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
