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Generalized Wilcoxon Test for Censored Data
Vařejková, Michaela ; Maciak, Matúš (advisor) ; Komárek, Arnošt (referee)
This paper deals with the generalized Wilcoxon test and its use for censored data. The introduction describes standard one-sample and two-samples Wilco- xon tests and their basic properties, censored data and methods of censoring. The main part of the paper is devoted to the introduction of the generalized Wilcoxon test and to its properties. First, a test for singly-censored data is de- scribed; the description of a test for doubly censored data follows. The paper concludes with a simulations part in which statistical properties of the test are demonstrated. The first example compares the generalized test with the stan- dard two-samples Wilcoxon test. The second example shows how the censoring rate affects the power and significance level of the generalized test. 1
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Estimation of probability distribution for censored data
Teichmannová, Zuzana ; Lachout, Petr (advisor) ; Antoch, Jaromír (referee)
In this thesis, we look into estimation of probability distribution for censored data. These data are not complete, because for some reason it was impossible to observe them all. We use the Kaplan-Meier estimator and study some of its properties. We also use the Nelson-Aalen estimator. In the end we make a compa- rison of these estimators with a naive estimator, which omits the censored data. The comparison is illustrated on two numerical examples where we can see the main differences in the accuracy of the estimators. We will see that it is better to include the censored data to our estimations. 1
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Estimates in Survival Analysis
Čabla, Adam ; Malá, Ivana (advisor) ; Tomášek, Ladislav (referee)
This thesis introduces methods used in time-to-date analysis. It is written generally and so usable in dealing with any example. The thesis deals with problem of censoring, which means, that some observations occurred after the following, which is typical for the lifetime analysis. Methods mentioned in the thesis are nonparametric and parametric estimates of the survival function and their characteristics, and regression models, concretely Cox model and accelerated failure time model, which examine effect of the covariates on survival function. In the thesis is beside survival function presented hazard function, which express intensity of the analyzed event and cumulative hazard function, which is created as the name suggests by cumulative summation of the hazard function. Estimates of these functions are obtainable from survival function and for parametric estimate often exists formula resulting from parameters of used distribution. Empirical part of the thesis introduces influence of several different types and degrees of censoring on parametric and nonparametric estimates of the survival function, mean and median. The other empirical example is the usage of regression analysis on the data from the lungs cancer research made by Mayo Clinic.
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Nonparametric estimations in survival analysis
Svoboda, Martin ; Malá, Ivana (advisor) ; Tomášek, Ladislav (referee)
This work introduces nonparametric models which are used in time to event data analysis. It is focused on applying these methods in medicine where it is called survival analysis. The basic techniques and problems, which can appear in survival analysis, are presented and explained here. The Kaplan -- Meier estimator of survival function is discussed in the main part. This is the most frequented method used for estimating the survival function in patients who have undergone a specific treatment. The Kaplan -- Meier estimator is also a common device in the statistical packets. In addition to estimation of survival function, the estimation of hazard function and cumulative hazard function is presented. The hazard function shows the intensity of an individual experiencing the particular event in a short time period. Special problems occur when analyzing time to event data. A distinctive feature, often present in such data, is known as censoring. That is the situation when the individual does not experience the event of interest at the time of study. The thesis covers also an empiric part, where the results of an analysis of patients with the larynx carcinoma diagnosis are shown. These patients were treated in a hospital located in České Budějovice. This analysis is based on a theory presented in the previous chapters.
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