Date of Award

2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Statistics

First Advisor

Dylan S. Small

Abstract

This thesis includes five chapters on evidence factors analysis of causal effect in various

observational study settings. Each of these chapters can be read independently without

knowledge of the content of any of the other chapters. Evidence factors allow for two

independent analyses to be constructed from the same data set. When combining the

evidence factors, the type-I error rate must be controlled to obtain valid inference. A

powerful method is developed for controlling the familywise error rate for sensitivity analyses

to unmeasured confounding with evidence factors. It is shown that the Bahadur efficiency of

sensitivity analysis for the combined evidence is greater than for either evidence factor alone.

The popular strategy of matching, for controlling the observed covariates, before inferring

about the treatment effect, requires solving an optimization problem. This problem can

be solved in polynomial time. In an evidence factors analysis we must consider multiple

comparisons, thus the matching problem is often of matching at least three groups. This

slightly different problem is much more difficult to solve. The third chapter proposes an

approximation algorithm to solve this (and more practical versions of this) problem. We

prove that the proposed algorithm provides a solution fast, that is provably not a lot further

than the optimal solution that is difficult calculate. Two chapters that follow show the

applicability of evidence factors analysis in more complicated study designs. The first of

these two chapters considers a case-control study with multiple case definitions and the latter

one considers studies with instrumental variables, where the instrument(s) may become

invalid. The final chapter of the thesis develops a frequentist method for quantification of

the degree of corroboration of causal hypothesis using the tool of evidence factors.

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