the framework of kernel estimates we draw our attention to the choice of the bandwidth and propose a special iterative method for estimation of it. The chapter also provides a bibliographical recent survey. As regards the applications we focus on applications in cancer research.

Selection of bandwidth for kernel regression

ABSTRACT The most important factor in kernel regression is a choice of a bandwidth. Considerable attention has been paid to extension the idea of an iterative method known for a kernel density estimate to kernel regression. Data-driven selectors of the bandwidth for kernel regression are considered. The proposed method is based on an optimally balanced relation between the integrated variance and the integrated square bias. This approach leads to an iterative quadratically convergent process. The analysis of statistical properties shows the rationale of the proposed method. In order to see statistical properties of this method the consistency is determined. The utility of the method is illustrated through a simulation study and real data applications.

Similarities within a multi-model ensemble: functional data analysisframework

Despite the abundance of available global and regi onal climate model outputs, their use for evaluatio n of past and future climate changes is often complicated by subs tantial differences between individual simulations, and the resulting uncertainties. In this study, we present a methodol ogy framework for the analysis of multi-model ensem bles based on functional data analysis approach. A set of two met rics that generalize the concept of similarity base d on the behaviour of 15 entire simulated climatic time series, encompassing both past and future periods, is introduced. As fa r as our knowledge, our method is the first to quantitatively assess simila rities between model simulations based on the tempo ral evolution of simulated values. To evaluate mutual distances of t he time series we used two semimetrics based on Euc lidean distances between the simulated trajectories and on differenc es in their first derivatives. Further, we introduc e an innovative way of visualizing climate model similarities based on a n etwork spatialization algorithm. Using the layout g raphs the data are 20 ordered on a 2-dimensional plane which enables an u n mbiguous interpretation of the results. The metho d is demonstrated using two illustrative cases of air temperature ove r th British Isles and precipitation in central Eu rope, 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 possibl e extensions are also discussed. 25