In this paper we propose a generalized rank test based on discrete interval-censored failure time data to determine whether two lifetime populations come from the same distribution. It reduces to the Logrank test or Wilcoxon test when one has exact or right-censored data. Simulation shows that the proposed test performs pretty satisfactory. An example is presented to demonstrate how the proposed test can be applied in AIDS study.

The chapters of this thesis focus two different issues that arise in clinical trials and propose novel methods to address them. The first issue arises in the analysis of data with non-ignorable missing observations. The second issue concerns the development of methods that provide physicians better tools to understand and treat diseases efficiently by using each patient's characteristics and personal biomedical profile. Inherent to most clinical trials is the issue of missing data, specially those that arise when patients drop out the study without further measurements. Proper handling of missing data is crucial in all statistical analyses because disregarding missing observations can lead to biased results. In the first two chapters of this thesis, we deal with the "worst-rank score" missing data imputation technique in pretest-posttest clinical trials. Subjects are randomly assigned to two treatments and the response is recorded at baseline prior to treatment (pretest response), and after a pre-specified follow-up period (posttest response). The treatment effect is then assessed on the change in response from baseline to the end of follow-up time. Subjects with missing response at the end of follow-up are assign values that are worse than any observed response (worst-rank score). Data analysis is then conducted using Wilcoxon-Mann-Whitney test. In the first chapter, we derive explicit closed-form formulas for power and sample size calculations using both tied and untied worst-rank score imputation, where the worst-rank scores are either a fixed value (tied score) or depend on the time of withdrawal (untied score). We use simulations to demonstrate the validity of these formulas. In addition, we examine and compare four different simplification approaches to estimate sample sizes. These approaches depend on whether data from the literature or a pilot study are available. In second chapter, we introduce the weighted Wilcoxon-Mann-Whitney test on un-tied worst-rank score (composite) outcome. First, we demonstrate that the weighted test is exactly the ordinary Wilcoxon-Mann-Whitney test when the weights are equal. Then, we derive optimal weights that maximize the power of the corresponding weighted Wilcoxon-Mann-Whitney test. We prove, using simulations, that the weighted test is more powerful than the ordinary test. Furthermore, we propose two different step-wise procedures to analyze data using the weighted test and assess their performances through simulation studies. Finally, we illustrate the new approach using data from a recent randomized clinical trial of normobaric oxygen therapy on patients with acute ischemic stroke. The third and last chapter of this thesis concerns the development of robust methods for treatment groups identification in personalized medicine. As we know, physicians often have to use a trial-and-error approach to find the most effective medication for their patients. Personalized medicine methods aim at tailoring strategies for disease prevention, detection or treatment by using each individual subject's personal characteristics and medical profile. This would result to (1) better diagnosis and earlier interventions, (2) maximum therapeutic benefits and reduced adverse events, (3) more effective therapy, and (4) more efficient drug development. Novel methods have been proposed to identify subgroup of patients who would benefit from a given treatment. In the last chapter of this thesis, we develop a robust method for treatment assignment for future patients based on the expected total outcome. In addition, we provide a method to assess the incremental value of new covariate(s) in improving treatment assignment. We evaluate the accuracy of our methods through simulation studies and illustrate them with two examples using data from two HIV/AIDS clinical trials.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-07-13T15:19:52Z No. of bitstreams: 2 Dissertação - Elvis Edgard Inga de La Cruz - 2015.pdf: 4690319 bytes, checksum: fb5f7a5ba3966e716246274700bab6ae (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-07-14T11:29:19Z (GMT) No. of bitstreams: 2 Dissertação - Elvis Edgard Inga de La Cruz - 2015.pdf: 4690319 bytes, checksum: fb5f7a5ba3966e716246274700bab6ae (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-07-14T11:29:19Z (GMT). No. of bitstreams: 2 Dissertação - Elvis Edgard Inga de La Cruz - 2015.pdf: 4690319 bytes, checksum: fb5f7a5ba3966e716246274700bab6ae (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-08-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This study aimed, expand the method of Production Systems Sustainability Perception Rice High -MPSAT Lands. The choice of this method is justified by the fact that it has a good theoretical framework and be easily understood by the actors; however, it lacks nonparametric statistical approach. They were interviewed actors in the production chain of upland rice in Mato Grosso on two occasions, in 2006/07, when the MPSATA and 2014 was developed as part of this research. The methodology transformed the qualitative elements that make up the MPSATA (questions, attributes, indicators, key variables, secondary counselors, primary guiding and sustainability dimensions) for ordinal type and identified the sense of the order of the categories of these elements. Then it verified the significance of matched elements, considering the 2007 and 2014 surveys, with the IBM-SPSS 21. Later the element values were calculated. These elements have as a data source practices and managements carried out along the production chain. The end result of the research was the development of Parametric Method Not for Perception Sustainability Highlands Rice Production System - MPSATA-NP. The results obtained by MPSATA-NP allowed to accept or reject in statistical terms, if there were significant differences between the values of the features found in different eras who were surveyed, revealing that the 221 questions elements, eleven have statistical difference between their medians (three environmental dimension, two of the socioeconomic scale, four in the economic dimension and two territorial dimension). The other sustainability factors have changes compared to paired terms, however, it can´t be said that these elements are in fact different and represent more or less sustainable production conditions. So it follows that not hear significant change in the perception of the actors with respect to the sustainability of the land rice production system in the region. / O presente trabalho teve como objetivo, ampliar o método da Percepção de Sustentabilidade de Sistemas de Produção Arroz de Terras Altas -MPSAT1. A escolha desse método se justifica pelo fato do mesmo possuir uma boa estrutura teórica e ser de fácil compreensão pelos atores, no entanto, carece de abordagem estatística não paramétrica. Foram entrevistados atores da cadeia produtiva de arroz de terras altas em Mato Grosso em dois momentos, em 2006/07, quando o MPSATA foi desenvolvido e 2014, como parte integrante da presente pesquisa. A metodologia utilizada transformou os elementos qualitativos que compõem o MPSATA (quesitos, atributos, indicadores, variáveis essenciais, orientadores secundários, orientadores primários e dimensões de sustentabilidade) para o tipo ordinal e identificou o sentido da ordem das categorias desses elementos. Em seguida foi verificada a significância dos elementos emparelhados, considerando os levantamentos de 2007 e 2014, com o software IBM-SPSS 21. Posteriormente foram calculados os valores dos elementos. Estes elementos possuem como fonte de dados as práticas e manejos realizados ao longo da cadeia produtiva. O resultado final da pesquisa foi a elaboração do Método Não Paramétrico para a Percepção de Sustentabilidade de Sistema de produção de Arroz de Terras Altas – MPSATA-NP. Os resultados obtidos pelo MPSATA-NP permitiram aceitar ou rejeitar em termos estatísticos, se havia diferenças significativa entre os valores dos elementos quesitos encontrados nas diferentes épocas que foram pesquisados, revelando que dos 221 elementos quesitos, onze possuem diferença estatística entre as suas medianas (três da dimensão ambiental, duas da dimensão socioeconômica, quatro da dimensão econômica e dois da dimensão territorial). Os outros elementos de sustentabilidade possuem mudanças, no entanto, não pode-se se afirmar sejam de fato diferentes e que representem condições de produção mais ou menos sustentáveis. Assim, se conclui que não ouve mudança significativa na percepção dos atores com respeito à sustentabilidade do sistema de produção de arroz de terras na região.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-12T14:04:00Z No. of bitstreams: 1 Rosangela Silveira do Nascimento.pdf: 1012353 bytes, checksum: b5f0d139481ab0bfdd6a1f689175c1f6 (MD5) / Made available in DSpace on 2016-08-12T14:04:00Z (GMT). No. of bitstreams: 1 Rosangela Silveira do Nascimento.pdf: 1012353 bytes, checksum: b5f0d139481ab0bfdd6a1f689175c1f6 (MD5) Previous issue date: 2008-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the present work we analyze the dynamics of electrical cortical activity during the phenomenon of spreading depression (DA) and during the periods before and after this phenomenon. The characteristic of DA is reduced amplitude of spontaneous electrical activity that occurs in neural tissue after the application of stimulus that can be electrical, chemical, mechanical, luminous etc. In order to study properties of time series of electrical cortical activity recorded by ECoG (electrocortiogram) before,during and after DA, we apply Detrended Fluctuation Analysis(DFA). This method is designed to quantify long term correlations (memory) in temporal series such ECoG register. The method was successfully applied in studies of DNA sequences and non-stationary time series as heart rate variability, stride intervals, financial time series etc. The application of DFA results in scaling exponentα that quantifies correlation properties of nonlinear dynamical systems. This experiment indicates if temporal series posses long term correlations. In this work we calculate exponent α for different intervals: control (before the stimulus), after the stimulus, during the avalanche, during DA and after DA for two experimental groups of rats, nourished and malnourished. For both experimental groups the values of exponent α indicates persistent behavior for all intervals except during the avalanche in which correlations degrade. The presence of long term correlations in physiological time series observed in healthy organisms represents complexity that guaranties the organism’s adaptability to stress and disease. The absence of correlations during the avalanche indicates the loss of this complexity. Non-parametric Wilcoxon test was used to compare mean values of exponents α for all intervals of analyzed time series. In cases of nourished rats, the mean values ofα are significantly different for control, stimulus, avalanche, DA and after-DA intervals. Wilcoxon test was also used to compare mean values of α for corresponding intervals for the two experimental groups. The result is significant difference in mean values of α for control, stimulus avalanche, DA and after DA intervals between two experimental groups. The hypothesis that α =0.5 for avalanche intervals was not rejected by test, confirming the loss of correlations in this phase. Comparison of mean values of α for different intervals (control, stimulus, DA and after DA) with avalanche using the Wilcoxon test results in significant difference between two groups. / O presente estudo se propõe a analisar a dinâmica da atividade elétrica cortical durante o fenômeno da depressão alastrante (DA) e nos períodos que antecede e sucede o fenomêno. A DA é caracterizada pela redução da amplitude da atividade elétrica espontânea que ocorre no tecido neural, após a aplicação de um estímulo de natureza elétrica, química, mecânica, luminosa e outros. Visando estudar o comportamento da série temporal da atividade elétrica cortical, registrada no ECoG (eletrocorticograma), durante a DA e nos períodos que precede e sucede o fenômeno, foi aplicado o método do DFA (Detrended Fluctuation Analysis). Este método permite quantificar a existência de correlação de longo alcance (memória) numa série temporal, como é o caso do registro do ECoG. Anteriormente, o método foi aplicado em seqüências de DNA e no estudo de séries temporais não estacionárias, tais como, dinâmica da variabilidade cardíaca, flutuações de eletroencefalograma de humanos, intervalos entre passos sucessivos de humanos, séries econômicas e outros. A aplicação do DFA numa série temporal permite a determinação de um expoente de escalonamento α, que pode contribuir para a compreensão das propriedades dos sistemas dinâmicos não lineares. Este expoenteα revela se a série temporal apresenta correlação de longo alcance ou não. Neste trabalho os expoentes α foram calculados nas fases de controle, estímulo, avalanche, DA e após a DA para o ECoG, em dois grupos experimentais, ratos nutridos e ratos desnutridos. Em ambos os grupos experimentais, os valores obtidos para o expoente de escalonamento α denotam que a série temporal do ECoG apresenta correlação persistente (comportamento da série no presente se mantém no futuro) em todas as fases do processo com exceção da avalanche, período no qual ocorre perda de correlação. A presença de correlação de longo alcance numa série temporal biológica é uma resposta sempre observada em organismos saudáveis cuja complexidade do sinal registrado garante a adaptabilidade do organismo a situações de estresse e/ou distúrbios. Enquanto a ausência de correlação, observada na avalanche, indica a perda de propriedades fractais nos sistemas fisiológicos. O uso do método não-paramétrico de Wilcoxon, para comparar os valores médios dos expoentes α obtidos para o grupo de animais nutrido, durante as fases de controle, estimulação, DA, após DA, revelou que essas diferentes fasesdiferem significativamente. Os valores médios dos expoentes α obtidos para o grupo de animais desnutrido, durante as fases de controle, estimulação, DA, após DA, também não foram significativamente diferentes, quando comparados pelo método de Wilcoxon. Na comparação dos valores médios de α nas fases de controle, estimulação, DA, após DA entre os dois grupos de animais (nutrido e desnutrido) o teste de Wilcoxon revelou que as médias dos expoentes α em cada fase para os animais nutridos diferem significativamente daquelas obtidas para os animais desnutridos. Na avalanche a hipótese de que o expoente α é igual a 0,5, não foi rejeitada pelo teste de Wilcoxon, ou seja, o teste confirmou a perda de correlação nessa fase. Na comparação entre as médias dos expoentes α nos diferentes intervalos (controle, estimulação, DA, após DA) com o valor do expoente α na avalanche, o teste de Wilcoxon acusou diferença significativa tanto no grupo dos nutridos como no grupo dos desnutridos.

Indiana University-Purdue University Indianapolis (IUPUI) / Background: The hazard ratio (HR), representing the quantified estimate of treatment effect in survival analysis, measures the instantaneous relative difference of failure risk between two groups. The HR is typically assumed to be independent of time; however, this assumption is usually violated in practice. If the proportionality assumption holds, HR can be validly with the popular Cox proportional hazards model. When not proportional, the Wilcoxon-Gehan has been proposed to test the hypothesis of no difference. These have been recently generalized to evaluate differences in survival time for more than zero survival differences (the “net survival benefit”). Method: In this thesis, an attempt is made to illustrate the properties of generalized Wilcoxon Gehan tests as proposed by Buyse (2009). We use the concept of net survival benefit to re-analyze the trial by the Gastrointestinal Tumor Study Group (1982) by comparing chemotherapy versus combined chemotherapy and radiation in the treatment of locally unresectable gastric cancer. Survival times in days, for the 45 patients were recorded in each treatment arm. In that trial, a delayed treatment effect was observed, thus the HR is non-proportional. To provide a flexible assessment of the treatment effect, the net survival benefit was computed using datasets simulated under typical scenarios of proportional hazards, such as delayed treatment effect. Results: The generalized Wilcoxon statistic U, favored not adding radiation to chemotherapy, but only for survival up to 12 months. At Δ=0, U (0) = 491. In the simulated data sets, the confidence interval under the null hypothesis U (0) is (-152, 388). The test statistic 491 is outside this interval indicating radiation treatment might be beneficial. At U(12) = 219, it is inside the confidence interval of no treatment effect (-154,268) indicating the benefit of Chemo only is gone after 12 months. Conclusions: The net survival benefit measured via Buyse’s generalized Wilcoxon statistic is a measure of treatment effect that is meaningful whether or not hazards are proportional. The associated statistical test is more powerful than the standard log-rank test when a delayed treatment effect is anticipated.

This embedded mixed method study addresses the problems teachers have reported in believing themselves capable to implement the Common Core State Standards with students in special education. This study examines the effect professional development on implementing the Common Core State Standards had on the participating teachers’ self-efficacy beliefs. The participants (N=21) in this study were drawn from a 20-day professional development for teachers based on implementing the Common Core State Standards. The instrument used in the study was the Teacher Efficacy Beliefs System-Self. Data were subject to both statistical and qualitative analysis. The results of this study provide insight into the self-efficacy beliefs of the participants during and shortly after professional development about implementing the Common Core State Standards with students in special education. The Wilcoxon test of signed ranks revealed a significant increase in the TEB-S subscale areas of Accommodating Individual Differences and Managing Learning Routines, but not in Positive Classroom Climate. Qualitative analysis of data found both support for the statistical findings and also contradicted the statistical findings. Further qualitative analysis showed that practices presented in the professional development such as using the arts, formative assessment, and technology were effective in maintaining their teachers’ self-efficacy beliefs after professional development. Factors unrelated to the professional development, such as support from administrators and colleagues and poorly working technology were not supportive in carrying over the increase in teachers’ self-efficacy beliefs in implementing the Common Core State Standards with students in special education. The study is framed by Social Cognitive Theory and organized into 5 parts. Chapter I provides an overview of the study. Chapter II includes a review of literature related to teachers’ self-efficacy belief’s Common Core State Standards, and professional development. Chapter III describes the methodology of the study. Chapter IV presents the results of the analysis of data. Chapter IV reports the findings of the study and presents the conclusions of the study and ideas for future research.

對於生存時間的資料而言，通常我們所想要研究瞭解的是，至少存活到某特定時間點的機率，而這個機率亦即生存分析中的生存函數(survival function)。當有兩個不同的母體存在時，為了要知道這兩個母體的生存函數是否相同，在統計方法上，我們將進行一些檢定，常用的有Gehan-Wilcoxon和Cox-Mantel之兩樣本檢定，後來又有修飾型的Kolmogorov-Smirnov檢定。但是，前兩種檢定方法，只對此兩組生存函數呈現某特殊型式時，具有好的檢定力。因此，透過一些實證的研究，將上述檢定方法做有系統的整理，進而發展出一套簡單又有效率的檢定程序。再者，若檢定得此兩個母體之生存函數不相等時，如何利用Bootstrap方法，進一步對兩組生存函數之特定生存機率點或生存時間點所分別對應之生存時間或生存機率差距做推論與比較，本文將有詳細她說明；以提供研究人員更多有效的資訊，不再僅止於檢定虛無假設是否拒絕而已。最後，我們又藉由推廣上述Bootstrap方法，將其運用到檢定方法上，而另外發展出一種新的兩母體生存函數之檢定方法。 / When two different populations exist, we will take some tests by Cehan-Wilcoxon, Cox-Mantel or Modified Kolmogorov- Smirnov in satistical way. Therefore we develope a simple and efficient test process from arranging above test ways system- atically through some real study. How to use Bootstrap way to infer the difference of survival time or survival probability of specular point. We infer Bootstrap way on test work and then develope a new two populations survival function test way.