We detail study design options that generalize case-control sampling when longitudinal outcome data are already collected as part of a primary cohort study, but new exposure data must be retrospectively processed for a secondary analysis. Furthermore, we assume that cost will limit the size of the subsample that can be evaluated. We describe a novel class of stratified outcome-dependent sampling designs for longitudinal binary response data where distinct strata are created for subjects who never, sometimes, and always experienced the event of interest during longitudinal follow-up. Individual designs within this class are differentiated by the stratum-specific sampling probabilities. We show for parameters associated with time-varying exposures, subjects who experience the event/outcome at some but not at all of the follow-up times (i.e., those who exhibit response variation) are highly informative. If the time-varying exposure varies exclusively within individuals (i.e., intraclass correlation coefficient is 0), then sampling all subjects with response variability can yield highly precise parameter estimates even when compared with an analysis of the original cohort. The flexibility of the designs and analysis procedures also permits estimation of parameters that correspond to time-fixed covariates, and we show that with an imputation-based estimation procedure, baseline covariate associations can be estimated with very high precision irrespective of the design. We demonstrate features of the designs and analysis procedures via a plasmode simulation using data from the Lung Health Study.