The similarities between generations of living subjects are often quantified by heritability. By distinguishing genotypic variation, or variation due to parental pairings, from phenotypic variation, or normal intraspecies variation, the heritability of traits can be estimated. Due to the multivariate nature of many traits, such as size and shape, computation of heritability can be difficult. Also, assessment of the variation of the heritability estimate is extremely difficult. This study uses nonparametric methods, namely the randomization test and the bootstrap, to obtain both a measure of the extremity of the observed heritability and an assessment of the uncertainty.

Master of Science / Department of Statistics / Gary Gadbury / High-dimensional data (HDD) have been encountered in many fields and are characterized by a “large p, small n” paradigm that arises in genomic, lipidomic, and proteomic studies. This report used a simulation study that employed basic block diagonal covariance matrices to generate correlated HDD. Quantities of interests in such data are, among others, the number of ‘significant’ discoveries. This number can be highly variable when data are correlated. This project compared randomization tests versus usual t-tests for testing of significant effects across two treatment conditions. Of interest was whether the variance of the number of discoveries is better controlled in a randomization setting versus a t-test. The results showed that the randomization tests produced results similar to that of t-tests.

Objective: Anxiety and depression have been conceptualised as being associated with “an abundance of habit and a dearth of control” (Hertel, 2015, p. 1). There has been a recent and burgeoning interest toward understanding the role of habits in health psychology and in the psychological disorders of obsessive-compulsive disorder and addiction in particular. To the author’s knowledge, there has been no previous systematic review that aimed to summarise the research investigating the involvement of mental habits in anxiety and depression in clinical and non-clinical populations. Method: The term habit was operationalized and inclusion criteria were specified in the domains of habit measurement, research paradigms, and manipulation tasks. A search across four databases was conducted: Web of Science, EBSCOhost, PubMed and OVID (PsycARTICLES and Journals@OVID). A progressive screening procedure yielded 8 relevant studies related to mental habits in anxiety (n = 1), depression (n = 4) and both anxiety and depression (n = 3). Results: Self-report habit measures correlate with the presence of symptoms. Computational modelling reinforcement learning and goal-devaluation paradigms demonstrate that anxiety and depression are associated with deficits in goal-directed learning and decision-making in favour of habitual learning strategies. Cognitive bias modification meets the criteria for enabling habit change and can strengthen or weaken interpretative habits in response to training. Conclusions: Despite considerable variability and limitations in the design of the studies appraised in this review, overall findings indicate support for habitual thought processes being implicated in anxiety and depression. Treating problematic thought processes in anxiety and depression as habitual – cued automatically by contextual cues, not goal-dependent and resistant to change – may be beneficial for future research and clinical applications. Abstract (Experimental Study) This study investigated predictions from the habit-goal framework for depressive rumination (Watkins & Nolen-Hoeksema, 2014) using a simultaneous replication single case experimental design in a multiple baseline case series. Seven high ruminators were recruited from community and university settings (with one participant’s data later excluded due to insufficient baseline rumination). Following a baseline monitoring period, participants received an intervention that included (i) spotting personal triggers for rumination and (ii) the practice of a scripted concrete thinking exercise (CTE) in response to these triggers, utilising an implementation intention (If-Then plan). It was predicted that practice of the IF-THEN CTE, linked to warning signs, would result in a significant reduction in both frequency and automaticity of rumination in the intervention phase compared to baseline. At the group level, using randomization tests (Onghena & Edgington, 2005), reductions in automaticity of rumination were trending toward statistical significance whilst the impact of the intervention on rumination frequency was not statistically significant. Effect size calculations, using nonoverlap of all pairs, demonstrated a medium effect of the intervention on automaticity (NAP = .76) and weak to medium effect on frequency of rumination (NAP = .66). Visual and statistical analysis of individual data demonstrated that two participants experienced statistically significant benefits (p < .05) for a reduction in automaticity of rumination and one participant’s frequency of rumination was significantly reduced. These two participants also showed the greatest levels of automaticity for the IF-THEN-CTE intervention during the intervention phase. Five participants demonstrated a strong or medium effect of the intervention on automaticity and two participants demonstrated a medium effect on frequency. Taken together, the data is broadly consistent with the predictions made by the habit-goal framework. Pre and post measures indicate reductions for all participants in rumination as habit using the self-report habit index (SRHI) and overall rumination levels rated on the ruminative responses scale (RRS). At post intervention three participants no longer met criteria for inclusion to the study on the RRS. Despite mixed results, feedback at debrief indicated that the intervention was acceptable to participants who reported that they would carry on using it after the study ended.

This study analyzed the effects of a randomization-based inference teaching methodology on students’ content mastery in an introductory statistics college course. The sample was 125 undergraduate students from Miami Dade College, a large Hispanic Serving Institution in the Southeast. A pretest-posttest nonequivalent group design was used for the study. Students in the randomization-based teaching modality received exposure to simulation activities, specifically bootstrap confidence intervals and randomization test, that aim to enhance conceptual understanding of inferential statistics, an important component of statistical literacy. The instructional strategy was designed to trigger critical reflection that confronted students with their thinking and lead them through a process of reorganization, restructure, and improvement of their concepts. The 40 item Comprehensive Assessment of Outcomes in a first Statistics course (CAOS) instrument was used to measure students’ conceptual understanding of important statistical ideas along with a demographic and academic survey that collected data on student characteristics. A stepwise linear regression method was used to look at the effects of group membership while controlling for Pre-CAOS scores, age, gender, first generation, prior experience with statistics, student status (part/full time), native speaker, STEM or not-STEM major, Hispanic, highest math course taken in high school, and GPA. The full model showed that only Group and Pre-CAOS score were the only significant predictors of Post CAOS scores. None of the other variables were significant. The model was a significant predictor of Post CAOS score, F(2, 121) = 16.96, p The results supported the claim that the randomization-based teaching modality for inferential statistics help Hispanic students to achieve a better understanding of the learning outcomes associated with an undergraduate introductory statistics course.

This thesis studies inference to the complier treatment effect denoted LATE. The standard approach is to base the inference on the two-stage least squares (2SLS) estimator and asymptotic Neyman inference, i.e., the t-test. The paper suggests a Fisher Randomization Test based on the t-test statistic as an alternative to the Neyman inference. Based on the setup with a randomized experiment with noncompliance, for which one can identify the LATE, I compare the two approaches in a Monte Carlo (MC) simulations. The results from the MC simulation is that the Fisher randomization test is not a valid alternative to the Neyman’s test as it has too low power.

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.

Submitted by (ana.araujo@ufrpe.br) on 2016-05-20T12:26:11Z No. of bitstreams: 1 Ana Clara Paixao Campos.pdf: 1515481 bytes, checksum: 29c30eb35f6e7da1f6e63d0971def668 (MD5) / Made available in DSpace on 2016-05-20T12:26:11Z (GMT). No. of bitstreams: 1 Ana Clara Paixao Campos.pdf: 1515481 bytes, checksum: 29c30eb35f6e7da1f6e63d0971def668 (MD5) Previous issue date: 2013-02-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Knowing the spatial pattern of patients with genetic disease with physical disabilities in the treatment of Pernambuco AACD is of great importance because it makes it possible to guide the basic care assistance to these individuals and provide solid basis for planning public health policies. However, there are few references in the literature using the tools of spatial analysis in the context of disability. This dissertation was structured in the form of two papers. In the first article the global Moran's I index was used to characterize the spatial pattern of the rate of patients with genetic disease with physical disabilities in the AACD treatment of Pernambuco and the results were compared with those obtained with the randomization test. In both approaches we found the existence of spatial pattern for the rate of patients with genetic disease with physical disabilities in the treatment of Pernambuco AACD when we took into account the rates of four municipalities closest to each location. In the second article we evaluated the performance of the global Moran's I index and the Mantel test with Spearman correlation, both using randomization to assess the statistical significance, regarding the ability to detect spatial pattern for the rate of patients with diseases genetic with physical disabilities in the AACD treatment of Pernambuco. The results showed that the global Moran's I index proved to be a more satisfactory method for detecting the spatial pattern, since it uses the information in its calculations of the neighborhood, and provide greater control of the rejection rates of the null hypothesis under study. / Conhecer o padrão espacial dos portadores de doença genética com deficiência física em tratamento na AACD de Pernambuco é de grande importância, pois torna possível orientar a assistência aos cuidados básicos desses indivíduos e fornecer base sólida para o planejamento de políticas públicas de saúde. Entretanto, existem poucas referências na literatura utilizando o instrumental da análise espacial no contexto da deficiência física. A presente dissertação foi estruturada na forma de dois artigos científicos. No primeiro artigo o Índice I global de Moran foi utilizado para caracterizar o padrão espacial da taxa de pacientes portadores de doença genética com deficiência física em tratamento na AACD de Pernambuco e os resultados encontrados foram comparados com os obtidos através do teste de aleatorização. Em ambas as metodologias constatou-se a existência de padrão espacial agregado para a taxa de pacientes portadores de doença genética com deficiência física em tratamento na AACD de Pernambuco quando se levou em consideração as taxas dos 4 municípios mais próximos de cada localidade. No segundo artigo foi avaliado o desempenho do índice I global de Moran e do teste de Mantel com correlação de Spearman, ambos utilizando aleatorização para avaliar a significância da estatística, no que tange a capacidade de detectar padrão espacial para a taxa de pacientes portadores de doenças genéticas com deficiência física em tratamento na AACD de Pernambuco. Os resultados indicaram que o índice I global de Moran mostrou-se uma metodologia mais satisfatória para detectar do padrão espacial, uma vez que utiliza em seus cálculos as informações da vizinhança, além de proporcionar maior controle das taxas de rejeição da hipótese nula em estudo.

Indiana University-Purdue University Indianapolis (IUPUI) / In medical research, data analysis often requires complex statistical methods where no closed-form solutions are available. Under such circumstances, Monte Carlo (MC) methods have found many applications. In this dissertation, we proposed several novel statistical models where MC methods are utilized. For the first part, we focused on semicompeting risks data in which a non-terminal event was subject to dependent censoring by a terminal event. Based on an illness-death multistate survival model, we proposed flexible random effects models. Further, we extended our model to the setting of joint modeling where both semicompeting risks data and repeated marker data are simultaneously analyzed. Since the proposed methods involve high-dimensional integrations, Bayesian Monte Carlo Markov Chain (MCMC) methods were utilized for estimation. The use of Bayesian methods also facilitates the prediction of individual patient outcomes. The proposed methods were demonstrated in both simulation and case studies. For the second part, we focused on re-randomization test, which is a nonparametric method that makes inferences solely based on the randomization procedure used in clinical trials. With this type of inference, Monte Carlo method is often used for generating null distributions on the treatment difference. However, an issue was recently discovered when subjects in a clinical trial were randomized with unbalanced treatment allocation to two treatments according to the minimization algorithm, a randomization procedure frequently used in practice. The null distribution of the re-randomization test statistics was found not to be centered at zero, which comprised power of the test. In this dissertation, we investigated the property of the re-randomization test and proposed a weighted re-randomization method to overcome this issue. The proposed method was demonstrated through extensive simulation studies.