Spectral adjustment for spatial confounding

Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the exposure to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matern coherence function to more robust semiparametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.

Analysing spatiotemporal patterns of Covid-19 confirmed deaths at the NUTS-2 regional level

During the ongoing Covid-19 pandemic, understanding the spatiotemporal patterns of the virus is crucial for policymakers to intervene promptly. The relevance of spatial proximity in the spread of the pandemic necessitates adequate tools, and noisy data must be properly treated. This study proposes obtaining clusters of European regions using smoothed curves of daily deaths from March 2020-March 2022. A functional representation of the curves w<s implemented to extract the features used in a clustering algorithm that allows spatial proximity. In a spatial regression model, the authors also investigated the role of clusters and pre-existing conditions on cumulative deaths, and observed that air pollution, health conditions, and population age structure are significantly associated with Covid-19 confirmed deaths.

DeepDrive: A braking decision making approach using optimized GAN and Deep CNN for advanced driver assistance systems

Reduction of the number of traffic accidents is a vital requirement in many countries over the world. In these circumstances, the Human–Robot Interaction (HRI) mechanisms utilization is currently exposed as a possible solution to recompense human limits. It is crucial to create a braking decision-making model in order to produce the optimal decisions possible because many braking decision-making approaches are launched with minimal performance. An effective braking decision-making system, named Optimized Deep Drive decision model is developed for making braking decisions. The video frames are extracted and the segmentation process is done using a Generative Adversarial Network (GAN). GAN is trained using the newly developed optimization technique known as the Autoregressive Anti Corona Virus Optimization (ARACVO) algorithm. ARACVO is created by combining the Conditional Autoregressive Value at Risk by Regression Quantiles (CAViaR) and Anti Corona Virus Optimization (ACVO) models. After retrieving the useful information for processing, the Deep Convolutional Neural Network (Deep CNN) is next used to decide whether to apply the brakes. The proposed approach improved performance by achieving maximum values of 0.911, 0.906, 0.924, and 0.933 for segmentation accuracy, accuracy, sensitivity, and specificity. © 2023 Elsevier Ltd

Modeling the spread of COVID-19 in spatio-temporal context.

This study aims to use data provided by the Virginia Department of Public Health to illustrate the changes in trends of the total cases in COVID-19 since they were first recorded in the state. Each of the 93 counties in the state has its COVID-19 dashboard to help inform decision makers and the public of spatial and temporal counts of total cases. Our analysis shows the differences in the relative spread between the counties and compares the evolution in time using Bayesian conditional autoregressive framework. The models are built under the Markov Chain Monte Carlo method and Moran spatial correlations. In addition, Moran's time series modeling techniques were applied to understand the incidence rates. The findings discussed may serve as a template for other studies of similar nature.

A spatial model to jointly analyze self-reported survey data of COVID-19 symptoms and official COVID-19 incidence data.

This work presents a joint spatial modeling framework to improve estimation of the spatial distribution of the latent COVID-19 incidence in Belgium, based on test-confirmed COVID-19 cases and crowd-sourced symptoms data as reported in a large-scale online survey. Correction is envisioned for stochastic dependence between the survey's response rate and spatial COVID-19 incidence, commonly known as preferential sampling, but not found significant. Results show that an online survey can provide valuable auxiliary data to optimize spatial COVID-19 incidence estimation based on confirmed cases in situations with limited testing capacity. Furthermore, it is shown that an online survey on COVID-19 symptoms with a sufficiently large sample size per spatial entity is capable of pinpointing the same locations that appear as test-confirmed clusters, approximately 1 week earlier. We conclude that a large-scale online study provides an inexpensive and flexible method to collect timely information of an epidemic during its early phase, which can be used by policy makers in an early phase of an epidemic and in conjunction with other monitoring systems.

Bayesian Hierarchical Spatial Modeling of COVID-19 Cases in Bangladesh

This research aimed to investigate the spatial autocorrelation and heterogeneity throughout Bangladesh's 64 districts. Moran I and Geary C are used to measure spatial autocorrelation. Different conventional models, such as Poisson-Gamma and Poisson-Lognormal, and spatial models, such as Conditional Autoregressive (CAR) Model, Convolution Model, and modified CAR Model, have been employed to detect the spatial heterogeneity. Bayesian hierarchical methods via Gibbs sampling are used to implement these models. The best model is selected using the Deviance Information Criterion. Results revealed Dhaka has the highest relative risk due to the city's high population density and growth rate. This study identifies which district has the highest relative risk and which districts adjacent to that district also have a high risk, which allows for the appropriate actions to be taken by the government agencies and communities to mitigate the risk effect. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Adaptive Gaussian Markov random field spatiotemporal models for infectious disease mapping and forecasting.

Recent disease mapping literature presents adaptively parameterized spatiotemporal (ST) autoregressive (AR) or conditional autoregressive (CAR) models for Bayesian prediction of COVID-19 infection risks. These models were motivated to capture complex spatiotemporal dynamics and heterogeneities of infection risks. In the present paper, we synthesize, generalize, and unify the ST AR and CAR model constructions for models augmented by adaptive Gaussian Markov random fields, with an emphasis on disease forecasting. A general convolution construction is presented, with illustrative models motivated to (i) characterize local risk dependencies and influences over both spatial and temporal dimensions, (ii) model risk heterogeneities and discontinuities, and (iii) predict and forecast areal-level disease risks and occurrences. The broadened constructions allow rich options of intuitive parameterization for disease mapping and spatial regression. Illustrative parameterizations are presented for Bayesian hierarchical models of Poisson, zero-inflated Poisson, and Bernoulli data models, respectively. They are also discussed in the context of quantifying time-varying or time-invariant effects of (omitted) covariates, with application to prediction and forecasting areal-level COVID-19 infection occurrences and probabilities of zero-infection. The model constructions presented herein have much wider scope in offering a flexible framework for modelling complex spatiotemporal data and for estimation, learning, and forecasting purposes.

Bayesian disease mapping: Past, present, and future.

On the occasion of the Spatial Statistics' 10th Anniversary, I reflect on the past and present of Bayesian disease mapping and look into its future. I focus on some key developments of models, and on recent evolution of multivariate and adaptive Gaussian Markov random fields and their impact and importance in disease mapping. I reflect on Bayesian disease mapping as a subject of spatial statistics that has advanced to date, and continues to grow, in scope and complexity alongside increasing needs of analytic tools for contemporary health science research, such as spatial epidemiology, population and public health, and medicine. I illustrate (potential) utility and impact of some of the disease mapping models and methods for analysing and monitoring communicable disease such as the COVID-19 infection risks during an ongoing pandemic.

Variance partitioning in spatio-temporal disease mapping models.

Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that we name the variance partitioning model. The variance partitioning model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a penalized complexity prior on the mixing parameter aids in coding prior information in an intuitive way. We illustrate the advantages of the variance partitioning model using two case studies.

A joint hierarchical model for the number of cases and deaths due to COVID-19 across the boroughs of Montreal.

As of July 2021, Montreal is the epicentre of the COVID-19 pandemic in Canada with highest number of deaths. We aim to investigate the spatial distribution of the number of cases and deaths due to COVID-19 across the boroughs of Montreal. To this end, we propose that the cumulative numbers of cases and deaths in the 33 boroughs of Montreal are modelled through a bivariate hierarchical Bayesian model using Poisson distributions. The Poisson means are decomposed in the log scale as the sums of fixed effects and latent effects. The areal median age, the educational level, and the number of beds in long-term care homes are included in the fixed effects. To explore the correlation between cases and deaths inside and across areas, three different bivariate models are considered for the latent effects, namely an independent one, a conditional autoregressive model, and one that allows for both spatially structured and unstructured sources of variability. As the inclusion of spatial effects change some of the fixed effects, we extend the Spatial+ approach to a Bayesian areal set up to investigate the presence of spatial confounding. We find that the model which includes independent latent effects across boroughs performs the best among the ones considered, there appears to be spatial confounding with the diploma and median age variables, and the correlation between the cases and deaths across and within boroughs is always negative.

Unmet need for COVID-19 vaccination coverage in Kenya.

COVID-19 has impacted the health and livelihoods of billions of people since it emerged in 2019. Vaccination for COVID-19 is a critical intervention that is being rolled out globally to end the pandemic. Understanding the spatial inequalities in vaccination coverage and access to vaccination centres is important for planning this intervention nationally. Here, COVID-19 vaccination data, representing the number of people given at least one dose of vaccine, a list of the approved vaccination sites, population data and ancillary GIS data were used to assess vaccination coverage, using Kenya as an example. Firstly, physical access was modelled using travel time to estimate the proportion of population within 1 hour of a vaccination site. Secondly, a Bayesian conditional autoregressive (CAR) model was used to estimate the COVID-19 vaccination coverage and the same framework used to forecast coverage rates for the first quarter of 2022. Nationally, the average travel time to a designated COVID-19 vaccination site (n = 622) was 75.5 min (Range: 62.9 - 94.5 min) and over 87% of the population >18 years reside within 1 hour to a vaccination site. The COVID-19 vaccination coverage in December 2021 was 16.70% (95% CI: 16.66 - 16.74) - 4.4 million people and was forecasted to be 30.75% (95% CI: 25.04 - 36.96) - 8.1 million people by the end of March 2022. Approximately 21 million adults were still unvaccinated in December 2021 and, in the absence of accelerated vaccine uptake, over 17.2 million adults may not be vaccinated by end March 2022 nationally. Our results highlight geographic inequalities at sub-national level and are important in targeting and improving vaccination coverage in hard-to-reach populations. Similar mapping efforts could help other countries identify and increase vaccination coverage for such populations.

Association of Population Density and Distance to the City with the Risks of COVID-19: A Bayesian Spatial Analysis

The outbreak of Coronavirus disease-2019 (Covid-19) poses a severe threat around the world. Although several studies of modelling Covid-19 cases have been done, there appears to have been limited research into modelling Covid-19 using Bayesian hierarchical spatial models. This study aims to examine the most suitable Bayesian spatial CAR Leroux models in modelling the number of confirmed Covid-19 cases without and with covariates namely distance to the capital city and population density. Data on the number of confirmed positive cases of Covid-19 (March 20, 2020 - August 30, 2021) in 15 sub-districts in Makassar City, the number of populations, population density, and distance to the city are used. The best model selection is based on several criteria, namely Deviance Information Criteria (DIC), Watanabe Akaike Information Criteria (WAIC), residuals from Moran's I Modification (MMI), and the 95% credible interval does not contain zero. The results showed that the best model in modelling Covid-19 is spatial CAR Leroux with hyperprior Inverse-Gamma (0.5, 0.05) model with the incorporation of distance to the capital city. It is found that there was a negative correlation between the distance to the capital city and Covid-19 risk, but the association between population density and the relative risk of Covid-19 was not statistically significant. Ujung Pandang district and Sangkarrang Island have the highest and the lowest relative risk respectively. © 2021 Institute of Physics Publishing. All rights reserved.

Spatio-Temporal Modelling of Progression of the COVID–19 Pandemic

The recent novel coronavirus (COVID-19) pandemic has been the worst in recent history regarding disease fatalities. It is therefore critical to find suitable statistical models that can be used to predict progression of the COVID-19. Such models will allow us to monitor the spread of the virus in the targeted locations and time. Data on new COVID-19 cases data on four selected countries over time were collected via Situation Reports published by the World Health Organization. The data of the neighboring countries were also considered in modelling. The Bayesian Conditional autoregressive (CAR) models are applied to the data to account for the spatial dependency in the countries along with the temporal dimension of the disease. Moran measures were also computed to compare spatial trends of the new COVID-19 cases within each country and block. Different blocks evidenced discrepancies that could be used to direct guidelines and regulations specific to those countries. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Spatio-temporal modelling of COVID-19 incident cases using Richards' curve: An application to the Italian regions.

We introduce an extended generalised logistic growth model for discrete outcomes, in which spatial and temporal dependence are dealt with the specification of a network structure within an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. We compared a network based on geographic proximity and one built on historical data of transport exchanges between regions. Parameters are estimated under the Bayesian framework, using Stan probabilistic programming language. The proposed approach is motivated by the analysis of both the first and the second wave of COVID-19 in Italy, i.e. from February 2020 to July 2020 and from July 2020 to December 2020, respectively. We analyse data at the regional level and, interestingly enough, prove that substantial spatial and temporal dependence occurred in both waves, although strong restrictive measures were implemented during the first wave. Accurate predictions are obtained, improving those of the model where independence across regions is assumed.