Marginal modeling of longitudinal, binary response data: Semiparametric and parametric estimation with long response series and an efficient outcome dependent sampling design

Longitudinal data analysis is fundamental to characterizing changes that occur over time. The research contained in this dissertation is focused on models and estimation procedures for marginal regression modeling long series of binary response data. There are three primary topics: (1) Semiparametric estimation, (2) models for parametric estimation and (3) study design. Semiparametric estimators in the presence time-varying covariates are examined. We study the bias-efficiency tradeoff with covariance weighted, Generalized Estimating Equations (Liang and Zeger, 1986) estimators of cross-sectional mean model parameters [e.g., parameters in E(Y ij|Xij)] when the true model is given by the full covariate conditional mean, E( Yij|Xi1, Xi2,..., Xini ). While Pepe and Anderson (1994) showed that biased estimates will likely result in this scenario unless a diagonal working covariance weighting scheme is used, many authors (e.g., Zhao et al., 1992; Fitzmaurice, 1995; Mancl and Leroux, 1996) have shown that covariance weighted estimates are far more efficient. We examine the tradeoff between validity and efficiency by exploring data features. Next, we study marginalized regression models (Heagerty, 1999). Marginalized models are a flexible class of models that permit likelihood-based estimation of marginal regression model parameters. We extend this class by proposing a model to accommodate response dependence structures for long response series (e.g., those that exhibit short-range serial and long-range response dependence). We describe a maximum likelihood estimation procedure and evaluate asymptotic properties under dependence model misspecification. We also describe a strategy by which inference can be made with Bayesian methods. Finally, we propose an outcome dependent sampling design for longitudinal binary data when exposure ascertainment costs are high and when a large percentage of subjects do not exhibit variation in their response series (e.g., symptoms at every timepoint or no symptoms at any timepoint). Our design measures exposure only on subjects who exhibit response variation. We modify the marginalized model likelihood and propose a maximum conditional likelihood estimation procedure that acknowledges the study design. We evaluate asymptotic properties of the estimators, including showing that in plausible scenarios, they can be highly efficient compared to maximum likelihood estimators based on the entire cohort.