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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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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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Statistická analýza přežití a incidenční funkce
Djordjilović, Vera ; Volf, Petr (advisor) ; Kulich, Michal (referee)
Competing risks occur often in survival analysis. In present work, we study different ap- proaches to modeling competing risks data and use examples to illustrate the most impor- tant results. In the competing risks setting it is often of interest to calculate the cumulative incidence of a specific event. We first study non-parametric estimation and then present three approaches to regression modeling. We use simple numerical example to demonstrate the use of non-parametric methods and perform analysis of real data from Stanford Heart Transplant Program to illustrate and compare the chosen regression models.
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Bivariate Geometric Distribution and Competing Risks: Statistical Analysis and Application
Volf, Petr
The contribution studies the statistical model for discrete time two-variate duration (time-to-event) data. The analysis is complicated by partial data observation caused either by the right-side censoring or by the presence of dependent competing events. The case is modeled and analyzed with the aid of a two-variate geometric distribution. The model identifiability is discussed and it is shown that the model is not identifiable without proper additional assumptions. The method of analysis is illustrated both on artificially generated\nexample and on real unemployment data.
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Problem of competing risks with covariates: Application to an unemployment study
Volf, Petr
The study deals with the methods of statistical analysis in the situation of competing risks in the presence of regression. First, the problem of identification of marginal and joint distributions of competing random variables is recalled. The main objective is then to demonstrate that the parameters and, in particular, the correlation of competing variables, may depend on covariates. The approach is applied to solution of a real example with unemployment data. The model uses the Gauss copula and Cox’s regression model.
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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.
|
|
|
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)
|
|
|
Statistická analýza přežití a incidenční funkce
Djordjilović, Vera ; Volf, Petr (advisor) ; Kulich, Michal (referee)
Competing risks occur often in survival analysis. In present work, we study different ap- proaches to modeling competing risks data and use examples to illustrate the most impor- tant results. In the competing risks setting it is often of interest to calculate the cumulative incidence of a specific event. We first study non-parametric estimation and then present three approaches to regression modeling. We use simple numerical example to demonstrate the use of non-parametric methods and perform analysis of real data from Stanford Heart Transplant Program to illustrate and compare the chosen regression models.
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