|
|
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)
|
|
|
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.
|
|
|
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.
|
|
|
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.
|
guest ::
