Kruchten, Adam
(2024)
Theory and Methods for Spatiotemporal Point Processes.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In this dissertation we study several related problems under the general umbrella of spatiotemporal counting/point processes. We study counting processes in two distinct contexts.
First, we study a clinical problem of assessing medical response or non-response to a treatment on the basis of known biomarker values. This problem commonly occurs in oncology,
where measures of objective response are critical to drug approval, but may require long
periods of total follow-up with limited cohorts. In this context it is critical for researchers
to be able to efficiently estimate biomarker cutoff values as soon as possible. However, as
trials take long periods of time there will generally be substantial incomplete data at interim
analysis. We find that conventional estimators for handling missing data may reduce bias
relative to conventional estimators in realistic scenarios. We provide recommendations that
applied researchers use a variety of estimators and use careful sensitivity analyses to guide
conclusions drawn from them.
Second, we study point processes in a spatial context, where we develop new methods for
utilizing point process valued data as covariates in spatial regression. We illustrate the new
method through several simulation scenarios and an analysis of the impact of contributory
sources of air pollution in western Pennsylvania.
Finally, we study a problem of causal inference with a point process valued outcome:
severe asthma exacerbation events in western Pennsylvania. We develop causal estimands
and associated estimators to study the relationship between unconventional natural gas
production and severe asthma in western Pennsylvania. As part of this work we develop a
formal theory for incorporation of mechanistic considerations in causal inference.
Contribution to Public Health:
This dissertation contributes to public health in multiple ways. In the clinical trials portion we assess the potential of common statistical methods for bias reduction in clinical trials
at interim analysis, an important objective for drug development. The spatial epidemiology
work contributes to a growing literature assessing the impact of industrial activity and air
pollution on human health. The theoretical work contributes to public health by providing foundations for causal interpretation of observational studies and enabling new research
designs.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
20 December 2024 |
| Date Type: |
Publication |
| Defense Date: |
13 December 2024 |
| Approval Date: |
20 December 2024 |
| Submission Date: |
13 December 2024 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
242 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
School of Public Health > Biostatistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Spatiotemporal, Point Processes, Generalized Additive Models, Causal Inference, Formal Methods |
| Date Deposited: |
20 Dec 2024 19:41 |
| Last Modified: |
20 Dec 2024 19:41 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/47279 |
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