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Survival analysis with STATISTICA
Kaderjáková, Zuzana ; Hudecová, Šárka (advisor) ; Hurt, Jan (referee)
Survival analysis is a separate statistical area. This paper discusses the~interpretation of basic concepts, principles and methods used and implemented in the software STATISTICA. First, we introduce censoring and ways of characterizing a distribution of survival time. We present Kaplan-Meier estimate of a survival function and also a method of mortality tables. Later, we discuss basic methods of comparison of the survival time distribution in two groups and their suitability for different situations. The paper also deals with application of the survival analysis methods in the financial sector, where we introduce Cox proportional hazards model. Finally, we apply theoretical knowledge to a real data set.
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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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Survival analysis with STATISTICA
Kaderjáková, Zuzana ; Hudecová, Šárka (advisor) ; Hurt, Jan (referee)
Survival analysis is a separate statistical area. This paper discusses the~interpretation of basic concepts, principles and methods used and implemented in the software STATISTICA. First, we introduce censoring and ways of characterizing a distribution of survival time. We present Kaplan-Meier estimate of a survival function and also a method of mortality tables. Later, we discuss basic methods of comparison of the survival time distribution in two groups and their suitability for different situations. The paper also deals with application of the survival analysis methods in the financial sector, where we introduce Cox proportional hazards model. Finally, we apply theoretical knowledge to a real data set.
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