Dissertation
Bayesian methods for estimation and mediation in disease mapping applications
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2022
DOI: 10.17077/etd.006407
Abstract
My dissertation is motivated by the need for improved statistical approaches for understanding differences in cancer risk in rural vs. urban areas. To accomplish this goal, we develop three statistical methods that can be used to model and explain differences in age-adjusted rates between small areas with differing characteristics. These methods allow researchers to draw meaningful inferences from sparse spatial or spatio-temporal datasets at the ZIP code or county levels. Furthermore, they can be used to identify regions that might require public health interventions and to motivate costly data collection efforts at the individual level.
The statistical methods we propose in this dissertation can be classified into two categories: estimation and mediation. Chapter 2 focuses on precisely estimating age-adjusted cancer mortality rates for small areas from spatio-temporal datasets with an excessive number of zeros. A large proportion of zeros are often present in datasets involving low-prevalence diseases and in datasets that include rural regions with small population sizes. When stratifying counts for each region and year by age group in the process of estimating age-adjusted rates, the proportion of zeros in the dataset is further inflated. We propose a novel Bayesian hierarchical hurdle model with spatial and temporal random effects for estimating age-adjusted rates in these settings. Via a simulation study and two data examples, we study the performance of this model and make recommendations as to when it should be used over a Bayesian hierarchical Poisson regression model for age-adjusted rates.
Chapters 3 and 4 address the goal of mediation. Specifically, Chapter 3 focuses on a method for performing a mediation analysis and Chapter 4 introduces a method for performing a decomposition analysis. Both chapters aim to explain a difference in age-adjusted rates at the ZIP code level based on either a ZIP code-level exposure (mediation) or a fixed characteristic (decomposition). We develop flexible statistical methods that use Bayesian hierarchical models with spatial random effects and a Bayesian version of the g-computation technique from causal inference. Both methods were designed to create counterfactual small area estimates of age-adjusted rates within the analysis and consequently stable estimates of the effects of interest.
Through a simulation study, we illustrate a high level of precision and minimal bias in the total, direct, and indirect effects when using our proposed mediation analysis method. We also compare our proposed mediation method to two methods used in the medical literature and show that our method exhibits the best trade-off of bias and variance. To demonstrate the performance of our decomposition method, we perform a data analysis to understand whether park access explains the disparity in age-adjusted colorectal cancer incidence rates in rural vs. urban ZIP codes in Iowa. We illustrate that precise inferences can be made from sparse ZIP code-level datasets when incorporating small area estimation techniques into each analysis.
Details
- Title: Subtitle
- Bayesian methods for estimation and mediation in disease mapping applications
- Creators
- Melissa Jay
- Contributors
- Jacob Oleson (Advisor)Grant Brown (Committee Member)Joseph Cavanaugh (Committee Member)Mary Charlton (Committee Member)Mary Kathryn Cowles (Committee Member)Gideon Zamba (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Biostatistics
- Date degree season
- Spring 2022
- DOI
- 10.17077/etd.006407
- Publisher
- University of Iowa
- Number of pages
- xi, 123 pages
- Copyright
- Copyright 2022 Melissa Jay
- Language
- English
- Description illustrations
- Charts, tables, graphs
- Description bibliographic
- Includes bibliographical references (pages 118-123).
- Public Abstract (ETD)
My dissertation is motivated by the need for improved statistical approaches for understanding differences in cancer risk in rural vs. urban areas. In this work, we classify counties and ZIP codes as either rural or urban. We focus on age-adjusted rates which are the number of cancer cases or deaths per 100,000 people adjusted for the age distribution in the area. Challenges in performing statistical analyses arise when calculating age-adjusted rates for small areas (for example, counties or ZIP codes) directly from the data. This approach can lead to unreliable results due to the small population sizes in each area, and thus can make it difficult to draw meaningful conclusions. In each of the new statistical methods proposed in my dissertation, we utilize statistical models that borrow information from neighboring regions in order to obtain more reliable small area estimates of the age-adjusted rates and mediated effects. This is done by estimating age-adjusted cancer mortality rates for small areas where many of the rural counties have zero deaths from a cancer type during a specified period of time. We also propose a mediation method to determine whether a ZIP code-level variable explains any of the relationship between a ZIP code-level exposure and the ZIP code-level age-adjusted rates.
- Academic Unit
- Biostatistics
- Record Identifier
- 9984271255302771
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