Inference of Inter-Individual Heterogeneity in Tuberculosis Transmission Open Access

Abstract

Objectives: Increasing evidence suggests that tuberculosis (TB) transmission is largely characterized by "superspreading," an extreme manifestation of inter-individual heterogeneity wherein a disproportionately small number of individuals contributes to the majority of secondary cases. Superspreading greatly undermines public health interventions and has a profound impact on disease emergence and outbreak trajectory. However, traditional methods used to quantify the propensity for superspreading in a population cannot be applied to TB since high resolution data describing individual-level TB transmission are rarely observed. Fortunately, recent advancements in genotyping have afforded surveillance systems the ability to more accurately identify TB transmission clusters, defined simply as the total number of cases in a given transmission chain. The overall goal of this dissertation was to develop, evaluate, and apply a novel method to quantify the propensity for superspreading in TB using transmission cluster distributions, without the need for more resource-intensive individual data.

Methods: In the first study we utilized branching process theory and a negative binomial offspring distribution to develop a novel method that infers inter-individual heterogeneity using only cluster level data. We then validated the inference procedure under real-world scenarios that lead to imperfect surveillance. In Study 2, we applied this method to TB surveillance data systematically abstracted from the literature and investigated the impact such heterogeneity had on transmission dynamics. In Study 3 we obtained empirical TB surveillance data from the United States Centers for Disease Control and Prevention (CDC) and estimated the propensity for superspreading in four of the most populous states in the US.

Results: Study 1 demonstrated the inference procedure was robust and inferred the same degree of inter-individual heterogeneity as more resource intensive individual level data. In Study 2, the inferred parameters indicated a similarly high propensity for superspreading across various global contexts. Study 3 demonstrated a similarly high propensity of superspreading the US, and that a small minority (~10%) of cases were responsible for all secondary transmission.

Conclusions: A high degree of inter-individual heterogeneity is a defining feature of TB epidemiology, and accounting for this heterogeneity in epidemic modeling will result in an improved understanding of TB transmission dynamics and subsequent public health efforts.

Table of Contents

1 Introduction and Background 1

1.1 Dissertation Approach and Summary . . . . . . . . . . . . . . . . . . 1

1.1.1 Study 1: Specic Aims and Summary . . . . . . . . . . . . . . 3

1.1.2 Study 2: Specic Aims and Summary . . . . . . . . . . . . . . 4

1.1.3 Study 3: Specic Aims and Summary . . . . . . . . . . . . . . 4

1.2 Tuberculosis Epidemiology and Transmission Dynamics . . . . . . . . 6

1.2.1 Global Tuberculosis Epidemiology . . . . . . . . . . . . . . . . 6

1.2.2 Inter-Individual Heterogeneity and Superspreading in Tuberculosis

Transmission . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Sources of Inter-Individual Heterogeneity in TB Transmission 11

1.3 Current Approaches to Addressing Heterogeneity in TB Transmission 17

1.4 Chapter 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Quantifying Inter-Individual Heterogeneity in Tuberculosis Trans-

mission 32

2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 Branching Process Analysis . . . . . . . . . . . . . . . . . . . . . . . 35

2.2.1 Branching Process Overview . . . . . . . . . . . . . . . . . . . 35

2.2.2 Incorporating Inter-Individual Heterogeneity in Branching Process

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.3 Parameter Inference from the Distribution of Final Transmission Cluster

Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.3.1 Relating the Individual Ospring Distribution and the Final

Cluster Distribution . . . . . . . . . . . . . . . . . . . . . . . 41

2.4 Chapter 2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 Evaluating a Method to Infer Inter-Individual Heterogeneity in TB

transmission Using Cluster Level Data 47

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3.1 Statistical Methods . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3.2 Maximum Likelihood Estimation of Transmission Parameters 53

3.3.3 Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3.4 Complications in TB Surveillance . . . . . . . . . . . . . . . . 54

3.3.5 United States National TB Surveillance System Data . . . . . 55

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4.1 Initial Validation the Inference Procedure . . . . . . . . . . . 56

3.4.2 Bias Arising Due to Complications in Surveillance . . . . . . . 57

3.4.3 Validation of Inference Procedure Under Real World Scenarios 58

3.4.4 Analysis of United States TB Surveillance Data . . . . . . . . 60

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

3.6 Supplemental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.7 Chapter 3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4 Estimates for the Propensity of Superspreading in Tuberculosis Trans-

mission from Global Surveillance Systems 87

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.1 Search Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.2 Inclusion and Exclusion Criteria . . . . . . . . . . . . . . . . . 91

4.3.3 Parameter Inference Using Cluster-level Data . . . . . . . . . 91

4.3.4 Cluster Size Probability Calculations . . . . . . . . . . . . . . 92

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.4.1 Characteristics of Included Datasets . . . . . . . . . . . . . . . 93

4.4.2 Transmission Parameter Estimates . . . . . . . . . . . . . . . 93

4.4.3 Cluster Size Probabilities . . . . . . . . . . . . . . . . . . . . . 94

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.6 Supplemental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.7 Chapter 4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5 Estimating individual heterogeneity in tuberculosis transmission in

the United States 108

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.3.1 Data Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.3.2 Inference Procedure and Model . . . . . . . . . . . . . . . . . 111

5.3.3 Transmission Cluster Denitions . . . . . . . . . . . . . . . . . 113

5.3.4 Burden of Secondary Transmission . . . . . . . . . . . . . . . 113

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.6 Supplemental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.7 Chapter 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6 Summary and Conclusions 132

6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.2 Public Health and Epidemiological Implications . . . . . . . . . . . . 134

6.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.4 Remaining Gaps in Knowledge and Future Directions . . . . . . . . . 137

Appendix A Key Formulas 141

A.1 Probability Density Function . . . . . . . . . . . . . . . . . . . . . . . 141

A.2 Likelihood Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Appendix B Relevant R Code for Inference Procedure 142

B.1 Branching Process Function . . . . . . . . . . . . . . . . . . . . . . . 142

B.2 Imperfect Simulation Function . . . . . . . . . . . . . . . . . . . . . . 143

B.3 Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

B.4 Parameter Estimation Function . . . . . . . . . . . . . . . . . . . . . 153

About this Dissertation

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School	Laney Graduate School
Department	Epidemiology
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Health Sciences, Public Health Biology, Biostatistics Health Sciences, Epidemiology
Keyword	Branching Process Superspreading Tuberculosis Transmission Dynamics
Committee Chair / Thesis Advisor	Neel Gandhi, Emory University Michael Kramer, Emory University
Committee Members	Benjamin Lopman, Emory University Theodore Cohen, Yale University David Benkeser, Emory University

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