## Advisory Committee Chair

Inmaculada B Aban

## Advisory Committee Members

Sadeep Shrestha

Hemant K Tiwari

O Dale Williams

## Document Type

Dissertation

## Date of Award

2011

## Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

## Abstract

Pool screening is a method that combines individual items into pools. Each pool will either test positive (at least one of the items is positive) or negative (all items are negative). Pool screening is commonly applied to the study of tropical diseases where pools consist of vectors (e.g. black flies) that can transmit the disease. The goal is to estimate the proportion of infected vectors. In paper 1, we present a frequentist Bernoulli-Beta hierarchical model to relax the constant prevalence assumption underlying the traditional frequentist prevalence estimation approach. This assumption is called into question when sampling from a large geographic area. Using the hierarchical model an investigator can determine the probability of the prevalence being below a pre-specified threshold value, a value at which no reemergence of the disease is expected. Intermediate estimators (model parameters) and estimators of ultimate interest (pertaining to prevalence) are evaluated by standard measures of merit, such as bias, variance and mean squared error making extensive use of expansions. An investigation into the least biased choice of the alpha parameter in the Beta (alpha,beta) prevalence distribution leads to the choice of alpha = 1. In paper 2, we propose and evaluate the performance of a sequential Bayesian approach for the case that zero positive pools are observed in a particular year. Such observations become more likely the longer an elimination program is in place. A Bayesian approach can incorporate results from previous years and will provide a more sensible prevalence estimate compared to the estimate of zero from the traditional approach. Through simulation, we investigate the amount of data (number of years for which pool screen results are available) required such that the type of objective prior chosen does not make a significant difference with respect to the prevalence estimate. We also evaluate the accuracy of the estimates and propose three strategies to improve the performance of this Bayesian estimation approach. In the last paper we make the case for the Bayesian estimation approach when the elimination programs are close to succeeding by presenting and comparing numerical results calculated from real data using different approaches.

## Recommended Citation

Birkner, Thomas, "Hierarchical and Bayesian Approaches for Estimating Prevalence Based on Pool Screening" (2011). *All ETDs from UAB*. 1169.

https://digitalcommons.library.uab.edu/etd-collection/1169