Spatial Latent Process Models to Overcome Preferential Sampling in Disease Surveillance Systems Open Access
Conroy, Brian (Fall 2019)
Abstract
Disease surveillance systems are crucial to monitor and predict outbreaks, epidemics and pandemics, as well as to understand the dynamics and trends of diseases over space and time. These systems increasingly rely on complex data collection mechanisms which present particular challenges to the statistician, entailing sampling processes which often violate key assumptions of standard statistical methods. One such mechanism is known as preferential sampling, referring to a stochastic dependency between a spatial process and the locations at which it is observed. While this sampling strategy can lead to considerably biased spatial predictions, few solutions to confront preferential sampling have been proposed in the realm of disease surveillance, despite this potentially deleterious impact. In the first chapter, we propose a novel shared latent process model to correct for preferential sampling in disease surveillance applications, and show by simulation that the practical benefits of such development are reduced bias in parameter estimates and greater accuracy of the estimated disease risk surface. We apply the model to a disease surveillance dataset targeting plague in the rodent population of California, obtaining a substantially improved risk map in comparison to benchmark approaches. In the second chapter, we develop a new multivariate geostatistical model which corrects for preferential sampling when estimating the risk surfaces of a disease common across multiple host species, one which improves spatial predictions by sharing information between species in a hierarchical modeling framework. In the final chapter, we address the dearth of methods to correct for preferential sampling in temporally referenced data by developing a spatiotemporal preferential sampling model, capable of capturing important temporal trends in underlying the disease and sampling processes, yielding more accurate disease risk maps as a result.
Table of Contents
1 Preferential Sampling in Disease Surveillance 1
1.1 Introduction................................ 1
1.2 Methods.................................. 7
1.2.1 Introduction............................ 7
1.2.2 Point Processes .......................... 8
1.2.3 Gaussian Processes ........................ 11
1.2.4 Spatial Process Models...................... 15
1.2.5 Preferential Sampling....................... 20
1.2.6 Model Fitting........................... 32
1.2.7 Hamiltonian Monte Carlo .................... 35
1.2.8 Spatial Downscaling ....................... 39
1.3 Simulation 1:ComparativePerformance ................ 41
1.3.1 Introduction............................ 41
1.3.2 Data................................ 44
1.3.3 ModelFitting........................... 47
1.3.4 Results............................... 49
1.3.5 Discussion............................. 56
1.4 Simulation 2: Parameter Initialization ................. 57
1.4.1 Introduction............................ 57
1.4.2 Results............................... 63
1.4.3 Discussion............................. 66
1.5 Analysis.................................. 70
1.5.1 Introduction............................ 70
1.5.2 Data................................ 73
1.5.3 Results............................... 76
1.5.4 Discussion............................. 89
2 A Multivariate Framework to Address Preferential Sampling 97
2.1 Introduction................................ 97
2.2 Methods.................................. 102
2.2.1 Introduction............................ 102
2.2.2 Multi-species Distribution Modeling. . . . . . . . . . . . . . . 103
2.2.3 Multivariate Gaussian Processes................. 107
2.2.4 Proposed Method......................... 115
2.2.5 Model Fitting........................... 119
2.3 Simulation1: Comparative Performance ................ 125
2.3.1 Introduction............................ 125
2.3.2 Data................................ 126
2.3.3 Results............................... 130
2.3.4 Discussion............................. 146
2.4 Simulation 2: Model Robustness..................... 149
2.4.1 Introduction............................ 149
2.4.2 Data................................ 151
2.4.3 Results............................... 154
2.4.4 Discussion............................. 162
2.5 Analysis.................................. 165
2.5.1 Introduction............................ 165
2.5.2 Data................................ 168
2.5.3 Results............................... 171
2.5.4 Discussion............................. 190
3 A Spatiotemporal Preferential Sampling Model 196
3.1 Introduction................................ 196
3.2 Methods.................................. 201
3.2.1 Introduction............................ 201
3.2.2 Spatiotemporal Modeling in Disease Surveillance . . . . . . . . 203
3.2.3 Spatiotemporal Species Distribution Modeling . . . . . . . . . 213
3.2.4 ProposedMethod......................... 215
3.2.5 SignificanceMaps......................... 222
3.3 Simulations ................................ 225
3.3.1 Introduction............................ 225
3.3.2 Data................................ 229
3.3.3 Results............................... 234
3.3.4 Discussion............................. 241
3.4 Analysis.................................. 244
3.4.1 Introduction............................ 244
3.4.2 Data................................ 246
3.4.3 Results............................... 251
3.4.4 Discussion............................. 262
Bibliography 271
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