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Dissertation
Estimating the Informativeness of the Conditional Autoregressive Model Framework with Applications
Doctor of Philosophy (Ph.D.), Drexel University
Dec 2022
DOI:
https://doi.org/10.17918/00001456
Abstract
The use of the conditional autoregressive (CAR) model framework of Besag et al. (1991) is ubiquitous in Bayesian disease mapping. While it is understood that Bayesian inference is based on a combination of the information contained in the data and the information contributed by the model, quantifying the contribution of the model relative to the information in the data is often non-trivial. The primary focus of this thesis is to further develop the methodology to measure and control the information contributed by the spatial models. We begin by first introducing the concept of model's informativeness and its application to Poisson distributed data by Quick et al. (2021). Our major objective here is to extend their work by developing a measure of the model's informativeness of Besag et al. (1991) in the case of binomially distributed count data, while also providing a guidance to control the model's informativeness from the framework of Besag et al. (1991). In addition to using our methodology on a data set comprising county-level low weight births in Pennsylvania, stratified by the mothers' race/ethnicity, we also demonstrate the extent to which the excess model's informativeness can overwhelm the information in the data and oversmooth the inferential results. We then reparameterize the CAR model framework of Besag et al. (1991) and propose a new prior specification for the purpose of controlling the model's informativeness in a more straightforward way. After illustrating the use of our methodology on a Poisson distributed data set containing heart disease-related deaths among those aged 35-54 years in 1980 in North Carolina, we show how the method can be implemented to analyze binomially distributed data using the county-level low weight births in Pennsylvania, stratified by mothers' race/ethnicity. Last, we assess the degree of oversmoothing in multiple spatial models for disease mapping via comparing the relative precision of the estimates from each model with those from the CAR model framework of Besag et al. (1991). We believe that users can gain a deeper understanding of the importance of the model's informativeness through these methods. Furthermore, the implications of the model's informativeness - which closely relates to the concept of degree of oversmoothing - to disease mapping are enormous, affecting decisions regarding data collection, prior specifications, data analyses, and policy making.
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Details
- Title
- Estimating the Informativeness of the Conditional Autoregressive Model Framework with Applications
- Creators
- Guangzi Song
- Contributors
- Harrison S. Quick (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xi, 78 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- Dana and David Dornsife School of Public Health; Epidemiology and Biostatistics; Drexel University
- Other Identifier
- 991020034314804721