published_or_final_version / Mathematics / Master / Master of Philosophy

In longitudinal and spatio-temporal data analysis, repeated measurements from a subject can be either regional- or temporal-dependent. The correct specification of the within-subject covariance matrix cultivates an efficient estimation for mean regression coefficients. In this thesis, robust estimation for the mean and covariance jointly for the regression model of longitudinal data within the framework of generalized estimating equations (GEE) is developed. The proposed approach integrates the robust method and joint mean-covariance regression modeling. Robust generalized estimating equations using bounded scores and leverage-based weights are employed for the mean and covariance to achieve robustness against outliers. The resulting estimators are shown to be consistent and asymptotically normally distributed. Robust variable selection method in a joint mean and covariance model is considered, by proposing a set of penalized robust generalized estimating equations to estimate simultaneously the mean regression coefficients, the generalized autoregressive coefficients and innovation variances introduced by the modified Cholesky decomposition. The set of estimating equations select important covariate variables in both mean and covariance models together with the estimating procedure. Under some regularity conditions, the oracle property of the proposed robust variable selection method is developed. For these two robust joint mean and covariance models, simulation studies and a hormone data set analysis are carried out to assess and illustrate the small sample performance, which show that the proposed methods perform favorably by combining the robustifying and penalized estimating techniques together in the joint mean and covariance model. Capturing dynamic change of time-varying correlation structure is both interesting and scientifically important in spatio-temporal data analysis. The time-varying empirical estimator of the spatial correlation matrix is approximated by groups of selected basis matrices which represent substructures of the correlation matrix. After projecting the correlation structure matrix onto the space spanned by basis matrices, varying-coefficient model selection and estimation for signals associated with relevant basis matrices are incorporated. The unique feature of the proposed model and estimation is that time-dependent local region signals can be detected by the proposed penalized objective function. In theory, model selection consistency on detecting local signals is provided. The proposed method is illustrated through simulation studies and a functional magnetic resonance imaging (fMRI) data set from an attention deficit hyperactivity disorder (ADHD) study. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 64-66). Also available on the World Wide Web.

Considerable amounts of event history data are collected through longitudinal surveys. These surveys have many particularities or features that are the results of the dynamic nature of the population under study and of the fact that data collected through longitudinal surveys involve the use of complex survey designs, with clustering and stratification. These particularities include: attrition, seam-effect, censoring, left-truncation and complications in the variance estimation due to the use of complex survey designs. This thesis focuses on the last two points. Statistical methods based on the stratified Cox proportional hazards model that account for intra-cluster dependence, when the sampling design is uninformative, are proposed. This is achieved using the theory of estimating equations in conjunction with empirical process theory. Issues concerning analytic inference from survey data and the use of weighted versus unweighted procedures are also discussed. The proposed methodology is applied to data from the U. S. Survey of Income and Program Participation (SIPP) and data from the Canadian Survey of Labour and Income Dynamics (SLID). Finally, different statistical methods for handling left-truncated sojourns are explored and compared. These include the conditional partial likelihood and other methods, based on the Exponential or the Weibull distributions.

Background/Aims: Case-control designs are commonly employed in genetic association studies. In addition to the primary trait of interest, data on additional secondary traits, related to the primary trait, are often collected. Traditional association analyses between genetic variants and secondary traits can be biased in such cases, and several methods have been proposed to address this issue, including the inverse-probability-of-sampling-weighted (IPW) approach and semi-parametric maximum likelihood (SPML) approach. Methods: Here, we propose a set of new estimating equation based approach that combines observed and counter-factual outcomes to provide unbiased estimation of genetic associations with secondary traits. We extend the estimating equation framework to both generalized linear models (GLM) and non-parametric regressions, and compare it with the existing approaches. Results: We demonstrate analytically and numerically that our proposed approach provides robust and fairly efficient unbiased estimation in all simulations we consider. Unlike existing methods, it is less sensitive to the sampling scheme and underlying disease model specification. In addition, we illustrate our new approach using two real data examples. The first one is to analyze the binary secondary trait diabetes under GLM framework using a stroke case-control study. The second one is to analyze the continuous secondary trait serum IgE levels under linear and quantile regression models using an asthma case-control study. Conclusion: The proposed new estimating equation approach is able to accommodate a wide range of regressions, and it outperforms the existing approaches in some scenarios we consider.

Considerable amounts of event history data are collected through longitudinal surveys. These surveys have many particularities or features that are the results of the dynamic nature of the population under study and of the fact that data collected through longitudinal surveys involve the use of complex survey designs, with clustering and stratification. These particularities include: attrition, seam-effect, censoring, left-truncation and complications in the variance estimation due to the use of complex survey designs. This thesis focuses on the last two points. Statistical methods based on the stratified Cox proportional hazards model that account for intra-cluster dependence, when the sampling design is uninformative, are proposed. This is achieved using the theory of estimating equations in conjunction with empirical process theory. Issues concerning analytic inference from survey data and the use of weighted versus unweighted procedures are also discussed. The proposed methodology is applied to data from the U. S. Survey of Income and Program Participation (SIPP) and data from the Canadian Survey of Labour and Income Dynamics (SLID). Finally, different statistical methods for handling left-truncated sojourns are explored and compared. These include the conditional partial likelihood and other methods, based on the Exponential or the Weibull distributions.

Generalized estimating equations (GEEs) are commonly used in the modelling of correlated data. However, in the presence of informative cluster sizes, estimates obtained using GEEs may be biased. In order to correct for this bias a weighted GEE may be used. Previous research has extended the use of weighted GEEs to a longitudinal setting but requires that cluster sizes remain constant over time. In this thesis, two new weighting schemes are investigated to allow for valid parameter estimation in a longitudinal setting where cluster sizes are informative and may change over time. Specifically, this thesis considers weighting by the inverse of the time-dependent cluster size, and by the total number of observations for a given cluster. Through Monte Carlo simulation, the performance of traditional GEEs, GEEs under previously proposed weighting schemes, and these two new models are compared. Results of these studies show that weighting by the total number of observations results in unbiased parameter estimates with excellent coverage.

This thesis aimed to apply the causal framework with potential outcomes to examine the causal effect of air temperature on reported violent crimes in Swedish municipalities. The Generalized Estimating Equations method was used on yearly, monthly and also July only data for the time period 2002-2014. One significant causal effect was established but the majority of the results pointed to there being no causal effect between air temperature and reported violent crimes.

Thesis (M.Phil.) - University of St Andrews, January 2008.

abstract: When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses. / Dissertation/Thesis / Arizona Medicare Data on Rehospitalization / Philippine Data on Children's Morbidity / M.S. Statistics 2012