Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models. Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was proposed to handle uneven follow-up assessments or skipped visits, resulting in the interval censored data. Simulations were used to compare the performance of the proposed model with the traditional discrete time stationary Markov chain under different types of observation schemes. We applied these two methods to the well-known Nun study, a longitudinal study of 672 participants aged ≥ 75 years at baseline and followed longitudinally with up to ten cognitive assessments per participant. Secondly, we constructed a non-homogenous Markov model for this type of panel data. The baseline intensity was assumed to be Weibull distributed to accommodate the non-homogenous property. The proportional hazards method was used to incorporate risk factors into the transition intensities. Simulation studies showed that the Weibull assumption does not affect the accuracy of the parameter estimates for the risk factors. We applied our model to data from the BRAiNS study, a longitudinal cohort of 531 subjects each cognitively intact at baseline. Last, we presented a parametric method of fitting semi-Markov models based on Weibull transition intensities with interval censored cognitive data with death as a competing risk. We relaxed the Markov assumption and took interval censoring into account by integrating out all possible unobserved transitions. The proposed model also allowed for incorporating time-dependent covariates. We provided a goodness-of-fit assessment for the proposed model by the means of prevalence counts. To illustrate the methods, we applied our model to the BRAiNS study.

Recent large-N studies conclude that inequality and ethnic distribution have no significant impact on the risk of civil conflict. This study argues that such conclusions are erroneous and premature due to incorrect specification of independent variables and functional forms. Case studies suggest that measures of inter-group inequality (horizontal inequality) and polarization (ethnic distribution distance from a bipolar equilibrium) are more accurate predictors of civil conflict, as they better capture the group-motivation aspect of conflict. This study explores whether indicators of inequality and ethnic distribution impact the probability of civil conflict across 38 developing countries in the period 1986 to 2004. Analysis reveals that horizontal inequality and polarization have significant, robust relationships with civil conflict. Furthermore, vertical, or individual, inequality is a robust, significant predictor of civil conflict when specified as a nonlinear function.

Census data indicates people with higher levels of education are leaving Appalachian Kentucky as they do in other rural areas. Aside from anecdotal information and primarily qualitative community studies, there is little quantitative evidence of the factors which may influence these migration decisions. State policies and regional efforts to increase educational attainment of people in the region have focused on producing more college degrees however may be contributing to the out-migration of those with higher levels of education. The study incorporates community level data with demographic, academic, and employment data from a cohort of 2005-06 college graduates from Appalachian Kentucky. The study includes an analysis of migration rates for a variety of different types of graduates and a set of three complimentary logistic regression models developed to understand the impact of individual demographic and academic factors, factors about the communities where these graduates came from, and the factors related to the communities where they went after completing their degrees and credentials to predict likelihood of migrating. This study builds upon previous efforts by providing extensive, externally validated data about a large population of individuals. It leverages sociological, demographic, and neoclassical microeconomic research methods and leverages data from Kentucky's statewide longitudinal data system to serve as an illustration for how these systems can be used for complex statistical analyses.

Latent variable models (LVMs) are commonly used in the scenario where the outcome of the main interest is an unobservable measure, associated with multiple observed surrogate outcomes, and affected by potential risk factors. This thesis develops an approach of efficient handling missing surrogate outcomes and covariates in two- and three-level latent variable models. However, corresponding statistical methodologies and computational software are lacking efficiently analyzing the LVMs given surrogate outcomes and covariates subject to missingness in the LVMs. We analyze the two-level LVMs for longitudinal data from the National Growth of Health Study where surrogate outcomes and covariates are subject to missingness at any of the levels. A conventional method for efficient handling of missing data is to reexpress the desired model as a joint distribution of variables, including the surrogate outcomes that are subject to missingness conditional on all of the covariates that are completely observable, and estimate the joint model by maximum likelihood, which is then transformed to the desired model. The joint model, however, identifies more parameters than desired, in general. The over-identified joint model produces biased estimates of LVMs so that it is most necessary to describe how to impose constraints on the joint model so that it has a one-to-one correspondence with the desired model for unbiased estimation. The constrained joint model handles missing data efficiently under the assumption of ignorable missing data and is estimated by a modified application of the expectation-maximization (EM) algorithm.

Event history analysis is the most prevalent modeling technique used to model event occurrence with longitudinal data (Cox & Oakes, 1984; Menard, 1991; Singer & Willett, 1993, 2003). An alternative is to model longitudinal data within the SEM framework, known as latent variable growth modeling (McArdle, 1988; Meredith & Tisak, 1990), which can provide a more robust framework. Whether or not a student remains in college presents an appropriate context within which to examine the modeling of event occurrence with longitudinal data. The purpose of the study was to compare event history and latent growth modeling as for predicting change in college student perseverance, with college student persistence literature serving as the framework. Students are defined as having persevered if they have earned hours and the end of the semester rather than if they are enrolled at the beginning of the semester, which is the traditional definition of persistence.The population for the study was the 2001 and 2002 cohorts of first-time, full-time freshmen at a large mid-Atlantic urban research university. Stopouts and transfer students were excluded. Data was analyzed for the first five semesters for each cohort. The results showed that parameter estimates were quite consistent across model type and time frame and were mostly consistent with previous research. No one method outperformed the others in terms of predicting correct classification. Using event history analysis with the structural equation modeling framework, however, appeared to be a very promising alternative to event history analysis with logistic regression since one can model error term and examine the differential effects of predictors at each time period. Finally, while latent growth modeling did not outperform the other methods in predictive classification, the study demonstrated it can be used for event occurrence analysis to test more complex theories.

O mamão (Carica papaya L.) tem importância destacada na fruticultura e se encontra entre os seis principais produtos que somam mais de 50% da produção nacional desse setor. O mamão tem uma maturação relativamente rápida. Visando aumentar o potencial de comércio e possivelmente diminuir as perdas pós-colheita, a análise de imagens digitais é um recurso tecnológico para avaliar a tonalidade e intensidade da cor da casca dos frutos no período de maturação, que serve de base para estabelecer modelos funcionais para mensurações realizadas num período de tempo. Nesse contexto tem como motivação um estudo longitudinal envolvendo a avaliação da intensidade e tonalidade da cor da casca do mamão da espécie Carica papaya L. no período de maturação. Para a análise dos dados é utilizada a metodologia dos modelos lineares de efeitos mistos e para selecionar os modelos que melhor se ajustavam aos dados, utilizou-se teste da razão de verossimilhanças e teste F, em um método de seleção top-down. Verifica-se que modelo polinomial quadrático com efeito aleatório em todos os parâmetros descreve de maneira satisfatória a variável tonalidade. Para a variável intensidade obteve-se um modelo polinomial cúbico para os efeitos aleatórios e apenas o intercepto como parâmetro de efeito fixo. As análises de diagnóstico confirmaram o ajuste satisfatório dos modelos. / The papaya (Carica papaya L.) has important importance in fruticulture and is among the six main products that add up to more than 50% of the national production of this sector. Papaya has a relatively rapid maturation. In order to increase commercial potential and possibly reduce post-harvest losses, digital image analysis is a technological tool to evaluate the color tone and intensity of fruit peel during the maturation period, which serves as the basis for establishing functional models for measurements performed over a period of time. In this context it has as motivation a longitudinal study involving the evaluation of the intensity and color tone of the shell of the papaya of the species Carica papaya L. in the maturation period. For the analysis of the data the methodology of the linear models of mixed effects is used and to select the models that best fit the data, was used a test of the likelihood ratio and test F, in a method of selection top-down. It can be verified that the quadratic polynomial model with random effect in all the parameters describes in a satisfactory way the variable tonality. For the intensity variable we obtained a cubic polynomial model for the random effects and only the intercept as a fixed effect parameter. Diagnostic analyzes confirmed the satisfactory fit of the models.

Orientador: Carlos Roberto Padovani / Banca: Carlos Roberto Padovani / Banca: Adalberto José Crocci / Banca: Jacinta Ludovico Zambotti / Banca: Luciano Soares de Souza / Banca: José Carlos Martinez / Resumo: O presente trabalho discutiu aspectos teóricos e práticos do comportamento da variável resposta nos diferentes grupos e condições de avaliação utilizando o Ajuste de Curvas de Crescimento, procedimento multivariado de análise de dados experimentais que possibilita fazer previsões sobre o comportamento médio da resposta para situações diferentes daquelas para as quais o estudo foi planejado, além de propiciar análise comparativa das curvas dos grupos de interesse. Considerando a dificuldade existente quanto a programas computacionais acessíveis a pesquisadores das áreas agronômicas, biológicas e da saúde, e a falta de entendimento da complexidade da estrutura de análise dos dados longitudinais, elaborou-se programa computacional em linguagem que permita ao usuário facilidade de manuseio, e torná-lo disponível, para pesquisadores das áreas aplicadas e, finalmente, discutir as vantagens do procedimento multivariado na preservação da estrutura de dependência dos dados em relação aos procedimentos convencionais utilizados na experimentação agronômica. / Abstract: The purpose of the present paper is to discuss theoretical and practical aspects of the behavior of response variables in different groups and evaluation conditions by using Growth Curves methodology. This methodology refers to a multivariate procedure of experimental data analysis that makes forecasts about the average behavior of the response variable for different situations from that for which the study was planned. In additien, the methodology enables comparative analysis of the curves between each of the experimental groups. Considering the lack of easy-use computer programs for researchers in the agronomical, biological and health fields, and the difficulty to understand the complexity of the data structure in longitudinal studies, a computer program will be proposed and written using high level language. The software will be of simple handling, easy access to researchers of applied areas and available. This work will also discuss the advantages of using the multivariate procedure of analysis compared to the conventional procedures commonly used in agronomic experimentation, related to the preservation of the structure of data dependence. / Doutor

COELHO-BARROS, E. A. Analise estatstica para dados de contagem longitudinais na presenca de covariaveis: Aplicações na area medica. Dissertação (mestrado) - Faculdade de Medicina de Ribeirão Preto - USP, Ribeirão Preto - SP - Brasil, 2009. Dados de contagem ao longo do tempo na presenca de covariaveis são muito comuns em estudos na area da saude coletiva, por exemplo; numero de doenças que uma pessoa, com alguma caracteristica especifica, adquiriu ao longo de um período de tempo; numero de internações hospitalares em um período de tempo, devido a algum tipo de doença; numero de doadores de orgãos em um período de tempo. Nesse trabalho são apresentados diferentes modelos estatsticos de\\fragilidade\" de Poisson para a analise estatística de dados de contagem longitudinais. Teoricamente, a distribuição de Poisson exige que a media seja igual a variância, quando isto não ocorre tem-se a presenca de uma variabilidade extra-Poisson. Os modelos estatsticos propostos nesta dissertação incorporam a variabilidade extra-Poisson e capturam uma possvel correlação entre as contagens para o mesmo indivduo. Para cada modelo foi feito uma analise Bayesiana Hierarquica considerando os metodos MCMC (Markov Chain Monte Carlo). Utilizando bancos de dados reais, cedidos por pesquisadores auxiliados pelo CEMEQ (Centro de Metodos Quantitativos, USP/FMRP), foram discutidos alguns aspectos de discriminação Bayesiana para a escolha do melhor modelo. Um exemplo de banco de dados reais, discutido na Seção 4 dessa dissertação, que se encaixa na area da saude coletiva, e composto de um estudo prospectivo, aberto e randomizado, realizado em pacientes infectados pelo HIV que procuraram atendimento na Unidade Especial de Terapia de Doencas Infecciosas (UETDI) do Hospital das Clnicas da Faculdade de Medicina de Ribeirão Preto da Universidade de São Paulo (HCFMRP-USP). Os esquemas terapêuticos estudados consistiam em zidovudina e lamivudina, associadas ao efavirenz ou lopinavir. Entre setembro de 2004 e maio de 2006 foram avaliados 66 pacientes, sendo 43 deles includos no estudo. Destes, 39 participantes alcançaram a semana 24 de acompanhamento, enquanto 27 atingiram a semana 48. Os grupos de pacientes apresentavam características basais semelhantes, quanto a idade, sexo, mediana de CD4 e carga viral. O interesse desse experimento e estudar a contagem de CD4 considerando os dois esquemas terapêuticos (efavirenz e lopinavir). / COELHO-BARROS, E. A. Analise estatstica para dados de contagem longitudinais na presenca de covariaveis: Aplicac~oes na area medica. Dissertac~ao (mestrado) - Faculdade de Medicina de Ribeir~ao Preto - USP, Ribeir~ao Preto - SP - Brasil, 2009. Longitudinal counting data in the presence of covariates is very common in many applications, especially considering medical data. In this work we present dierent \\frailty\"models to analyze longitudinal Poisson data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. A hierarchical Bayesian analysis is introduced for each dierent model considering usual MCMC (Markov Chain Monte Carlo) methods. Considering reals biological data set (obtained from CEMEQ, Medical School of Ribeir~ao Preto, University of S~ao Paulo, Brazil), we also discuss some Bayesian discrimination aspects for the choice of the best model. In Section 4 is considering a data set related to an open prospective and randomized study, considering of HIV infected patients, free of treatments, which entered the Infection Diseases Therapy Special Unit (UETDI) of the Clinical Hospital of the Medical School of Ribeir~ao Preto, University of S~ao Paulo (HCFMRP-USP). The therapeutic treatments consisted of the drugs Zidovudine and Lamivudine, associated to Efavirenz and Lopinavir. The data set was related to 66 patients followed from September, 2004 to may, 2006, from which, 43 were included in the study. The patients groups presented similar basal characteristics in terms of sex, age, CD4 counting median and viral load. The main goal of this study was to compare the CD4 cells counting for the two treatments, based on the drugs Efavirenz and Lopinavir, recently adopted as preferencial for the initial treatment of the disease.

Este trabalho tem como objetivo aplicar a teoria de modelos mistos ao estudo do teor de nitrogênio e carbono no solo, em diversas profundidades. Devido a grande quantidade de matéria orgânica no solo, o teor de nitrogênio e carbono apresentam alta variabilidade nas primeiras profundidades, além de apresentar um comportamento não linear. Assim, fez-se necessário utilizar a abordagem de modelos não lineares mistos a dados longitudinais. A utilização desta abordagem proporciona um modelo que permite modelar dados não lineares, com heterogeneidade de variâncias, fornecendo uma curva para cada amostra. / This paper has as an objective to apply the theory of mixed models to the content of nitrogen and carbon in the soil at various depths. Due to the large amount of organic material in the soil, the content of nitrogen and carbon present high variability in the depths of soil surface, and present a nonlinear behavior. Thus, it was necessary to use the approach of nonlinear mixed models to longitudinal data analysis. The use of this approach provides a model that allows to model nonlinear data with heterogeneity of variances by providing a curve for each sample.

Em ensaios clínicos é muito comum a ocorrência de dados longitudinais discretos. Para sua análise é necessário levar em consideração que dados observados na mesma unidade experimental ao longo do tempo possam ser correlacionados. Além dessa correlação inerente aos dados é comum ocorrer o fenômeno de superdispersão (ou sobredispersão), em que, existe uma variabilidade nos dados além daquela captada pelo modelo. Um caso que pode acarretar a superdispersão é o excesso de zeros, podendo também a superdispersão ocorrer em valores não nulos, ou ainda, em ambos os casos. Molenberghs, Verbeke e Demétrio (2007) propuseram uma classe de modelos para acomodar simultaneamente a superdispersão e a correlação em dados de contagens: modelo Poisson, modelo Poisson-gama, modelo Poisson-normal e modelo Poisson-normal-gama (ou modelo combinado). Rizzato (2011) apresentou a abordagem bayesiana para o ajuste desses modelos por meio do Método de Monte Carlo com Cadeias de Markov (MCMC). Este trabalho, para modelar a incerteza relativa aos parâmetros desses modelos, considerou a abordagem bayesiana por meio de um método determinístico para a solução de integrais, INLA (do inglês, Integrated Nested Laplace Approximations). Além dessa classe de modelos, como objetivo, foram propostos outros quatros modelos que também consideram a correlação entre medidas longitudinais e a ocorrência de superdispersão, além da ocorrência de zeros estruturais e não estruturais (amostrais): modelo Poisson inacionado de zeros (ZIP), modelo binomial negativo inacionado de zeros (ZINB), modelo Poisson inacionado de zeros - normal (ZIP-normal) e modelo binomial negativo inacionado de zeros - normal (ZINB-normal). Para ilustrar a metodologia desenvolvida, um conjunto de dados reais referentes à contagens de ataques epilépticos sofridos por pacientes portadores de epilepsia submetidos a dois tratamentos (um placebo e uma nova droga) ao longo de 27 semanas foi considerado. A seleção de modelos foi realizada utilizando-se medidas preditivas baseadas em validação cruzada. Sob essas medidas, o modelo selecionado foi o modelo ZIP-normal, sob o modelo corrente na literatura, modelo combinado. As rotinas computacionais foram implementadas no programa R e são parte deste trabalho. / Discrete and longitudinal structures naturally arise in clinical trial data. Such data are usually correlated, particularly when the observations are made within the same experimental unit over time and, thus, statistical analyses must take this situation into account. Besides this typical correlation, overdispersion is another common phenomenon in discrete data, defined as a greater observed variability than that nominated by the statistical model. The causes of overdispersion are usually related to an excess of observed zeros (zero-ination), or an excess of observed positive specific values or even both. Molenberghs, Verbeke e Demétrio (2007) have developed a class of models that encompasses both overdispersion and correlation in count data: Poisson, Poisson-gama, Poisson-normal, Poissonnormal- gama (combined model) models. A Bayesian approach was presented by Rizzato (2011) to fit these models using the Markov Chain Monte Carlo method (MCMC). In this work, a Bayesian framework was adopted as well and, in order to consider the uncertainty related to the model parameters, the Integrated Nested Laplace Approximations (INLA) method was used. Along with the models considered in Rizzato (2011), another four new models were proposed including longitudinal correlation, overdispersion and zero-ination by structural and random zeros, namely: zero-inated Poisson (ZIP), zero-inated negative binomial (ZINB), zero-inated Poisson-normal (ZIP-normal) and the zero-inated negative binomial-normal (ZINB-normal) models. In order to illustrate the developed methodology, the models were fit to a real dataset, in which the response variable was taken to be the number of epileptic events per week in each individual. These individuals were split into two groups, one taking placebo and the other taking an experimental drug, and they observed up to 27 weeks. The model selection criteria were given by different predictive measures based on cross validation. In this setting, the ZIP-normal model was selected instead the usual model in the literature (combined model). The computational routines were implemented in R language and constitute a part of this work.