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


  • Jonathan S. Schildcrout,

    Corresponding author
    1. Departments of Biostatistics and Anesthesiology, Vanderbilt University School of Medicine, 1161 21st Avenue South, S-2323 Medical Center North, Nashville, Tennessee 37232, U.S.A.
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  • Paul J. Rathouz

    Corresponding author
    1. Department of Health Studies, University of Chicago, 5841 South Maryland Avenue, MC 2007, Chicago, Illinois 60637, U.S.A.
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Summary 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 an ancillary model for subjects' case–control status. In this 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 time-invariant covariate parameter estimates, other than the intercept, are 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.