Model-Based Statistical Methods for Public Health Surveillance Subject to Imperfect Observations Open Access

Abstract

We examine statistical modeling issues in three areas of public health surveillance: estimation of vaccination coverage, linking local observations and remotely sensed covariates, and adjustment for zero inflation due to underreporting.

When the proportion of the vaccinated population is an unknown value less than 100%, we explore application of logistic growth models, namely the standard logistic growth model and a reparameterization naturally constraining vaccination coverage parameter estimates. We compare the performance of three methods of estimation for each model (nonlinear least squares, maximum likelihood estimation, and Bayesian estimation).

Buruli ulcer is a neglected tropical disease affecting Australia and West Africa. We examine both on-site local water characteristics and broad scale remotely sensed environmental attributes with respect to the presence of the causative pathogen, Mycobacterium ulcerans. Our findings support hypotheses regarding conditions suitable for M. ulcerans growth, but diverge from other published results regarding the distribution of and factors related to Buruli ulcer disease. In addition, our findings suggest locations of reported cases and pathogen presence need not coincide, supporting the notion that human interaction with the environment plays a role in transmission.

In Buruli ulcer surveillance, districts which do not report cases are programmatically treated as districts without cases but are not actually confirmed as disease-free districts. Moreover, there is substantial reason to believe that some non-reporting districts actually have cases; consequently, our data are subject to 'false' zeros. We evaluate the performance of the zero inflated Poisson model in the presence of false zeros, as well as propose a hierarchical zero inflated Poisson model with the ability to estimate an observation's conditional probability of being a false zero given that a zero was observed.

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vaccination Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Neglected Tropical Diseases . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Surveillance of NTDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Constraining Parameter Estimates in a Logistic Growth Model . .4
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 The Logistic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Methods of Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Nonlinear least squares . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . 14
2.4.3 Bayesian Estimation . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.1 Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Application to Kenya 2003 DHS . . . . . . . . . . . . . . . . . . . . . 19
2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Linking Remotely Sensed Data to Local Observations . . . . . 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2 Detection of M. ulcerans . . . . . . . . . . . . . . . . . . . . . 29
3.2.3 Water Characteristics . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.4 Remotely Sensed Covariates . . . . . . . . . . . . . . . . . . . 30
3.3 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5.1 Water Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5.2 Land Use/Land Cover Variables . . . . . . . . . . . . . . . . . 45
3.5.3 Terrain Variables . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.4 Overall Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.5 Comparing Environmental Associations with M. ulcerans and
Buruli ulcer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.6 Associations with Reported Buruli ulcer Cases . . . . . . . . . 49
3.5.7 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Assessments of and Modications to Techniques Utilized for Data
with False Zero Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2 Traditional ZIP Models . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 ZIP Models Applied to Processes with Imperfect Detection . . . . . . 64
4.4 Hierarchical Zero-Inflated Models . . . . . . . . . . . . . . . . . . . . 68
4.5 Assessment of Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.6.1 Generating the Data . . . . . . . . . . . . . . . . . . . . . . . 80
4.6.2 Models Evaluated . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.6.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 86
4.7 Back to the Motivating Data . . . . . . . . . . . . . . . . . . . . . . . 104
4.7.1 Details on the Available Data . . . . . . . . . . . . . . . . . . 104
4.7.2 Data We Would Like to Obtain . . . . . . . . . . . . . . . . . 105
4.8 Conclusion/Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.9 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A Likelihood-based approach to non-linear logistic growth model . . . . . .126

B Figures for logistic growth model results . . . . . .129

C Selection of parameter values for hierarchical ZIP data generation . . . . . .135

D WinBUGS code for ZIP Models. . . . . . 140

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Statistics
Keyword	Mycobacterium ulcerans underreporting vaccination coverage zero inflated Poisson models Buruli ulcer Bayesian
Committee Chair / Thesis Advisor	Waller, Lance, Emory University
Committee Members	Long, Qi, Emory University Strickland, Matthew J, Emory University Hill, Andrew , Emory University

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