Longitudinal studies rely on data collected at several occasions from a set of selected individuals. The purpose of these studies is to use a regression-type model to express a response variable as a function of explanatory variables, or covariates. In this thesis, we use marginal models for the analysis of such data, which, coupled with the method of estimating equations, provide estimators of the main regression parameter. When some of the responses are missing or there is error in the recorded covariates, the original estimating equation may be biased. We use techniques available in the literature to modify it and regain the unbiasedness property. We prove the asymptotic normality of the regression estimator obtained under these more realistic circumstances, and provide theoretical and numerical examples to illustrate this approach.

Three longitudinal pulmonary function data sets were analyzed by several statistical methods for the purposes of: 1) determining to what degree the conclusions of an analysis for a given data set are method dependent; 2) assessing the properties of each method across the different data sets; 3) studying the correlates of FEV₁ decline including physical, behavioral, and respiratory factors, as well as city of residence and type of work. 4) assessing the appropriateness of modelling the standard linear relationship of FEV₁ with time and providing alternative approaches; 5) describing longitudinal change in various lung function variables, apart from FEV₁. The three data sets were comprised of (1) yearly data on 141 veterans with mild chronic bronchitis, taken at three Canadian centres, for a maximum of 23 years of follow-up; their mean age at the start of the study was 49 years (s.d.=9) and only 10.6% were nonsmokers during the follow-up; (2) retrospective data on 384 coal workers categorized into four groups according to vital status (dead or alive) and smoking behavior, with irregular follow-up intervals ranging from 2 to 12 measurements per individual over a period of 9 to 30 years; (3) a relatively balanced data set on 269 grain workers and a control group of 58 civic workers, which consisted of 3 to 4 measurements taken over an average follow-up of 9 years. Their mean age at first measurement was 37 years (s.d.=10) and 53.2% of the subjects did not smoke. A review of the pulmonary and statistical literature was carried out to identify methods of analysis which had been applied to calculate annual change in FEV₁. Five methods chosen for the data analyses were variants of ordinary least squares approaches. The other four methods were based on the use of transformations, weighted least squares, or covariance structure models using generalized least squares approaches. For the coal workers, the groups that were alive at the time of ascertainment had significantly smaller average FEV₁ declines than the deceased groups. Post-retirement decline in FEV₁ was shown by one statistical method to significantly increase for coal workers who smoked, while a significant decrease was observed for nonsmokers. Veterans from Winnipeg consistently showed the lowest decline estimates in comparison to Halifax and Toronto; recorded air pollution measurements were found to be the lowest for Winnipeg, while no significant differences in smoking behavior were found between the veterans of each city. The data set of grain workers proved most ameniable to all the different analytical techniques, which were consistent in showing no significant differences in FEV₁ decline between the grain and civic workers groups and the lowest magnitude of FEV₁ decline. It was shown that quadratic and allometric analyses provided additional information to the linear description of FEV₁ decline, particularly for the study of pulmonary decline among older or exposed populations over an extended period of time. Whether the various initial lung function variables were each predictive of later decline was dependent on whether absolute or percentage decline was evaluated. The pattern of change in these lung function measures over time showed group differences suggestive of different physiological responses. Although estimates of FEV₁ decline were similar between the various methods, the magnitude and relative order of the different groups and the statistical significance of the observed inter-group comparisons were method-dependent No single method was optimal for analysis of all three data sets. The reliance on only one model, and one type of lung function measurement to describe the data, as is commonly found in the pulmonary literature, could lead to a false interpretation of the result Thus a comparative approach, using more than one justifiable model for analysis is recommended, especially in the usual circumstances where missing data or irregular follow-up times create imbalance in the longitudinal data set. / Graduate and Postdoctoral Studies / Graduate

Methods of testing for a location shift between two populations in a longitudinal study are investigated when the data of interest are ordered, categorical and non-linear. A non-standard analysis involving modelling of data over time with transition probability matrices is discussed. Next, the relative efficiencies of statistics more frequently used for the analysis of such categorical data at a single time point are examined. The Wilcoxon rank sum, McCullagh, and 2 sample t statistic are compared for the analysis of such cross sectional data using simulation and efficacy calculations. Simulation techniques are then utilized in comparing the stratified Wilcoxon, McCullagh and chi squared-type statistic in their efficiencies at detecting a location shift when the data are examined over two time points. The distribution of a chi squared-type statistic based on the simple contingency table constructed by merely noting whether a subject improved, stayed the same or deteriorated is derived. Applications of these methods and results to a data set of Multiple Sclerosis patients, some of whom were treated with interferon and some of whom received a placebo are provided throughout the thesis and our findings are summarized in the last Chapter. / Science, Faculty of / Statistics, Department of / Graduate

Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadul de Campinas, Instituto de Matematica, Estatistica e Ciencia da Computação / Made available in DSpace on 2018-07-19T15:02:38Z (GMT). No. of bitstreams: 1 Matsushita_RaulYukihiro_M.pdf: 5069321 bytes, checksum: 33e68cb30c3d4e7f0619337f45412af1 (MD5) Previous issue date: 1994 / Resumo: O presente trabalho apresenta alguns modelos lineares para dados longitudinais observados no tempo, enfocando-se o modelo de efeitos mistos. A matriz de covariância associada a esse modelo pode ser representada de forma estruturada. O interesse do trabalho é estudar formas da matriz de covariância que requerem poucos parâmetros a serem estimados (parcimoniosidade). Como os dados são observados ao longo do tempo, uma forma de parametrização parcimoniosa pode ser obtida através de estruturas de correlação temporal nos erros ou nos efeitos aleatórios. Apesar das variedades de estruturas temporais existentes, o que nos interessa estudar são estruturas simples como o AR( 1) e algumas variações, pois, em séries curtas, essas estruturas simples podem ser aproximações razoáveis de estruturas mais complexas. Discute-se também algumas questões sobre o problema da escolha do modelo adequado e alguns critérios de seleção do modelo. Essencialmente, a abordagem de estimação dos parâmetros do modelo de efeitos mistos é via máxima verossimilhança (MV) e MV restringi da. Para o cálculo numérico das estimativas, alguns algo ritmos numéricos são apresentados brevemente como o método de Newton-Raphson e o filtro de Kalman (este último é um algo ritmo útil para o cálculo da verossimilhança e das predições dos efeitos aleatórios). Algumas técnicas de diagnóstico são apresentadas como, por exemplo, o gráfico de probabilidade normal ponderado para checar a hipótese de normalidade dos efeitos aleatórios e o uso do semivariograma empírico para checar existência ou não de estrutura de correlação nos resíduos. O trabalho fornece apenas uma visão geral sobre modelos lineares em dados longitudinais. Dada a abrangência do tema é impossível tratar de todos os aspectos de forma detalhada. Desta forma, certas abordagens não serão consideradas, como a abordagem Bayesiana, ou foram dadas de forma superficial, como o algo ritmo EM, por exemplo. / Abstract: This work presents some linear models for longitudinal data observed at time points, specially the mixed effects model. The covariance matrix associated with this model can be represented in a structured form. This work's interest is to study some covariance forms that require few parameters to be estimate. A way of parsimonious parametrization can be obtained through time correlation structures on the errors or time-varying effects. In despite of the variety of time structures, we are concerned to study simple structures as the AR(1) and some variations, because, in short series, these simple structures can approximate more complex structures. Some questions about the adequate model choice and some model selection criterions also are discussed. The parameters estimation approaches of the random effects model considered are essentially the maximum likelihood (ML) and restricted ML (ReML). To compute estimates, some numeric algorithms are briefly presented as Newton-Raphson method and Kalman filter (this is a useful algorithm to compute exact likelihood and make predictions). Some diagnostics are presented; e.g., weighted normal probability plot to check normality of the random effects and the use of the empirical semivariogram to check residuals correlation structure. The work gives only an overview about linear models for longitudinal data. Because very broadly, it is impossible to take detailed the all features of this theme. So, certain approaches will not be considered, as the Bayesian approach, or will be superficially, as the EM algorithm, for example. / Mestrado / Mestre em Estatística

Background: While the physical and mental health advantages of regular physical activity are evident, 68% of adult Canadians are not meeting PA guidelines. Over the last thirty years, exercise behaviour has been mostly studied under the guise of the social cognitive framework, but emerging findings have shown identity to demonstrate predictive validity with physical activity independent of social cognitions. Exercise identity has been associated with increased frequency, duration, and intensity of exercise behaviour. Despite the bivariate correlation between identity and PA, the literature currently lacks longitudinal research to enhance the understanding of identity formation in new exercisers. Objective: The purpose of this study was to understand changes in identity among new exercisers based on the Physical Activity Self-Definition model and investigate whether exercise identity can predict exercise behaviour variations over nine weeks. Methods: Participants for this study were healthy adults (18-65) who were recruited from local gyms and recreation centres in Victoria, BC. The inclusion criteria were that participants must be new exercisers (new exercisers are those who just decided to exercise regularly or started exercising for less than 2 weeks, before baseline measurement) who were not meeting the Canadian Physical Activity guidelines upon recruitment. The study used a prospective, observational design with four measurement periods across nine weeks. Demographics were collected and exercise identity, affective attitude, commitment, capability and exercise behaviour were measured using questionnaires. The exercise Identity questionnaire was administered at 1 week, 3 weeks, 6 weeks and 9 weeks. Data analysis and longitudinal models used HLM and descriptive were generated with SPSS. Results: Affective attitude and commitment had significant correlations with identity, and identity had a significant correlation with exercise behaviour across all measurement times. Affective attitude, however, was the only significant predictor of exercise identity change over time. Capability was not associated with exercise identity. Furthermore, identity did not predict change in exercise over time. Discussion: This study provided insight into some of the factors that influence shifting exercise identity of new exercisers by testing the physical activity self-definition model (Kendzierski & Morganstein, 2009a) with longitudinal modelling. Based on the present results, it is recommended that health promoters focus on designing enjoyable programs for their novice clients, and provide a positive affective attitude toward exercising during each session. Although, exercise behaviours of the participants improved significantly during the course of this study, exercise identity was not able to predict the variation in exercise behaviour over 9 weeks. Overall, exercise identity formation can be a time-consuming process in adults, however, engaging in identity-related behaviours that are enjoyable can accelerate this process. / Graduate

abstract: The present study aimed to advance the current understanding of the relation between disability and subjective well-being by examining the extent to which different facets of subjective well-being (life satisfaction, positive affect, and negative affect) change before and after disability onset, and the extent to which age and type of disability moderate such changes. Multiphase growth-curve models to prospective longitudinal survey data from Waves 1-16 of the Household, Income and Labour Dynamics in Australia (HILDA) survey (N = 3,795; mean age = 50.22; age range: 16-99; 51% women). On average, life satisfaction remained relatively stable across the disability transition, whereas positive affect declined and negative affect increased the year surrounding disability onset; in the years thereafter, neither positive affect nor negative affect returned to pre-onset levels. Individuals who acquired disability in old age were more likely to report sustained declines in subjective well-being than were individuals who became disabled in midlife or young adulthood. Psychological disability was associated with the strongest declines across each indicator of subjective well-being at disability onset but also greater adaptation in the years thereafter. The findings provide further evidence against the set-point theory of hedonic adaptation and for a more moderate viewpoint that allows for processes of adaptation to vary based on the outcome examined, the type of stressor, and individual characteristics. The discussion focuses on possible mechanisms underlying the moderating roles of age and type of disability. / Dissertation/Thesis / Masters Thesis Psychology 2019

Indiana University-Purdue University Indianapolis (IUPUI) / Alzheimer’s Disease (AD) is one of the most common forms of dementia and is known to have a strong genetic component, but known genetic loci do not fully account for the observed genetic heritability of late onset AD. This genetic complexity is further complicated by disease heterogeneity, with non-uniform presentation and progression of AD neuropathology. Endophenotypes lie upstream of observed AD clinical outcomes and downstream of genetic contributors, allowing for a biological understanding of genetic effects. Understanding the genetic architecture of AD endophenotypes can aid in breaking down AD genetic complexity and heterogeneity. In this study we utilized a variety of models to evaluate the genetic contributors to pathological change and heterogeneity in the top markers of AD pathology: amyloid, tau, neurodegeneration, and cerebrovascular (A/T/N/V framework). Additional composite quantitative measures of cognitive performance were used to relate to downstream AD presentation. These biomarkers allow the investigation of genetic effects contributing to the disease over the stages of disease progression from amyloid deposition to neurofibrillary tangle formation, disruption of metabolism, brain atrophy, and finally to clinical outcomes. First, we performed genome-wide association studies (GWAS) for AD endophenotypes at baseline using a cross-sectional regression model. This method identified sixteen novel or replicated loci, with six (SRSF10, MAPT, XKR3, KIAA1671, ZNF826P, and LOC100507506) associated across multiple A/T/N biomarkers. Cross-sectional data was further utilized to identify three genetic loci (BACH2, EP300, PACRG-AS1) that showed disease stage specific interaction effects. We built upon those results by performing a longitudinal association analysis with linear-mixed effects modeling. Gene enrichment analysis of these results identified 19 significant genetic regions associated with linear longitudinal change in AD endophenotypes. To further break down longitudinal heterogeneity, a latent class mixed model approach was utilized to identify subgroups of longitudinal progression within cognitive and MRI measures, with 16 genetic loci associated with membership in different classes. The genetic patterns of these subgroups show biological relevance in AD. The methods and results from this study provide insight into the complex genetic architecture of AD endophenotypes and a foundation to build upon for future studies into AD genetic architecture. / 2022-11-26

Indiana University-Purdue University Indianapolis (IUPUI) / Joint models for longitudinal and time-to-event data has been introduced to study the association between repeatedly measured exposures and the risk of an event. The use of joint models allows a survival outcome to depend on some characteristic functions from the longitudinal measures. Current estimation methods include a two-stage approach, Bayesian and maximum likelihood estimation (MLEs) methods. The twostage method is computationally straightforward but often yields biased estimates. Bayesian and MLE methods rely on the joint likelihood of longitudinal and survival outcomes and can be computationally intensive. In this work, we propose a joint generalized estimating equation framework using an inverse intensity weighting approach for parameter estimation from joint models. The proposed method can be used to longitudinal outcomes from the exponential family of distributions and is computationally e cient. The performance of the proposed method is evaluated in simulation studies. The proposed method is used in an aging cohort to determine the relationship between longitudinal biomarkers and the risk of coronary artery disease.

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Kernel mixture models are proposed to cluster univariate, independent multivariate and dependent bivariate longitudinal data. The Gaussian distribution in finite mixture models is replaced by the Gaussian and gamma kernel functions, and the expectation-maximization algorithm is used to estimate bandwidths and compute log-likelihood scores. For dependent bivariate longitudinal data, the bivariate Gaussian copula is used to reveal the correlation between two attributes. After that, we use AIC, BIC and ICL to select the best model. In addition, we also introduce a kernel distance-based clustering method to compare with the kernel mixture models. A simulation is performed to illustrate the performance of this mixture model, and results show that the gamma kernel mixture model performs better than the kernel distance-based clustering method based on misclassification rates. Finally, these two models are applied to COVID-19 data, and sixty countries are classified into ten clusters based on growth rates and death rates. / Thesis / Master of Science (MSc)