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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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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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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 variables. Later we explain utility of models logit and probit and demonstrate it at a practical example. Third chapter deals with limited explained variables, specifically censored and variables representing some time to event. We show how to work with the most used parametric models and Kaplan-Meier estimator. 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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Residents of retirements homes in region of Zlín in point of demographic view
Lukácsová, Hana ; Šídlo, Luděk (advisor) ; Hulíková Tesárková, Klára (referee)
Residents of retirements homes in region of Zlín in point of demographic view Abstract Presented work introduces the law no. 108/2006 on social services that determines retirements homes as one of the facilities providing social services. The capacity of these facilities in the Zlín region is evaluated with the help of availability indices and facility normatives. More detailed attention was drawn to an analysis of age, gender, former permanent address and dependence degree of residents in selected retirement homes. This part of the research is based on data provided by five retirement homes in Zlín region. Obtained data was evaluated with the Kaplan-Meier method in order to estimate surviving function for these clients. The resemblance was tested employing the determination of the null hypothesis by log-rank test or Wilcoxon test. Keywords: ageing, residents of retirements homes, law on social services, survival analysis
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Determinants of the circulatory system diseases among the Czech population
Lustigová, Michala
Determinants of circulatory system diseases among the Czech population Abstract The determinants of circulatory system diseases are very well known, modifiable risk factors and factors widely spread among populations are in focus for the public health research. The aim of this thesis is a quantification of main cardiovascular risk factors in the Czech population using the survival analysis and HAPIEE cohort data. The epidemiologic situation, trends in the Czech population health including "the cardiovascular revolution" is discussed in the first part of the thesis. Among the Czech population high prevalence of many risk factors were found. The education had the strongest impact on cardiovascular health from sociodemographic characteristics. The negative effect of smoking, prevalence of high blood pressure, prevalence of diabetes and physical inactivity was confirmed. On the other hand the impact of obesity, binge drinking and high blood cholesterol level was not significant among the Czech population. The population approach in cardiovascular epidemiology and cardiovascular health promotion as well are discussed in the last chapter. Keywords: diseases of the circulatory system, mortality, health transition, cardiovascular health, risk factors, survival analysis, health promotion
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Unemployment Duration in the Czech Republic Through the Lens of Survival Analysis
Čabla, Adam ; Malá, Ivana (advisor) ; Komárková, Lenka (referee) ; Popelka, Jan (referee)
In the presented thesis the aim is to apply methods of survival analysis to the data from the Labour Force Survey, which are interval-censored. With regard to this type of data, I use specific methods designed to handle them, especially Turnbull estimate, weighted log-rank test and the AFT model. Other objective of the work is the design and application of a methodology for creating a model of unemployment duration, depending on the available factors and its interpretation. Other aim is to evaluate evolution of the probability distribution of unemployment duration and last but not least aim is to create more accurate estimate of the tail using extreme value theory. The main benefits of the thesis can include the creation of a methodology for examining the data from the Labour Force Survey based on standard techniques of survival analysis. Since the data are internationally comparable, the methodology is applicable at the level of European Union countries and several others. Another benefit of this work is estimation of the parameters of the generalized Pareto distribution on interval-censored data and creation and comparison of the models of piecewise connected distribution functions with solution of the connection problem. Work brought empirical results, most important of which is the comparison of results from three different data approaches and specific relationship between selected factors and time to find a job or spell of unemployment.
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Survival Analysis in R
Pásztor, Bálint ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
Survival analysis is a statistical discipline that analyzes the time to occurrence of certain events. The aim of this thesis is to describe the possibilities of survival analysis in the environment of statistical software R. Theoretical knowledge is applied to real data, parametric and nonparametric estimates of survival functions are evaluated by different methods and compared with each other. In the section focusing on nonparametric models Kaplan-Meier and Nelson-Aalen functions are described. Among the parametric estimates there were included well-known probability distributions, survival functions and risk functions derived from these distributions are presented and there is discussed their usefulness in survival analysis. Another aim is to show the possibility of deriving transition probabilities from estimates and building a Markov chain model to capture the changes of studied cohort over time. The second part of the work contains a description of the applications of the theory of survival analysis. In this section there are shown possibilities of statistical modeling in the field of survival analysis using the software R. Outputs from R were used to create Markov model. There are presented possibilities of pharmacoeconomic models and description of the basic concepts of HTA. Cost-effectiveness calculations using ICER were conducted in accordance with the methodology of SUKL. It was shown that the statistical modelling of survival plays an important role in the evaluation of the cost-effectiveness of medicines.
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Comparing of length of employment before and during the financial crisis
Vágner, Hubert ; Čabla, Adam (advisor) ; Malá, Ivana (referee)
In this bachelor thesis I introduce survival analysis and distribution of time-to-event. The analyzied subject is the resignation from work. It means that I find out and compare how long on average people had work before the financial recession of 2008-2009 and during the time period of the 2010-2011 recession. The data gathered is from the Labor Force Survey, which is produced by the Czech Statistical Office. I used interval censoring to gather the data for the average length of the working ratio. This means that we know that the observed event happened in a given interval, in this case the intervals are individual survays. First of all, it's necessary to estimate the survival function. We shall do this with the help of the nonparametrical Turnbull's estimate for data in interval censoring. Than we calculate individual averages. The empirical part will consist of individual comparisons of the survival function and the average lengths of the working ratio, first for the overall population, second for separate genders and finally for various education levels.
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