Causal Inference Using Variation in Treatment over Time

This thesis and related research is motivated by my interest in understanding the use of time-varying treatments in causal inference from complex longitudinal data, which play a prominent role in public health, economics, and epidemiology, as well as in biological and medical sciences. Longitudinal data allow the direct study of temporal changes within individuals and across populations, therefore give us the edge to utilize time this important factor to explore causal relationships than static data. There are also a variety challenges that arise in analyzing longitudinal data. By the very nature of repeated measurements, longitudinal data are multivariate in various dimensions and have completed random-error structures, which make many conventional causal assumptions and related statistical methods are not directly applicable. Therefore, new methodologies, most likely data-driven, are always encouraged and sometimes necessary in longitudinal causal inference, as will be seen throughout this thesis. As a result of the various topics explored, this thesis is split into four parts corresponding to three dierent patterns of variation in treatment. The rst pattern is the one-directional change of a binary treatment assignment, meaning that each study participant is only allowed to experience the change from untreated to treated at the staggered time. Such pattern is observed in a novel cluster-randomized design called the stepped-wedge. The second pattern is the arbitrary switching of a binary treatment caused by changes in person-specic characteristics and general time trend. The patterns is the most common thing one would observe in longitudinal data and we develop a method utilizing trends in treatment to account for unmeasured confounding. The third pattern is that the underlying treatment, outcome, covariates are time-continuous, yet are only observed at discrete time points. Instead of modeling cross-sectional and pooled longitudinal data, we take a mechanistic view by modeling reactions among variables using stochastic dierential equations and investigate whether it is possible to draw sensible causal conclusions from discrete measurements