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Exercise-based predictors of atrial fibrillation recurrence in patients undergoing catheter ablation.
Mátych, Martin ; Pešl, Martin (referee) ; Hejč, Jakub (advisor)
Atrial fibrillation (AF) is the most frequently treated heart arrhythmia. Radiofrequency catheter ablation is a treatment option with a success rate ranging from 60 % to 80 % for paroxysmal AF. This work aimed to determine parameters associated with AF recurrence to identify high-risk patients. Data from 98 patients who underwent pulmonary vein isolation were analyzed. Out of these patients, 19 experienced AF recurrence. Exercise and echocardiographic parameters differed significantly between the recurrence and non-recurrence groups and were used in regression analysis. Peak oxygen consumption (pVO2) was found to be a strong predictor of AF recurrence after adjusting for gender and age (hazard ratio 0.43). Four parameters were identified as the ideal combination in multivariable analysis: pVO2, septal peak late diastolic mitral annulus velocity, post-exercise systolic blood pressure, and left atrial volume index. These findings highlight the importance of stress and echocardiographic parameters in predicting the success of ablation procedures.
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Analysis of incidence of competting risks and application of copula models
Hujer, Peter ; Volf, Petr (advisor) ; Dvořák, Jiří (referee)
This thesis first introduces the basic notions of univariate survival analysis. Then the survival analysis setting is extended to competing risk models, i.e. the cases considering several events of interest or several causes of one event. In the competing risk model, we discuss the problem of identification, which means that it is not possible to identify marginal distributions from observed competing risk data. Next, we present copula models, which are a suitable mathematical tool for modelling dependence structure between random variables. We explain their basic characteristics, present some useful copula families and the relationship of copula parameters with certain dependence (correlation) measures. Further, we show the utilization of copulas within competing risks models and how they can be helpful in the solution of identifiability problem. Finally, we apply the listed theoretical knowledge in a simulated example. Powered by TCPDF (www.tcpdf.org)
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Regression models in survival analysis and reliability
Novák, Petr ; Volf, Petr (advisor) ; Antoch, Jaromír (referee) ; Dohnal, Gejza (referee)
Regression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1
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Methods of survival analysis in the case of competing risks
Böhm, David ; Volf, Petr (advisor) ; Hurt, Jan (referee)
The thesis presents fundamental characteristics of survival analysis in the case of competing risks and their relationships. In the case without regression, basic nonparametric estimates and a logarithmic likelihood function for parameter estimates is given. The main focus is on Cox's proportional hazards model (PH), a model with accelerated time (AFT) and a flexible regression model (FG) are also mentioned. The identifiability of the associated survival function is solved using copulas. Basics of copula theory and the measurement of dependence by correlation coefficients (Pearson, Spearman and Kendal) are described in a separate chapter. A substantial part of the theory is practically used in a generated case without regression.
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Limited and censored explained variables
Kostka, Rudolf ; Bejda, Přemysl (advisor) ; Komárek, Arnošt (referee)
In this thesis at first we focus on theory of dealing with limited and censored explained variables. We begin with discrete variables and show the theory of binary and categorical variables. Later we explain utility of models logit and probit and demonstrate it at a practical example. We also provide a comparison of these two models. Third chapter deals with limited explained variables, specifically censored, truncated and variables representing some time to event. In the last chapter we describe some functions, which might be used to plot a graph of a survival function using softwares R or Mathematica. Some options in Excel are also mentioned, but they are very limited. Described functions are then demonstrated in use at a practical example with our gained data. Powered by TCPDF (www.tcpdf.org)
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Kernel estimates of hazard function
Selingerová, Iveta ; Horová, Ivanka (advisor) ; Prášková, Zuzana (referee)
Kernel estimates of hazard function Abstract This doctoral dissertation is devoted to methods for analysis of censored data in survival analysis. The main attention is focused on the hazard function that reflects the instantaneous probability of the event occurrence within the next time instant. The thesis introduces two approaches for a kernel esti- mation of this function. In practice, the hazard function can be affected by other variables. The most frequently used model suggested by D. R. Cox is presented and moreover two types of kernel estimates to estimate a condi- tional hazard function are proposed. For kernel estimates, there is derived some statistical properties and proposed methods of bandwidths selection. The part of the thesis is extensive simulation study where theoretical results are verified and the proposed methods are compared. The last chapter of the thesis is devoted to an analysis of real data sets obtained from different fields.
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Kernel estimates of hazard function
Selingerová, Iveta ; Horová, Ivanka (advisor) ; Prášková, Zuzana (referee)
Kernel estimates of hazard function Abstract This doctoral dissertation is devoted to methods for analysis of censored data in survival analysis. The main attention is focused on the hazard function that reflects the instantaneous probability of the event occurrence within the next time instant. The thesis introduces two approaches for a kernel esti- mation of this function. In practice, the hazard function can be affected by other variables. The most frequently used model suggested by D. R. Cox is presented and moreover two types of kernel estimates to estimate a condi- tional hazard function are proposed. For kernel estimates, there is derived some statistical properties and proposed methods of bandwidths selection. The part of the thesis is extensive simulation study where theoretical results are verified and the proposed methods are compared. The last chapter of the thesis is devoted to an analysis of real data sets obtained from different fields.
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Nové metody ve schvalování úvěrů
Rychnovský, Michal ; Arlt, Josef (advisor) ; Pecáková, Iva (referee) ; Veselý, Petr (referee)
This thesis contributes to the field of applied statistics and financial modeling by analyzing mathematical models used in retail credit underwriting processes. Specifically, it has three goals. First, the thesis aims to challenge the performance criteria used by established statistical approaches and propose focusing on predictive power instead. Secondly, it compares the analytical leverage of the established and other suggested methods according to the newly proposed criteria. Third, the thesis seeks to develop and specify a new comprehensive profitability-based underwriting model and critically reflect on its strengths and weaknesses. In the first chapter I look into the area of probability of default modeling and argue for comparing the predictive power of the models in time rather than focusing on the random testing sample only, as typically suggested in the scholarly literature. For this purpose I use the concept of survival analysis and the Cox model in particular, and apply it to a real Czech banking data sample alongside the commonly used logistic regression model to compare the results using the Gini coefficient and lift characteristics. The Cox model performs comparably on the randomly chosen validation sample and clearly outperforms the logistic regression approach in the predictive power. In the second chapter, in the area of loss given default modeling I introduce two Cox-based models, and compare their predictive power with the standard approaches using the linear and logistic regression on a real data sample. Based on the modified coefficient of determination, the Cox model shows better predictions. Third chapter focuses on estimating the expected profit as an alternative to the risk estimation itself and building on the probability of default and loss given default models, I construct a comprehensive profitability model for fix-term retail loans underwriting. The model also incorporates various related risk-adjusted revenues and costs, allowing more precise results. Moreover, I propose four measures of profitability, including the risk-adjusted expected internal rate of return and return on equity and simulate the impact of the model on each of the measures. Finally, I discuss some weaknesses of these approaches and solve the problem of finding default or fraud concentrations in the portfolio. For this purpose, I introduce a new statistical measure based on a pre-defined expert critical default rate and compare the GUHA method with the classification tree method on a real data sample. While drawing on the comparison of different methods, this work contributes to the debates about survival analysis models used in financial modeling and profitability models used in credit underwriting.
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Comparing the effectiveness of selected methods of cancer treatment. Prostate cancer, breast cancer and lung cancer via survival analysis
Šimonková, Karolína ; Šimpach, Ondřej (advisor) ; Pechholdová, Markéta (referee)
This diploma thesis deals with various ways of treatment of selected oncological diseases and the effectiveness of treatment methods and evaluation of the influence of various factors influencing the survival of patients. The activity of individual healing processes is evaluated by survival analysis. The subjects of the study are patients with breast, lung and prostate cancer. The survival analysis considers the sex of the patient, the age and stage of his illness, and other factors to avoid distorted results. The aim of the work is to find out the effects of selected therapeutic procedures on patients' health and to identify factors that have a significant impact on the survival of patients. The data for the diploma thesis was provided by the Institute of Health Information and Statistics of the Czech Republic, the Statistical Office, the National Cancer Register (NOR), the US SEER database and the German Breast Cancer Study.
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