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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Estimation of the survival function in the reliability analysis
 Vojtěch, Jonáš ; Novák, Petr (advisor) ; Hurt, Jan (referee)
Present Bachelor thesis deals with the basic concepts and methods used in the survival analysis. Both nonparametric and parametric approaches to the estimation of the survival function are described. Nonparametric Kaplan Meier method is presented in order to estimate the survival function and consequently derive its basic properties. From the point of the probability distributions used in the analysis of reliability, exponential, Weibull's and logarithmic-normal distri- butions are applied. Parameters in the parametric approach to the estimation of the survival function are determined by the modification of maximum likelihood method for censored data. From the tests that are proper for the comparison of distribution of the duration of survival of more groups, nonparametric logrank test and parametric likelihood ratio test are mentioned. In the last section of the Bachelor thesis the theoretical findings are illustrated on simulated as well as actual data using Mathematica 9. Keywords: survival function, Kaplan-Meier estimator, logrank test, maximum likelihood method, likelihood-ratio test 1 Literatura 2 Seznam obrázků 3 Seznam tabulek 4
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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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