Many applied statistical applications face the potential problem of model contamination and measurement error. The form and degree of contamination as well as the measurement error are usually unknown and sample-specific, which brings additional challenges for researchers. In this thesis, we have proposed several Bayesian inference models to address these issues, with the application to one type of special data for allergen concentration measurement, which is called serial dilution data and is self-calibrated.
In our first chapter, we address the problem of model contamination by using a multilevel model to simultaneously flag problematic observations and estimate unknown concentrations in serial dilution data, a problem where the current approach can lead to noisy estimates and difficulty in estimating very low or high concentrations.
In our second chapter, we propose the Bayesian joint contamination model for modeling multiple measurement units at the same time while adjusting for differences between experiments using the idea of global calibration, and it could account for uncertainty in both predictors and response variables in Bayesian regression. We are able to get efficacy gain by analyzing multiple experiments together while maintaining robustness with the use of hierarchical models.
In our third chapter, we develop a Bayesian two-step inference model to account for measurement uncertainty propagation in regression analysis when the joint inference model is infeasible. We aim to increase model inference reliability while providing flexibility to users by not restricting the type of inference model used in the first step. For each of the proposed methods, We also demonstrate how to integrate multiple model building blocks through the idea of Bayesian workflow.
In extensive simulation studies, we show that our proposed methods outperform other commonly used approaches. For the data applications, we apply the proposed new methods to the New York City Neighborhood Asthma and Allergy Study (NYC NAAS) data to estimate indoor allergen concentrations more accurately as well as reveal the underlying associations between dust mite allergen concentrations and the exhaled nitric oxide (NO) measurement for asthmatic children. The methods and tools developed here have a wide range of applications and can be used to improve lab analyses, which are crucial for quantifying exposures to assess disease risk and evaluating interventions.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/10x4-7g11 |
| Date | January 2023 |
| Creators | Wang, Siquan |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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