Models for Statistical Analyses of Infectious Disease Data Open Access

An, Qian (2014)

Permanent URL: https://etd.library.emory.edu/concern/etds/t148fh631?locale=en
Published

Abstract

This dissertation aims at developing new statistical methods to monitor changes in HIV testing behaviors and to evaluate the influenza vaccine effectiveness (VE). The proposed approaches can help evaluate the quality of public health programs and provide guidance for expanding future public health responses.

In the first project, we propose a two-level Bayesian hierarchical model to estimate the HIV testing rate using annual acquired immunodeficiency syndrome (AIDS) and HIV diagnosis data. We introduce a new class of priors for the HIV incidence rate and testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique (ARMS). The proposed approach is illustrated via simulation studies and the analysis of the national HIV surveillance data in the United States. In the second project, we propose a novel Bayesian model to estimate the influenza VE using data collected from the test negative design (TND). Given that a person is sampled into TND, the joint probability of this person's vaccination status and influenza infection status is modeled as a function of the influenza VE. To improve the estimation accuracy, subjective priors are elicited from published literatures. We resort to ARMS for efficient posterior computation. To demonstrate the superiority of our approach, we perform simulation studies where model-based estimates of influenza VE are compared with existing odds ratio estimates. In the third project, we propose an improved nonhomogeneous probability model for evaluating bias and precision of the estimates of influenza VE from traditional case-control design (CCD) and TND. The proposed model describes the data generation process in real life composed of five steps: latent health status, vaccination, acute respiratory illness (ARI) and influenza infection; seeking medical care for ARI and testing for influenza infection. By including a parameter for the latent health status, this model facilitates the evaluation of an important bias resulting from the unobserved variable. We present and compare the numerical results of the bias and the standard error of the VE estimates from the CCD and the TND.

Table of Contents

1 Introduction 1

2 A Bayesian Hierarchical Model with Novel Prior Specifications to estimate HIV Testing

Rate 9

2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Data and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 A Hierarchical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.3 Prior Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.4 Posterior Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.1 Analysis of the United States HIV surveillance data . . . . . . . . . . . . . . 30

2.4.2 Model Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 A Bayesian Model to Estimate the Influenza Vaccine Effectiveness from a Test Negative Design 38

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.1 Model representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.2 Prior specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.3 Posterior Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.1 Analysis of the seasonal 2010-2011 influenza vaccine TND study . . . 54

3.4.2 Model assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 A Nonhomogeneous Probability Model for Evaluating Bias and Precision of Estimates of

the Influenza Vaccine Effectiveness from Case-Control Studies 62

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.1.1 Main sources of bias in case-control studies . . . . . . . . . . . . . . . . . . . . 64

4.1.2 Medically-attended influenza and symptomatic influenza . . . . . . . . . . 66

4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.2.1 The study population and designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.2.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.3 Outcome of interest and true VE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2.4 VE estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.2.5 Standard errors of the VE estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.6 Determining the values of the parameters . . . . . . . . . . . . . . . . . . . . . . . 77

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.3.1 Analytic results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.3.2 Numeric results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3.3 Summary of sources of bias under non-random vaccination . . . . . . . . . 95

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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