A spatially discrete approximation to log-Gaussian Cox processes for modelling aggregated disease count data

PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.

How does the community COVID-19 level of risk impact on that of a care home?

Objectives

To model the risk of COVID-19 mortality in British care homes conditional on the community level risk.

Methods

A two stage modeling process (“doubly latent”) which includes a Besag York Mollie model (BYM) and a Log Gaussian Cox Process. The BYM is adopted so as to estimate the community level risks. These are incorporated in the Log Gaussian Cox Process to estimate the impact of these risks on that in care homes.

Results

For an increase in the risk at the community level, the number of COVID-19 related deaths in the associated care home would be increased by exp (0.833), 2. This is based on a simulated dataset. In the context of COVID-19 related deaths, this study has illustrated the estimation of the risk to care homes in the presence of background community risk. This approach will be useful in facilitating the identification of the most vulnerable care homes and in predicting risk to new care homes.

Conclusions

The modeling of two latent processes have been shown to be successfully facilitated by the use of the BYM and Log Gaussian Cox Process Models. Community COVID-19 risks impact on that of the care homes embedded in these communities.

A modelling framework for developing early warning systems of COPD emergency admissions

Chronic Obstructive Pulmonary Disease (COPD) is one of the leading causes of mortality worldwide and is a major contributor to the number of emergency admissions in the UK. We introduce a modelling framework for the development of early warning systems for COPD emergency admissions. We analyse the number of COPD emergency admissions using a Poisson generalised linear mixed model. We group risk factors into three main groups, namely pollution, weather and deprivation. We then carry out variable selection within each of the three domains of COPD risk. Based on a threshold of incidence rate, we then identify the model giving the highest sensitivity and specificity through the use of exceedance probabilities. The developed modelling framework provides a principled likelihood-based approach for detecting the exceedance of thresholds in COPD emergency admissions. Our results indicate that socio-economic risk factors are key to enhance the predictive power of the model.

Dealing with spatial misalignment to model the relationship between deprivation and life expectancy: a model-based geostatistical approach

BACKGROUND : Life expectancy at birth (LEB), one of the main indicators of human longevity, has often been used to characterise the health status of a population. Understanding its relationships with the deprivation is key to develop policies and evaluate interventions that are aimed at reducing health inequalities. However, methodological challenges in the analysis of LEB data arise from the fact that different Government agencies often provide spatially aggregated information on LEB and the index of multiple deprivation (IMD) at different spatial scales. Our objective is to develop a geostatistical framework that, unlike existing methods of inference, allows to carry out spatially continuous prediction while dealing with spatial misalignment of the areal-level data. METHODS : We developed a model-based geostatistical approach for the joint analysis of LEB and IMD, when these are available over different partitions of the study region. We model the spatial correlation in LEB and IMD across the areal units using inter-point distances based on a regular grid covering the whole of the study area. The advantages and strengths of the new methodology are illustrated through an analysis of LEB and IMD data from the Liverpool district council. RESULTS : We found that the effect of IMD on LEB is stronger in males than in females, explaining about 63.35% of the spatial variation in LEB in the former group and 38.92% in the latter. We also estimate that LEB is about 8.5 years lower between the most and least deprived area of Liverpool for men, and 7.1 years for women. Finally, we find that LEB, both in males and females, is at least 80% likely to be above the England wide average only in some areas falling in the electoral wards of Childwall, Woolton and Church. CONCLUSION : The novel model-based geostatistical framework provides a feasible solution to the spatial misalignment problem. More importantly, the proposed methodology has the following advantages over existing methods used model LEB: (1) it can deliver spatially continuous inferences using spatially aggregated data; (2) it can be applied to any form of misalignment with information provided at a range of spatial scales, from areal-level to pixel-level.

A spatially discrete approximation to log-Gaussian Cox processes for modelling aggregated disease count data

In this paper, we develop a computationally efficient discrete approximation to log-Gaussian Cox process (LGCP) models for the analysis of spatially aggregated disease count data. Our approach overcomes an inherent limitation of spatial models based on Markov structures, namely, that each such model is tied to a specific partition of the study area, and allows for spatially continuous prediction. We compare the predictive performance of our modelling approach with LGCP through a simulation study and an application to primary biliary cirrhosis incidence data in Newcastle upon Tyne, UK. Our results suggest that, when disease risk is assumed to be a spatially continuous process, the proposed approximation to LGCP provides reliable estimates of disease risk both on spatially continuous and aggregated scales. The proposed methodology is implemented in the open-source R package SDALGCP.