Date of Award

2016

Document Type

Open Access Dissertation

Department

Statistics

Sub-Department

College of Arts and Sciences

First Advisor

Joshua M. Tebbs

Abstract

In the simplest form of group testing, pools are formed by compositing a fixed number of individual specimens (e.g., blood, urine, swab, etc.) and then the pools are tested for a binary characteristic, such as presence or absence of a disease. Group testing is commonly used to screen for a variety of sexually transmitted diseases in epidemiological applications where the main goal is to increase testing efficiency. In this dissertation, we study three estimation problems that are motivated by real-life applications. We propose new methods to model group testing data for both single and multiple infections. In the first problem, we propose a Bayesian approach to estimate the prevalence of multiple infections. This relaxes the unreliable assumption that diagnostic accuracies are constant. Also, when historical data are taken into account, our method provides more efficient estimation than do existing approaches. In the second problem, we propose a regression method to capture dilution effects due to pooling. In addition to offering reliable inference, our parametric approach enables one to perform a hypothesis test for dilution. In the third problem, we propose Bayesian measurement error models. Our approach provides flexibility to the structural modeling approach which requires the availability of a known probability distribution for true (unobserved) covariates. This work generalizes existing regression methods to account for covariate measurement error. We also discuss several problems for future research.

Rights

© 2016, Md Shamim Sarker

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