Thesis--Tübingen. / Vita. Includes bibliographical references (p. 448-484).

The main goal of this thesis is to analyse the fluctuation of the employees in a well established Czech manufacturing company. Due to the GDPR regulations, the underlying company is kept anonymised in this thesis. The data were transformed into longitudinal data and the GEE methodology was used for the analysis of the fluctuation. In the first chapter, an introduction to the problem and a short description of the data is provided. The second chapter contains some theoretical description of the GEE methodology and the QIC information criterion. In the third chapter, multiple models for a binary and multinomial response are fitted to the data and their results are described in detail. This allows us to describe the influence of various factors to the fluctuation of the employees in the underlying company. 1

Longitudinal surveys have emerged in recent years as an important data collection tool for population studies where the primary interest is to examine population changes over time at the individual level. The National Longitudinal Survey of Children and Youth (NLSCY), a large scale survey with a complex sampling design and conducted by Statistics Canada, follows a large group of children and youth over time and collects measurement on various indicators related to their educational, behavioral and psychological development. One of the major objectives of the study is to explore how such development is related to or affected by familial, environmental and economical factors. The generalized estimating equation approach, sometimes better known as the GEE method, is the most popular statistical inference tool for longitudinal studies. The vast majority of existing literature on the GEE method, however, uses the method for non-survey settings; and issues related to complex sampling designs are ignored. This thesis develops methods for the analysis of longitudinal surveys when the response variable contains missing values. Our methods are built within the GEE framework, with a major focus on using the GEE method when missing responses are handled through hot-deck imputation. We first argue why, and further show how, the survey weights can be incorporated into the so-called Pseudo GEE method under a joint randomization framework. The consistency of the resulting Pseudo GEE estimators with complete responses is established under the proposed framework. The main focus of this research is to extend the proposed pseudo GEE method to cover cases where the missing responses are imputed through the hot-deck method. Both weighted and unweighted hot-deck imputation procedures are considered. The consistency of the pseudo GEE estimators under imputation for missing responses is established for both procedures. Linearization variance estimators are developed for the pseudo GEE estimators under the assumption that the finite population sampling fraction is small or negligible, a scenario often held for large scale population surveys. Finite sample performances of the proposed estimators are investigated through an extensive simulation study. The results show that the pseudo GEE estimators and the linearization variance estimators perform well under several sampling designs and for both continuous response and binary response.

Longitudinal surveys have emerged in recent years as an important data collection tool for population studies where the primary interest is to examine population changes over time at the individual level. The National Longitudinal Survey of Children and Youth (NLSCY), a large scale survey with a complex sampling design and conducted by Statistics Canada, follows a large group of children and youth over time and collects measurement on various indicators related to their educational, behavioral and psychological development. One of the major objectives of the study is to explore how such development is related to or affected by familial, environmental and economical factors. The generalized estimating equation approach, sometimes better known as the GEE method, is the most popular statistical inference tool for longitudinal studies. The vast majority of existing literature on the GEE method, however, uses the method for non-survey settings; and issues related to complex sampling designs are ignored. This thesis develops methods for the analysis of longitudinal surveys when the response variable contains missing values. Our methods are built within the GEE framework, with a major focus on using the GEE method when missing responses are handled through hot-deck imputation. We first argue why, and further show how, the survey weights can be incorporated into the so-called Pseudo GEE method under a joint randomization framework. The consistency of the resulting Pseudo GEE estimators with complete responses is established under the proposed framework. The main focus of this research is to extend the proposed pseudo GEE method to cover cases where the missing responses are imputed through the hot-deck method. Both weighted and unweighted hot-deck imputation procedures are considered. The consistency of the pseudo GEE estimators under imputation for missing responses is established for both procedures. Linearization variance estimators are developed for the pseudo GEE estimators under the assumption that the finite population sampling fraction is small or negligible, a scenario often held for large scale population surveys. Finite sample performances of the proposed estimators are investigated through an extensive simulation study. The results show that the pseudo GEE estimators and the linearization variance estimators perform well under several sampling designs and for both continuous response and binary response.

The case-control studies are primary tools for the study of risk factors (exposures) related to the disease interested. The case-control studies using longitudinal data are cost and time efficient when the disease is rare and assessing the exposure level of risk factors is difficult. Instead of GEE method, the method of using a prospective logistic model for analyzing case-control longitudinal data was proposed and the semiparametric inference procedure was explored by Park and Kim (2004). In this thesis, we apply an empirical likelihood ratio method to derive limiting distribution of the empirical likelihood ratio and find one likelihood-ratio based confidence region for the unknown regression parameters. Our approach does not require estimating the covariance matrices of the parameters. Moreover, the proposed confidence region is adapted to the data set and not necessarily symmetric. Thus, it reflects the nature of the underlying data and hence gives a more representative way to make inferences about the parameter of interest. We compare empirical likelihood method with normal approximation based method, simulation results show that the proposed empirical likelihood ratio method performs well in terms of coverage probability.

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.

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.

Doctor of Philosophy / Department of Statistics / Shie-Shien Yang / When the primary research interest is in the marginal dependence between the response and the covariates, logistic GEE (Generalized Estimating Equation) models are often used to analyze clustered binary data. Relative to ordinary logistic regression, very little work has been done to assess the lack of fit of a logistic GEE model. A new method addressing the LOF of a logistic GEE model was proposed. Simulation results indicate the proposed method performs better than or as well as other currently available LOF methods for logistic GEE models. A SAS macro was developed to implement the proposed method. Nonlinear regression models are widely used in medical science. Before the models can be fit and parameters interpreted, researchers need to decide which design points in a prespecified design space should be included in the experiment. Careful choices at this stage will lead to efficient usage of limited resources. We proposed a cost efficient Bayesian optimal design method for nonlinear combinations of parameters in a nonlinear model with quantitative predictors. An R package was developed to implement the proposed method.

Data obtained from longitudinal surveys using complex multi-stage sampling designs contain cross-sectional dependencies among units caused by inherent hierarchies in the data, and within subject correlation arising due to repeated measurements. The statistical methods used for analyzing such data should account for stratification, clustering and unequal probability of selection as well as within-subject correlations due to repeated measurements. <p>The complex multi-stage design approach has been used in the longitudinal National Population Health Survey (NPHS). This on-going survey collects information on health determinants and outcomes in a sample of the general Canadian population. <p>This dissertation compares the model-based and design-based approaches used to determine the risk factors of asthma prevalence in the Canadian female population of the NPHS (marginal model). Weighted, unweighted and robust statistical methods were used to examine the risk factors of the incidence of asthma (event history analysis) and of recurrent asthma episodes (recurrent survival analysis). Missing data analysis was used to study the bias associated with incomplete data. To determine the risk factors of asthma prevalence, the Generalized Estimating Equations (GEE) approach was used for marginal modeling (model-based approach) followed by Taylor Linearization and bootstrap estimation of standard errors (design-based approach). The incidence of asthma (event history analysis) was estimated using weighted, unweighted and robust methods. Recurrent event history analysis was conducted using Anderson and Gill, Wei, Lin and Weissfeld (WLW) and Prentice, Williams and Peterson (PWP) approaches. To assess the presence of bias associated with missing data, the weighted GEE and pattern-mixture models were used.<p>The prevalence of asthma in the Canadian female population was 6.9% (6.1-7.7) at the end of Cycle 5. When comparing model-based and design- based approaches for asthma prevalence, design-based method provided unbiased estimates of standard errors. The overall incidence of asthma in this population, excluding those with asthma at baseline, was 10.5/1000/year (9.2-12.1). For the event history analysis, the robust method provided the most stable estimates and standard errors. <p>For recurrent event history, the WLW method provided stable standard error estimates. Finally, for the missing data approach, the pattern-mixture model produced the most stable standard errors <p>To conclude, design-based approaches should be preferred over model-based approaches for analyzing complex survey data, as the former provides the most unbiased parameter estimates and standard errors.

Data obtained from longitudinal surveys using complex multi-stage sampling designs contain cross-sectional dependencies among units caused by inherent hierarchies in the data, and within subject correlation arising due to repeated measurements. The statistical methods used for analyzing such data should account for stratification, clustering and unequal probability of selection as well as within-subject correlations due to repeated measurements. <p>The complex multi-stage design approach has been used in the longitudinal National Population Health Survey (NPHS). This on-going survey collects information on health determinants and outcomes in a sample of the general Canadian population. <p>This dissertation compares the model-based and design-based approaches used to determine the risk factors of asthma prevalence in the Canadian female population of the NPHS (marginal model). Weighted, unweighted and robust statistical methods were used to examine the risk factors of the incidence of asthma (event history analysis) and of recurrent asthma episodes (recurrent survival analysis). Missing data analysis was used to study the bias associated with incomplete data. To determine the risk factors of asthma prevalence, the Generalized Estimating Equations (GEE) approach was used for marginal modeling (model-based approach) followed by Taylor Linearization and bootstrap estimation of standard errors (design-based approach). The incidence of asthma (event history analysis) was estimated using weighted, unweighted and robust methods. Recurrent event history analysis was conducted using Anderson and Gill, Wei, Lin and Weissfeld (WLW) and Prentice, Williams and Peterson (PWP) approaches. To assess the presence of bias associated with missing data, the weighted GEE and pattern-mixture models were used.<p>The prevalence of asthma in the Canadian female population was 6.9% (6.1-7.7) at the end of Cycle 5. When comparing model-based and design- based approaches for asthma prevalence, design-based method provided unbiased estimates of standard errors. The overall incidence of asthma in this population, excluding those with asthma at baseline, was 10.5/1000/year (9.2-12.1). For the event history analysis, the robust method provided the most stable estimates and standard errors. <p>For recurrent event history, the WLW method provided stable standard error estimates. Finally, for the missing data approach, the pattern-mixture model produced the most stable standard errors <p>To conclude, design-based approaches should be preferred over model-based approaches for analyzing complex survey data, as the former provides the most unbiased parameter estimates and standard errors.