Date of Award

2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Statistics

First Advisor

Dylan S. Small

Abstract

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.

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