Indiana University-Purdue University Indianapolis (IUPUI) / Time-to-event outcomes are widely utilized in medical research. Assessing the cumulative effects of time-varying exposures on time-to-event outcomes poses challenges in statistical modeling. First, exposure status, intensity, or duration may vary over time. Second, exposure effects may be delayed over a latent period, a situation that is not considered in traditional survival models. Third, exposures that occur within a time window may cumulatively in uence an outcome. Fourth, such cumulative exposure effects may be non-linear over exposure latent period. Lastly, exposure-outcome dynamics may differ among groups defined by individuals' characteristics. These challenges have not been adequately addressed in current statistical models. The objective of this dissertation is to provide a novel approach to modeling group-specific dynamics between cumulative timevarying exposures and a time-to-event outcome. A framework of group-specific dynamic models is introduced utilizing functional time-dependent cumulative exposures within an etiologically relevant time window. Penalizedspline time-dependent Cox models are proposed to evaluate group-specific outcome-exposure dynamics through the associations of a time-to-event outcome with functional cumulative exposures and group-by-exposure interactions. Model parameter estimation is achieved by penalized partial likelihood. Hypothesis testing for comparison of group-specific exposure effects is performed by Wald type tests. These models are extended to group-specific non-linear exposure intensity-latency-outcome relationship and group-specific interaction effect from multiple exposures. Extensive simulation studies are conducted and demonstrate satisfactory model performances. The proposed methods are applied to the analyses of group-specific associations between antidepressant use and time to coronary artery disease in a depression-screening cohort using data extracted from electronic medical records.