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Master's Dissertation
DOI
10.11606/D.55.2013.tde-11072013-143209
Document
Author
Full name
Daiane de Souza Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Pinto Junior, Dorival Leão (President)
Noveli, Cibele Maria Russo
Simas, Alexandre de Bustamante
Title in Portuguese
Comparações múltiplas para dados censurados
Keywords in Portuguese
Estatísticas dependentes
FWER
Melhoramentos do método de Bonferroni
Método de Simes
Métodos de comparações múltiplas
Modelos com censura
Abstract in Portuguese
O objetivo deste trabalho é estudar a performance de alguns métodos de comparações múltiplas (MCMs) que ajustam o valor-p quando as estatísticas empregadas nos testes são a log-rank e a Cramér-von Mises, ambas não paramétricas e com estrutura de dependência. A vantagem dos MCMs que ajustam o valor-p é que eles controlam as taxas de erro tipo I e tipo II para cada hipótese, afim de atingir um poder estatístico elevado, mantendo a taxa de erro da família dos testes (FWER) menor ou igual ao nível de significância escolhido. Trabalhamos com o procedimento clássico de Bonferroni e com outros métodos vistos como seu melhoramento, com especial atenção a certos procedimentos derivados do método de Simes que permitem realizar inferências sob as hipóteses individuais. Foi verificado teoricamente que a estatística log-rank pertence à classe multivariada totalmente positiva de ordem 2 ('MTP IND. 2'), uma vez que o método de Simes garante o controle da FWER quando as estatísticas dependentes assumem esta condição. O controle da FWER empregando a estatística de Cramér-von Mises foi observado apenas por meio de simulações. Os MCMs foram analisados através de estudos computacionais em modelos discretos e contínuos sob censura com foco no problema de comparar um tratamento versus controle
Title in English
Multiple comparisons for censored data
Keywords in English
Censoring data
Dependent statistics
FWER control
Improved Benferroni method
Multiple compareison methods
Simes's method
Abstract in English
The aim of this work is to study the performance of some Multiple Comparison Methods (MCMs) that adjust the p-value when the log-rank-type and Cramér-von Mises statistics are used, both nonparametric and with dependency structure. The advantage of these methods is that they control the error rates of type I and type II for each hypothesis in order to achieve high statistical power while keeping the Family Wise Error Rate (FWER) lower or equal than a given significance level. The classical Bonferroni procedure is used as well as others seen as its improvement, with special attention to certain procedures derived from Simes' method for making inferences on individual hypothesis. It is theoretically proved that the weighted Log-Rank statistics belongs to the multivariate totally positive of order 2 ('MTP IND. 2') class, which is needed in order to apply Simes' method, that guarantees control of the FWER of dependent statistics in this case. The control of the FWER when the Cramér-von Mises statistics is used is only veried by means of computational simulations. The MCMs are also analyzed by means of computational experiments with discrete and continuous data under censoring with focus on the problem of comparisons of treatment versus a control
 
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Publishing Date
2013-07-11
 
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