Longitudinal Studies of Binary Response Data Following Case-Control and Stratified Case-Control Sampling: Design and Analysis

We discuss design and analysis of longitudinal studies after case control sampling, wherein interest is in the relationship between a longitudinal binary response that is related to the sampling (case control) variable, and a set of covariates. We propose a semiparametric modeling framework based on a marginal longitudinal binary response model and ancillary model for subjects' case control status. In tins approach, the analyst must posit the population prevalence of being a case, which is then used to compute an offset term in the ancillary model. Parameter estimates from this model are used to compute offsets for the longitudinal response model. Examining the impact of population prevalence and ancillary model misspecification, we show that tune-invariant covariate parameter estimates, other than the intercept. ore reasonably robust, but intercept and time-varying covariate parameter estimates can be sensitive to such misspecification. We study design and analysis issues impacting study efficiency, namely: choice of sampling variable and the strength of its relationship to the response, sample stratification, choice of working covariance weighting, and degree of flexibility of the ancillary model. The research is motivated by a longitudinal study following case control sampling of the time course of attention deficit hyperactivity disorder (ADHD) symptoms.