Title: Modeling the Dynamic Association Structure in Clustered Longitudinal Data
Chair: Associate Professor Kerby Shedden
Committee Members: Professor Tailen Hsing, Assistant Professor Yves Atchade, Professor Robert Zucker (Psychiatry)
Abstract: This work considers several modeling problems involving clustered longitudinal data, in which interest focuses on the association structure rather than the means and, in particular, on its change over time. Interest in this non-stationary, or "dynamic" aspect of the association structure is motivated by applications involving the study of behavioral traits in children observed from early childhood to adulthood. In nearly all longitudinal data there are two timing variables: "age" and chronological time. To begin we consider situations where the two timing variables are equivalent, such as when multiple measurements are taken on the same individual. A natural approach to characterizing the dynamic association structure in this setting is to "regress" a univariate measure on time. Applications of this framework include the comorbidity of pairs of traits within an individual. In this section we consider binary associations quantified by the log odds ratio. The first method for this problem uses penalized maximum likelihood to estimate the log odds ratio trajectory semi-parametrically as a smooth function of time in the bivariate case. A second method, appropriate for any number of variables, is proposed that allows for the pairwise log odds ratio trajectories to be estimated in isolation. By using a composite, conditional likelihood approach we no longer need to model means or dependencies of secondary interest. We next consider the setting where the longitudinal data are observed in clusters (e.g. siblings). The children in a family are exposed to events that occur at specific calendar times, and also are influenced by developmental processes that are agespecific. Since the children in different families have different birth spacings, these two influences are offset to varying degrees in different families, prompting us to ask whether both age and time are modulating the association structure and can we disaggregate these effects? Existing methods for such data only account for a single timing variable (typically age), effectively marginalizing over the other. We present a modeling framework for jointly estimating how age and time distinctly affect the association structure and extensive empirical results are presented to clarify our ability to decompose these effects successfully. Difficult computational problems arise in this model, requiring the development of new estimators and approaches to computing.