Use of kernel embeddings in the context of spatial disease mapping
Keywords: kernel
disease modelling
Bayesian
geostatistics
risk mapping
malaria
Madagascar
non-parametric
causal inference

Over the last 20 years, high resolution mapping of estimated disease risk has become an important tool for disease control, facilitating the efficient allocation of limited resources. Maps of malaria risk, in particular, are widely used for operational planning and informing public health policy. Contemporary maps are typically made using Bayesian geostatistical models, informed by prevalence information from national health surveys and remote-sensed environmental and socioeconomic covariates. Increasingly, additional sources of data on malaria burden are available, including incidence data from routine surveillance, as are modelled products that may explain variation in risk, such as high resolution population estimates and intervention and travel time surfaces. Using these data, there is potential to improve estimates of risk and apply other statistical tools to answer policy-relevant questions. I develop novel statistical methods with two main aims—to learn the causal relationships between spatial and epidemiological variables from observational data and to improve estimates of malaria risk by combining prevalence and incidence data. These methods frequently necessitate the use of non-parametric approaches to accurately model complex relationships and account for a variety of possible sampling distributions. I use non-parametric methods based on the theory of kernel embeddings, which are computationally efficient and remain effective in high dimensions.
Learning causal relationships using spatial and epidemiological data is challenging for a number of reasons. Many existing causal inference methods rely on restrictive parametric assumptions that may not be satisfied in these cases. These data also include spatiotemporal structure that can confound relationships. Furthermore, variables are often observed at different resolutions, making comparisons difficult without aggregating to the lowest observed resolution. Such aggregation is an inefficient use of information and can interfere with learning fine-scale relationships. I develop a causal discovery procedure that combines constraint-based causal discovery algorithms, kernel-based independence tests and random Fourier feature approximations. I extend the theory of kernel-based tests to allow for variables observed at different resolutions. The result is a scalable, non-parametric causal discovery method that can be applied to data that includes spatiotemporal structure, non-linear relationships, and variables observed on different spatial or temporal scales. This is applied as a model-free feature selection method (`causal feature selection’) and shown to perform favourably in the case study of forecasting malaria incidence in Madagascar. In addition, I discuss the challenges of estimating sub-national variation in the effectiveness of malaria control methods from observational data and approaches for estimating these effects at the community and individual level.
I also develop a Bayesian modelling methodology for combining prevalence data from national health surveys with routine surveillance incidence data to improve estimates of prevalence and make these estimates at a higher temporal cadence. Health facility catchment populations and treatment-seeking behaviour are modelled based on travel time to health facilities and a modular structure is used to limit the impact of bias in the incidence data on the final results. This method is used to produce high resolution estimates of monthly malaria prevalence in Madagascar from 2013 to 2016.