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Survival Analysis in R
Pásztor, Bálint ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
Survival analysis is a statistical discipline that analyzes the time to occurrence of certain events. The aim of this thesis is to describe the possibilities of survival analysis in the environment of statistical software R. Theoretical knowledge is applied to real data, parametric and nonparametric estimates of survival functions are evaluated by different methods and compared with each other. In the section focusing on nonparametric models Kaplan-Meier and Nelson-Aalen functions are described. Among the parametric estimates there were included well-known probability distributions, survival functions and risk functions derived from these distributions are presented and there is discussed their usefulness in survival analysis. Another aim is to show the possibility of deriving transition probabilities from estimates and building a Markov chain model to capture the changes of studied cohort over time. The second part of the work contains a description of the applications of the theory of survival analysis. In this section there are shown possibilities of statistical modeling in the field of survival analysis using the software R. Outputs from R were used to create Markov model. There are presented possibilities of pharmacoeconomic models and description of the basic concepts of HTA. Cost-effectiveness calculations using ICER were conducted in accordance with the methodology of SUKL. It was shown that the statistical modelling of survival plays an important role in the evaluation of the cost-effectiveness of medicines.
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Neural Networks in R
Arzumanov, Eduard ; Bašta, Milan (advisor) ; Žižka, David (referee)
The aim of this work was to present the issue of neural network, which is still, despite the fact it exist and has been applied for several years, remains quite unknown for a considerably big part of public and academical environment. The aim of the practical part was to verify via practical application if neural network are truly a better instrument of statistical analysis, than the commonly used ones, especially when the goal is to analyze and describe complex processes and relationships between them. Further aim of the work was to investigate and describe the relationships between the development of trading volumes of Apple shares and the shares of competitive companies regarding the market of smart phones such as Google, HTC, Nokia, Samsung using neural network models. The attainment of these goals was realized through a rather extensive description of neural networks theory as well as the presentation of valuable theoretical tools for avoiding the frequent barriers occurring during the practical implementation. This practical application was realized via software called R, which has widely spread lately due to its availability and a vast range of flexibility, which is provided to users. The value of this work is familiarization and the creation of an integrated knowledge within readers about the issue of neural networks and the deliverance of a proof, that neural networks are indeed a better tool compared to the commonly used ones (ARMA models, linear regression). The author of the work gained a lot of useful knowledge about neural networks, learned how to use them in practice especially in the environment of R software, by which he shifted his proficiency with the current software to a whole new level.
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Calculation of Acceptance Sampling Plans for Inspection by Variables
Kaspříková, Nikola ; Klůfa, Jindřich (advisor) ; Dittrichová, Eva (referee) ; Slavík, Václav (referee)
Analysis of several acceptance sampling procedures is performed and improvement of the procedures is sug- gested in this thesis. The issue of an efficient calculation of exact (P1, P2) single sampling plans for sampling by variables and exact LTPD and AOQL single sampling plans for sampling by variables when the rejected lots are inspected is addressed. The calculation of the plans is done using exact formula for operating characteristic of acceptance sampling plan and the new plans have better characteristics compared to the plans computed in a usual way using just approximately valid formula for operating characteristic. The tables of plans calculated according to procedures suggested in this thesis are provided for a couple of input parameters combinations. Tools designed for working with acceptance sampling plans, tools for analysis and calculation of acceptance sampling plans is one of the outputs of this thesis. R language and environment for statistical computations was chosen for implementation. The tools are satisfactorily efficient and may be easily used even for acceptance sampling plans tables computation. Newly defined functions in R are supplied including their source code and basic documentation so that acceptance sampling plans can be computed as demanded in case that the particular input parameters set is out of the scope covered in the tables of plans provided here.
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Graphic Opportunities of the System R
Režný, Jan ; Komárková, Lenka (advisor) ; Bína, Vladislav (referee)
This work analyzes the graphical outputs of software R. The software R is a statistical free software with GNU license. A purpose of this work is to display images (outputs) and a source code. This work contains above all the statistical outputs. The images are accompanied by commentary on the data and display options. This work should facilitate the creation of graphic software R for readers.
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