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Survival function estimation
Chrenko, Jakub ; Komárek, Arnošt (referee) ; Hudecová, Šárka (advisor)
Nazev prace: Odhady funkcr pfeziti Autor: Jakub Chrenko Kalodra: Katcdra pravdepodobnosti a mateinaticke statistiky Vedouci ba.ka.la.fske pra.ce: Mgr. Sarka Dosla e-mail vedouciho: dosla'ii'karlin.mff.cimi.cz Abstrakt: V pfedlozene pnici so zabyvame funkci pfeziti a jejuni odharly. Popsany jsou jak paramrtrirke, tak i neparamelrickc' pf ist upv. V obou piipa- deeh je pfihledimto k pfi'padncuiu ccnzorovanf clat. NoiJaramotricke rriotody iifkladon /adno pozadavky ua rozdrloni dat, a proto jsou uuiverzalne po- uzitcliic. Z tcchlo nictod uvadi'nir Z(^jmciH^ Ka,pkui-M(ucruv odhad fiinkcc pfcziti, jchoz zakladni vlastnosti jsou popsany. Ziiu'iiena je l.ra analyza ta- bulck unirtnosti. Parauietricke piist.upy j)rcdpokl;idaji koiikrntui tvar tno- rciickclio rozdeleiii sludovniio nahodric voliriny. Z nojcast.eji pouzivanycii rozdclonf Tivadinic oxporinucialui, Woilnilluvo a logaritniicko iioriualni. V za- vc.i'u prac'c; jsou tyt.o inctody poT'Oviiauy a ilustrovauy ua koukretui'm da- tovom souboru a poinoci simulaci. Klfcova slova: Fuiikcc })feziti, hazard, Kaplan-Mcicruv odhad, rouzorovana dat.n Title: Estiiua.tioii oi' Survivalship Function Author: Jakub Chronko Department: Department of Probability and Mathematical statistics Supervisor: Mgr. Snrka Dosla Supervisor's e-mail address: doslaCO'karliii.iiifl.ciuii.cz...
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Parametric regression models in survival analysis
Otava, Martin ; Ševčík, Jaroslav (referee) ; Komárek, Arnošt (advisor)
Na'/cv prace: Paraniot.ricke regiesiri modely v analv'/e pfezitf Autor: Martin Otava Katedra (li.stav): Katedra pravdepoiiolmosti a niatcmatitke statistiky Vedouci bakalafske prace: Mgr. Amost Komarek, Ph.D. (j-inail vedonciho: komaiek( >karlin.mli.cuni.c /, Abst.rakl: \ pfcdlo/.ene. praci studujcme panunetricke re^resni modely v ana- lyze pre/.ili. Skrze pojem cen/orovani se se/namfme s podst.alou analy/.y pixv.iti a zavudrme si zakladnf pojiiiy ir/ivanr v souvislo^ti s ui. Uka'/niK1 si tvurbu vlicxlnc'lio rc^rcsni'lio inodcln a zpiiwoby odliadti paranictru s diua/,cni na inotixhi inaxiinalni vrrohodnosTi spolrriu"' s itcrarniini nu'l.odaini pro ... vyrt'seni. Vysvrtlnnr si vv'/nani iialiodiu'' chyliy inefriii. Die1 jcjilio roxdrlcni pak vyLvoriiuc nckolik ni/nycli pai'a.iiHit.i1itikycli niodrlu pro odhad li\i.s(oly etiyu do sclhani. Srovnanir inodcly s neparamctrirkym odliadnn, ktdiy nain poimizc ... i t . /da na.s model odpovi'da ri'aliTr. CV-lou [iraci bude provaxcT ihi- ,stra,ce na skiilcrnycli dal(irh slouxicf jako nkii/ka fuii^cjvani metody v pra.xi. KliVova slova: Analv/a prc/iti. iJarainrtrickr inodcly. Title: Accclcralfd iailurc t.inn1 models in survival analysis Ant hor: Mart in Otava Dqiart.nieiit.: Depart.mcnl of Proba.bilit.y a.nd Mat lunnatical St.atisl.ics Supervisor: Mgv. Arnost Komarck,...
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Supra-bayesovská kombinace pravděpodobnostních distribucí
Sečkárová, Vladimíra ; Komárek, Arnošt (referee) ; Kárný, Miroslav (advisor)
In this work we study problems of sharing of probabilistic information by using Supra-Bayesian approach. In 1st Chapter the methods and formulas used in the work are mentioned. 2nd Chapter contains the introduction to discussed topic. In 3rd Chapter the main method of sharing the probabilistic information, which is based on common domain, is derived. In 4th Chapter the types of given knowledge pieces are specified, which are then transformed into probabilistic terms and extended on the whole domain. In 5th Chapter the results from the previous chapters are assessed.
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Parameter estimation in case-cohort studies
Klášterecký, Petr ; Kulich, Michal (advisor) ; Volf, Petr (referee) ; Komárek, Arnošt (referee)
The concern of this thesis is parameter estimation in regression models in survival analysis, particularly in case-cohort studies. In case-cohort studies, observations are sampled to form a subcohort which is followed and analysed. As a result, the cost of performing such studies is reduced but standard procedures for parameter estimation need to be modified. This is usually done by incorporating weights into the estimating equations so that individual sampling probabilities are accounted for. In this thesis we show that this method can lead to biased estimators when the subcohort sampling probability is low and suggest an alternative estimator based on logistic regression.
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Clustering and regression analysis of micro panel data
Sobíšek, Lukáš ; Pecáková, Iva (advisor) ; Komárek, Arnošt (referee) ; Brabec, Marek (referee)
The main purpose of panel studies is to analyze changes in values of studied variables over time. In micro panel research, a large number of elements are periodically observed within the relatively short time period of just a few years. Moreover, the number of repeated measurements is small. This dissertation deals with contemporary approaches to the regression and the clustering analysis of micro panel data. One of the approaches to the micro panel analysis is to use multivariate statistical models originally designed for crosssectional data and modify them in order to take into account the within-subject correlation. The thesis summarizes available tools for the regression analysis of micro panel data. The known and currently used linear mixed effects models for a normally distributed dependent variable are recapitulated. Besides that, new approaches for analysis of a response variable with other than normal distribution are presented. These approaches include the generalized marginal linear model, the generalized linear mixed effects model and the Bayesian modelling approach. In addition to describing the aforementioned models, the paper also includes a brief overview of their implementation in the R software. The difficulty with the regression models adjusted for micro panel data is the ambiguity of their parameters estimation. This thesis proposes a way to improve the estimations through the cluster analysis. For this reason, the thesis also contains a description of methods of the cluster analysis of micro panel data. Because supply of the methods is limited, the main goal of this paper is to devise its own two-step approach for clustering micro panel data. In the first step, the panel data are transformed into a static form using a set of proposed characteristics of dynamics. These characteristics represent different features of time course of the observed variables. In the second step, the elements are clustered by conventional spatial clustering techniques (agglomerative clustering and the C-means partitioning). The clustering is based on a dissimilarity matrix of the values of clustering variables calculated in the first step. Another goal of this paper is to find out whether the suggested procedure leads to an improvement in quality of the regression models for this type of data. By means of a simulation study, the procedure drafted herein is compared to the procedure applied in the kml package of the R software, as well as to the clustering characteristics proposed by Urso (2004). The simulation study demonstrated better results of the proposed combination of clustering variables as compared to the other combinations currently used. A corresponding script written in the R-language represents another benefit of this paper. It is available on the attached CD and it can be used for analyses of readers own micro panel data.
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