Modeling Time-Dependent Covariates in Longitudinal Data Analyses

Often public health data contain variables of interest that change over the course of longitudinal data collection.  In this chapter a discussion is presented of analysis options for longitudinal data with time-dependent covariates.  Relevant definitions are presented and explained in the context of practical applications, such as different types of time-dependent covariates.  The consequences of ignoring the time-dependent nature of variables in models is discussed.  Modeling options for time-dependent covariate data are presented in two general classes: subject-specific models and population-averaged models.  Specific subject-specific models include random-intercept models and random-slopes models.  Decomposition of time-dependent covariates into ``within" and ``between" components within each subject-specific model is discussed.  Specific population-averaged models include the independent GEE model and various forms the GMM (Generalized Method of Moments) approach, including researcher-determined types of time-dependent covariates along with data-driven selection of moment conditions using the Extended Classification.  A practical data example is presented along with example programs for both SAS and R.