Correlated data frequently arise from epidemiological studies, especially familial and longitudinal studies. Longitudinal design has been used by researchers to investigate the changes of certain characteristics over time at the individual level as well as how potential factors influence the changes. Familial studies are often designed to investigate the dependence of health conditions among family members. Various models have been developed for this type of multivariate data, and a wide variety of estimation techniques have been proposed. However, data collected from observational studies are often far from perfect, as measurement error may arise from different sources such as defective measuring systems, diagnostic tests without gold references, and self-reports. Under such scenarios only rough surrogate variables are measured. Measurement error in covariates in various regression models has been discussed extensively in the literature. It is well known that naive approaches ignoring covariate error often lead to inconsistent estimators for model parameters. In this thesis, we develop inferential procedures for analyzing correlated data with response measurement error. We consider three scenarios: (i) likelihood-based inferences for generalized linear mixed models when the continuous response is subject to nonlinear measurement errors; (ii) estimating equations methods for binary responses with misclassifications; and (iii) estimating equations methods for ordinal responses when the response variable and categorical/ordinal covariates are subject to misclassifications. The first problem arises when the continuous response variable is difficult to measure. When the true response is defined as the long-term average of measurements, a single measurement is considered as an error-contaminated surrogate. We focus on generalized linear mixed models with nonlinear response error and study the induced bias in naive estimates. We propose likelihood-based methods that can yield consistent and efficient estimators for both fixed-effects and variance parameters. Results of simulation studies and analysis of a data set from the Framingham Heart Study are presented. Marginal models have been widely used for correlated binary, categorical, and ordinal data. The regression parameters characterize the marginal mean of a single outcome, without conditioning on other outcomes or unobserved random effects. The generalized estimating equations (GEE) approach, introduced by Liang and Zeger (1986), only models the first two moments of the responses with associations being treated as nuisance characteristics. For some clustered studies especially familial studies, however, the association structure may be of scientific interest. With binary data Prentice (1988) proposed additional estimating equations that allow one to model pairwise correlations. We consider marginal models for correlated binary data with misclassified responses. We develop “corrected” estimating equations approaches that can yield consistent estimators for both mean and association parameters. The idea is related to Nakamura (1990) that is originally developed for correcting bias induced by additive covariate measurement error under generalized linear models. Our approaches can also handle correlated misclassifications rather than a simple misclassification process as considered by Neuhaus (2002) for clustered binary data under generalized linear mixed models. We extend our methods and further develop marginal approaches for analysis of longitudinal ordinal data with misclassification in both responses and categorical covariates. Simulation studies show that our proposed methods perform very well under a variety of scenarios. Results from application of the proposed methods to real data are presented. Measurement error can be coupled with many other features in the data, e.g., complex survey designs, that can complicate inferential procedures. We explore combining survey weights and misclassification in ordinal covariates in logistic regression analyses. We propose an approach that incorporates survey weights into estimating equations to yield design-based unbiased estimators. In the final part of the thesis we outline some directions for future work, such as transition models and semiparametric models for longitudinal data with both incomplete observations and measurement error. Missing data is another common feature in applications. Developing novel statistical techniques for dealing with both missing data and measurement error can be beneficial.

Correlated data frequently arise from epidemiological studies, especially familial and longitudinal studies. Longitudinal design has been used by researchers to investigate the changes of certain characteristics over time at the individual level as well as how potential factors influence the changes. Familial studies are often designed to investigate the dependence of health conditions among family members. Various models have been developed for this type of multivariate data, and a wide variety of estimation techniques have been proposed. However, data collected from observational studies are often far from perfect, as measurement error may arise from different sources such as defective measuring systems, diagnostic tests without gold references, and self-reports. Under such scenarios only rough surrogate variables are measured. Measurement error in covariates in various regression models has been discussed extensively in the literature. It is well known that naive approaches ignoring covariate error often lead to inconsistent estimators for model parameters. In this thesis, we develop inferential procedures for analyzing correlated data with response measurement error. We consider three scenarios: (i) likelihood-based inferences for generalized linear mixed models when the continuous response is subject to nonlinear measurement errors; (ii) estimating equations methods for binary responses with misclassifications; and (iii) estimating equations methods for ordinal responses when the response variable and categorical/ordinal covariates are subject to misclassifications. The first problem arises when the continuous response variable is difficult to measure. When the true response is defined as the long-term average of measurements, a single measurement is considered as an error-contaminated surrogate. We focus on generalized linear mixed models with nonlinear response error and study the induced bias in naive estimates. We propose likelihood-based methods that can yield consistent and efficient estimators for both fixed-effects and variance parameters. Results of simulation studies and analysis of a data set from the Framingham Heart Study are presented. Marginal models have been widely used for correlated binary, categorical, and ordinal data. The regression parameters characterize the marginal mean of a single outcome, without conditioning on other outcomes or unobserved random effects. The generalized estimating equations (GEE) approach, introduced by Liang and Zeger (1986), only models the first two moments of the responses with associations being treated as nuisance characteristics. For some clustered studies especially familial studies, however, the association structure may be of scientific interest. With binary data Prentice (1988) proposed additional estimating equations that allow one to model pairwise correlations. We consider marginal models for correlated binary data with misclassified responses. We develop “corrected” estimating equations approaches that can yield consistent estimators for both mean and association parameters. The idea is related to Nakamura (1990) that is originally developed for correcting bias induced by additive covariate measurement error under generalized linear models. Our approaches can also handle correlated misclassifications rather than a simple misclassification process as considered by Neuhaus (2002) for clustered binary data under generalized linear mixed models. We extend our methods and further develop marginal approaches for analysis of longitudinal ordinal data with misclassification in both responses and categorical covariates. Simulation studies show that our proposed methods perform very well under a variety of scenarios. Results from application of the proposed methods to real data are presented. Measurement error can be coupled with many other features in the data, e.g., complex survey designs, that can complicate inferential procedures. We explore combining survey weights and misclassification in ordinal covariates in logistic regression analyses. We propose an approach that incorporates survey weights into estimating equations to yield design-based unbiased estimators. In the final part of the thesis we outline some directions for future work, such as transition models and semiparametric models for longitudinal data with both incomplete observations and measurement error. Missing data is another common feature in applications. Developing novel statistical techniques for dealing with both missing data and measurement error can be beneficial.

Made available in DSpace on 2016-04-28T14:58:36Z (GMT). No. of bitstreams: 1 2008 - Fabio Mathias Correa.pdf: 2421517 bytes, checksum: 7f7f9e77fc6d68db6e05dbd9994c1e38 (MD5) Previous issue date: 2008-02-28 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The late blight of the tomato, caused by Phytophthora infestans (Mont) of Bary it is one of the main diseases of the tomato. However, the quantification of the severity of the disease, doesn't possess a standard method of evaluation and that, it can interfere in the comparison of results among and inside of experiments, once the scale of evaluation of the disease should be standardized. A diagrammatic scale should represent all variation of the existent disease in the field and to make possible necessary evaluations and perfected, independent of the existent differences among appraisers. Another important factor in the epidemiological studys, is the correct application of the methodologies of evaluation of treatments or cultivars. Therefore, the present work has as objectives: 1) to develop and to validate a diagrammatic scale for quantification of the severity of the late blight in tomateiro leaves and 2) to compare the use of AUDPC (area under disease progress curve), certain according to Shanner & Finney (1977), with the use of mixed models and mixed lineal models widespread in the selection of gen?tipos of resistant tomateiro to the requeima. Three diagrammatics scales were proposed for evaluation of the late blight in tomato leaves. The first scale, denominated scale-detailed, it was composed by nine values of severity intensity (0, 3, 6, 12, 22, 40, 60, 77 and 90%), the second climb, call of having scale-simplified, it was composed by seven severity values (0, 3, 12, 22, 40, 60 and 77%) and the third scale, of having James-modified, composed by seven severity values (0, 1, 5, 10, 16, 32 and 50%). For the validation of the scales, 24 appraisers accomplished two evaluations in leaves 50 tomato leaves with different severity levels, where the precision, acuracy and repetibility were appraised through simple lineal regression, analysis of variance of the mistakes and correlation coefficient. Among the proposed scales, two came as tools that allow a good precision and acuracy in the evaluation of the severity of the late blight in tomato leaves, being the detailed scale and the simplified scale. With relationship to the analysis methods, the use of direct AACPD, calculated by the sum of Riemann, and of mixed and mixed models widespread, it was verified that the direct use of AUDPC, doesn't get to describe all existent variation in the sample, probably for the great number of treatments. The use of mixed models widespread, that it considers the distribution of Poisson, it was shown more appropriate for to describe the epidemic caused by late blight in tomato, being more suitable in the selection of tomato cultivars seeking to the resistance the this disease. / A requeima, causada por Phytophthora infestans ? uma das principais doen?as do tomateiro. Para quantificar a severidade da doen?a, n?o h? um m?todo padr?o, o que pode interferir na compara??o de resultados entre e dentro de experimentos, uma vez que a escala de avalia??o da doen?a deve ser padronizada. Uma escala diagram?tica deve representar toda a varia??o da severidade no campo e possibilitar avalia??es precisas e acuradas, independente das diferen?as entre avaliadores. Outro fator importante no estudo epidemiol?gico ? a correta aplica??o das metodologias de avalia??o de tratamentos ou gen?tipos. Portanto, o presente trabalho objetivou: 1) desenvolver e validar uma escala diagram?tica para quantifica??o da severidade da requeima em folhas de tomateiro e 2) comparar o uso da ?rea abaixo da curva de progresso da doen?a (AACPD), com o uso de modelos mistos e modelos lineares mistos generalizados na sele??o de gen?tipos de tomateiro resistentes ? requeima. Tr?s escalas diagram?ticas foram propostas para avalia?ar a requeima em folhas de tomateiro. A primeira, denominada escala-detalhada, foi composta por nove valores de intensidade de severidade (0, 3, 6, 12, 22, 40, 60, 77 e 90%). A segunda escala, chamada de escala-simplificada, foi composta por sete valores de severidade (0, 3, 12, 22, 40, 60 e 77%) e a terceira, de Jamesmodificada, composta por sete valores de severidade (0, 1, 5, 10, 16, 32 e 50%). Para a valida??o das escalas, 24 avaliadores realizaram duas avalia??es em 50 folhas de tomateiro com diferentes n?veis de severidade, e a precis?o, acur?cia e a repetibilidade dos avaliadores foram avaliados atrav?s de regress?o linear simples, an?lise de vari?ncia dos erros e coeficiente de correla??o de Pearson. Dentre as escalas propostas, duas (escala detalhada e escala simplificada) apresentaram uma boa precis?o e acur?cia para a avalia??o da severidade da requeima em folhas de tomateiro. Quanto aos m?todos de an?lise, constatou-se que o uso direto da AACPD, obtido pela soma de Riemann, n?o conseguiu descrever toda varia??o existente na amostra, provavelmente pelo grande n?mero de tratamentos. O uso de modelos mistos generalizados, que considera a distribui??o de Poisson, foi mais adequado para descrever a epidemia, sendo mais indicado na sele??o de gen?tipos de tomate resistentes a doen?a.

Indiana University-Purdue University Indianapolis (IUPUI) / The research ideas included in this dissertation are motivated by a large sexually trans mitted infections (STIs) study (IU Phone study), which is also an ecological momentary assessment (EMA) study implemented by Indiana University from 2008 to 2013. EMA, as a group of methods used to collect subjects’ up-to-date behaviors and status, can increase the accuracy of this information by allowing a participant to self-administer a survey or diary entry, in their own environment, as close to the occurrence of the behavior as possible. IU Phone study’s high reporting level shows one of the benefits gain from introducing EMA in STIs study. As a prospective study lasting for 84 days, participants in IU Phone study undergo STI testing and complete EMA forms with project-furnished cellular telephones according to the predetermined schedules. At pre-selected eight-hour intervals, participants respond to a series of questions to identify sexual and non-sexual interactions with specific partners including partner name, relationship satisfaction and sexual satisfaction with this partner, time of each coital event and condom use for each event. etc. STIs lab results of all the participants are collected weekly as well. We are interested in several variables related to the risk of infection and sexual or non-sexual behaviors, especially the relationship among the longitudinal processes of those variables. New statistical models and applications are established to deal with the data with complex dependence and sampling data structures. The methodologies covers various of statistical aspect like generalized mixed models, mul tivariate models and autoregressive and cross-lagged model in longitudinal data analysis, misclassification adjustment in imperfect diagnostic tests, and variable-domain functional regression in functional data analysis. The contribution of our work is we bridge the meth ods from different areas with EMA data in the IU Phone study and also build up a novel understanding of the association among all the variables of interest from different perspec tives based on the characteristic of the data. Besides all the statistical analyses included in this dissertation, variety of data visualization techniques also provide informative support in presenting the complex EMA data structure.