Date of Award

Fall 2021

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Alexander McLain

Abstract

The International Commission on Radiological Protection (ICRP) publishes biokinetic models that relate measurements of radioactive material in the body and excreta (bioassay) to the amount of the material taken into the body (intake). Given the intake and the biokinetic model, radiation dose to organs and tissues can be calculated. The ICRP approximates the biokinetics of radioactive materials in the body with compartmental models expressed mathematically as a system of ordinary differential equations, for which they provide point estimates of the rate constants. Inaccurate estimates of intake and radiation dose can result in cases where the biokinetics of an individual differ from the ICRP model (i.e., model misspecification), and currently there is no disciplined way to correct for this problem. In addition, the ICRP models don’t allow for the estimation of realistic uncertainties in the intakes and radiation doses. To address these limitations, proper probability distributions must be assigned to the rate constants. In this dissertation a proof-of-principle example is given showing how the ICRP 134 zirconium model can be calibrated with bioassay data from an experimental study and Bayesian hierarchical methods, which give the desired probability distributions for the rate constants. Once the ICRP 134 zirconium biokinetic model is calibrated, its posterior distributions are expressed as probability distributions that are used as “canned” priors in subsequent Bayesian evaluations of bioassay data from other individuals. Examples of canned prior Bayesian calculations are given and compared to the results obtained by 3 other methods: standard regression method, add-one-in Bayesian analysis, and MAP analysis of the canned prior Bayesian model. Both Bayesian analyses gave intake estimates with higher accuracy and more realistic uncertainties than the standard method, but the canned prior Bayesian analysis was approximately 60 times faster than the add-one-in Bayesian analysis. In addition, the canned priors are concise and can be provided along with the biokinetic model in ICRP publications. The MAP analysis gave some of the benefits of the Bayesian analysis with the speed of the standard method, and automatically comes along with the canned Bayesian analysis.

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Biostatistics Commons

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