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Predictive models in survival analysis
Hadwigerová, Michaela ; Vítek, Martin (referee) ; Škutková, Helena (advisor)
With ever-new methods of treatment in health care occures a requierement of comparing these new methods to the old methods in some effective way. This is particularly important for the further development of these methods. However, data that describe these facts could not be processed by normal procedures and therefore was in the field of statistics to create a new kind of methods. They are known as predictive models of survival analysis.
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Multivariate Pareto distribution
Novytskyi, Oleksandr ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
Title: Multivariate Pareto distribution Author: Oleksandr Novytskyi Department: Department of Probability and Mathematical Statistics (305. 32- KPMS) Supervisor: RNDr. Lucie Mazurová, Ph.D., Department of Probability and Mathematical Statistics (305. 32-KPMS) Abstract: This bachelor thesis focuses on three methods of constructing multiva- riate Pareto distribution, i.e. multivariate distribution, where marginal distributi- ons are univariate Pareto distributions. We provide survival and density functions for these models, which are used for the numerical studies and valuation of insu- rance product, specifically a yearly life annuity paid to each insured in the group, whose remaining life time is given by the multivariate Pareto distribution. Keywords: multivariate distribution, Pareto distribution, survival function, density, life annuity.
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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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Predictive models in survival analysis
Hadwigerová, Michaela ; Vítek, Martin (referee) ; Škutková, Helena (advisor)
With ever-new methods of treatment in health care occures a requierement of comparing these new methods to the old methods in some effective way. This is particularly important for the further development of these methods. However, data that describe these facts could not be processed by normal procedures and therefore was in the field of statistics to create a new kind of methods. They are known as predictive models of survival analysis.
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Survival analysis - probability distributions and their characteristics
Plocová, Michaela ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This bachelor thesis is concerned with probability distributions that are used in survival analysis and characteristics of these distributions (survival function, hazard rate, probability density function, mean residual life). The aim of this thesis is to provide a summary of probability distributions and their characteristics, then to graphically represent them and show the shapes they can take in dependence on different parameters of distributions. The thesis is divided in 4 parts, the first three parts are mainly theoretical and they focus on general definitions of the characteristics, the most widely used distributions in survival analysis and mixture distributions. The last part is practical and focuses mainly on graphic representation of the characteristics for separate distributions and different values of parameters. Also, for each distribution measures of location and variability are calculated. The characteristics of mixture distributions are also graphically represented.
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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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