Time introduces complexity in causal inference for observational studies. This thesis investigates two sources of bias for studies involving time-varying data. One is the missing data in longitudinal studies, and the other is the confounding temporal effects in studies that use time as the instrument. In longitudinal studies, excluding the missing data in analyses may lead to biased causal estimates. Multiple imputation (MI) is one approach that fills in plausible values for the non-responses. To guide researchers in handling missing data with MI, Chapter 1 evaluates current MI methods for different types of longitudinal variables and their implementation on widely accessible software. The performances of different imputation models are compared through simulation studies based on the National Health and Aging Trends Study for investigating the associations between health outcomes and chronic conditions using univariate and multivariate multilevel models and analyzing the trajectory of BMI over time with a growth curve model. Chapter 2 addresses the confounding effect of time in instrumental variable (IV) analysis. Previous studies used time as an instrument in IV analysis and relied on the exclusion restriction assumption. However, time may affect outcomes for all units, not through the intervention. Thus, the exclusion restriction assumption is violated. Chapter 2 proposes the cross-temporal design, which utilizes units from two-time points and introduces a temporal indicator as the instrument to mimic a randomized encouragement design. The temporal effect for each compliance group is defined using potential outcomes, and temporal assumptions are proposed to substitute for the exclusion restrictions. Chapter 3 generalizes the framework in Chapter 2 to multiple time points’ settings. An instrument variable with multiple discrete levels is introduced. The temporal effects and the treatment effect are defined by functions of time which are modeled by spline models. In Chapters 2 and 3, simulation studies are conducted to assess the efficacy of the proposed approaches. An application example is provided, which investigates the effect of Medicare Advantage programs on the risk of readmission within 30 days for post-acute care patients discharged to a skilled nursing home facility.
