Relative effects of climate factors and malaria control interventions on changes of parasitaemia risk in Burkina Faso from 2014 to 2017/2018.

BACKGROUND: In Burkina Faso, the prevalence of malaria has decreased over the past two decades, following the scale-up of control interventions. The successful development of malaria parasites depends on several climatic factors. Intervention gains may be reversed by changes in climatic factors. In this study, we investigated the role of malaria control interventions and climatic factors in influencing changes in the risk of malaria parasitaemia. METHODS: Bayesian logistic geostatistical models were fitted on Malaria Indicator Survey data from Burkina Faso obtained in 2014 and 2017/2018 to estimate the effects of malaria control interventions and climatic factors on the temporal changes of malaria parasite prevalence. Additionally, intervention effects were assessed at regional level, using a spatially varying coefficients model. RESULTS: Temperature showed a statistically important negative association with the geographic distribution of parasitaemia prevalence in both surveys; however, the effects of insecticide-treated nets (ITNs) use was negative and statistically important only in 2017/2018. Overall, the estimated number of infected children under the age of 5 years decreased from 704,202 in 2014 to 290,189 in 2017/2018. The use of ITNs was related to the decline at national and regional level, but coverage with artemisinin-based combination therapy only at regional level. CONCLUSION: Interventions contributed more than climatic factors to the observed change of parasitaemia risk in Burkina Faso during the period of 2014 to 2017/2018. Intervention effects varied in space. Longer time series analyses are warranted to determine the differential effect of a changing climate on malaria parasitaemia risk.

The impact of sustained malaria control in the Loreto region of Peru: a retrospective, observational, spatially-varying interrupted time series analysis of the PAMAFRO program.

Background: Although malaria control investments worldwide have resulted in dramatic declines in transmission since 2000, progress has stalled. In the Amazon, malaria resurgence has followed withdrawal of Global Fund support of the Project for Malaria Control in Andean Border Areas (PAMAFRO). We estimate intervention-specific and spatially-explicit effects of the PAMAFRO program on malaria incidence across the Loreto region of Peru, and consider the influence of the environmental risk factors in the presence of interventions. Methods: We conducted a retrospective, observational, spatial interrupted time series analysis of malaria incidence rates among people reporting to health posts across Loreto, Peru between the first epidemiological week of January 2001 and the last epidemiological week of December 2016. Model inference is at the smallest administrative unit (district), where the weekly number of diagnosed cases of Plasmodium vivax and Plasmodium falciparum were determined by microscopy. Census data provided population at risk. We include as covariates weekly estimates of minimum temperature and cumulative precipitation in each district, as well as spatially- and temporally-lagged malaria incidence rates. Environmental data were derived from a hydrometeorological model designed for the Amazon. We used Bayesian spatiotemporal modeling techniques to estimate the impact of the PAMAFRO program, variability in environmental effects, and the role of climate anomalies on transmission after PAMAFRO withdrawal. Findings: During the PAMAFRO program, incidence of P. vivax declined from 42.8 to 10.1 cases/1000 people/year. Incidence for P. falciparum declined from 14.3 to 2.5 cases/1000 people/year over this same period. The effects of PAMAFRO-supported interventions varied both by geography and species of malaria. Interventions were only effective in districts where interventions were also deployed in surrounding districts. Further, interventions diminished the effects of other prevailing demographic and environmental risk factors. Withdrawal of the program led to a resurgence in transmission. Increasing minimum temperatures and variability and intensity of rainfall events from 2011 onward and accompanying population displacements contributed to this resurgence. Interpretation: Malaria control programs must consider the climate and environmental scope of interventions to maximize effectiveness. They must also ensure financial sustainability to maintain local progress and commitment to malaria prevention and elimination efforts, as well as to offset the effects of environmental change that increase transmission risk. Funding: National Aeronautics and Space Administration, National Institutes of Health, Bill and Melinda Gates Foundation.

Bayesian Spatial Modeling of Diabetes and Hypertension: Results from the South Africa General Household Survey.

Determining spatial links between disease risk and socio-demographic characteristics is vital in disease management and policymaking. However, data are subject to complexities caused by heterogeneity across host classes and space epidemic processes. This study aims to implement a spatially varying coefficient (SVC) model to account for non-stationarity in the effect of covariates. Using the South Africa general household survey, we study the provincial variation of people living with diabetes and hypertension risk through the SVC model. The people living with diabetes and hypertension risk are modeled using a logistic model that includes spatially unstructured and spatially structured random effects. Spatial smoothness priors for the spatially structured component are employed in modeling, namely, a Gaussian Markov random field (GMRF), a second-order random walk (RW2), and a conditional autoregressive (CAR) model. The SVC model is used to relax the stationarity assumption in which non-linear effects of age are captured through the RW2 and allow the mean effect to vary spatially using a CAR model. Results highlight a non-linear relationship between age and people living with diabetes and hypertension. The SVC models outperform the stationary models. The results suggest significant provincial differences, and the maps provided can guide policymakers in carefully exploiting the available resources for more cost-effective interventions.

Observer-based output feedback control design for a fractional ODE and a fractional PDE cascaded system.

This paper considers a new bi-directional cascaded system of a fractional ordinary differential equation (FODE) and a fractional partial differential equation (FPDE) which interacts at an intermediate point. The space-dependent coefficients, interaction between the FODE and FPDE at an intermediate point and the presence of fractional calculus makes the FODE-FPDE cascaded system, representative. In this note, we first apply an invertible integral transformation to convert the system into a FODE-FPDE coupled system, as the target system, which is Mittag-Leffler stable. Using the backstepping method and under some assumptions of the space-dependent coefficients, we work out the kernel functions in the transformation and we design a boundary controller. Also, by the invertibility of the transformation, we show the Mittag-Leffler stability of the closed-loop system via the Lyapunov approach. Second, we propose an observer for which we prove that it can well estimate the original cascaded system. Then, we design an output feedback boundary control law and show that the closed-loop system is Mittag-Leffler stable under the designed output feedback control law. Finally, we present some numerical illustrations to show the correctness of the theoretical results.

A Bayesian spatio-temporal analysis of neighborhood pediatric asthma emergency department visit disparities.

Asthma disparities have complex, neighborhood-level drivers that are not well understood. Consequently, identifying particular contextual factors that contribute to disparities is a public health goal. We study pediatric asthma emergency department (ED) visit disparities and neighborhood factors associated with them in South Carolina (SC) census tracts from 1999 to 2015. Leveraging a Bayesian framework, we identify risk clusters, spatially-varying relationships, and risk percentile-specific associations. Clusters of high risk occur in both rural and urban census tracts with high probability, with neighborhood-specific associations suggesting unique risk factors for each locale. Bayesian methods can help clarify the neighborhood drivers of health disparities.

A spatially varying distributed lag model with application to an air pollution and term low birth weight study.

Distributed lag models have been used to identify critical pregnancy periods of exposure (i.e. critical exposure windows) to air pollution in studies of pregnancy outcomes. However, much of the previous work in this area has ignored the possibility of spatial variability in the lagged health effect parameters that may result from exposure characteristics and/or residual confounding. We develop a spatially varying Gaussian process model for critical windows called 'SpGPCW' and use it to investigate geographic variability in the association between term low birth weight and average weekly concentrations of ozone and PM2:5 during pregnancy by using birth records from North Carolina. SpGPCW is designed to accommodate areal level spatial correlation between lagged health effect parameters and temporal smoothness in risk estimation across pregnancy. Through simulation and a real data application, we show that the consequences of ignoring spatial variability in the lagged health effect parameters include less reliable inference for the parameters and diminished ability to identify true critical window sets, and we investigate the use of existing Bayesian model comparison techniques as tools for determining the presence of spatial variability. We find that exposure to PM2:5 is associated with elevated term low birth weight risk in selected weeks and counties and that ignoring spatial variability results in null associations during these periods. An R package (SpGPCW) has been developed to implement the new method.

Spatially varying age-period-cohort analysis with application to US mortality, 2002-2016.

Many public health databases index disease counts by age groups and calendar periods within geographic regions (e.g., states, districts, or counties). Issues around relative risk estimation in small areas are well-studied; however, estimating trend parameters that vary across geographic regions has received less attention. Additionally, small counts (e.g., $<10$) in most publicly accessible databases are censored, further complicating age-period-cohort (APC) analysis in small areas. Here, we present a novel APC model with left-censoring and spatially varying intercept and trends, estimated with correlations among contiguous geographic regions. Like traditional models, our model captures population-scale trends, but it can also be used to characterize geographic disparities in relative risk and age-adjusted trends over time. To specify the joint distribution of our three spatially varying parameters, we adapt the generalized multivariate conditional autoregressive prior, previously used for multivariate disease mapping. Specified in this manner, region-specific parameters are correlated spatially, and also to one another. Estimation is performed using the No-U-Turn Hamiltonian Monte Carlo sampler in Stan. We conduct a simulation study to assess the performance of the proposed model relative to the standard model, and conclude with an application to US state-level opioid overdose mortality in men and women aged 15-64 years.

Extending multilevel spatial models to include spatially varying coefficients.

Multilevel models have long been used by health geographers working on questions of space, place, and health. Similarly, health geographers have pursued interests in determining whether or not the effect of an exposure on a health outcome varies spatially. However, relatively little work has sought to use multilevel models to explore spatial variability in the effects of a contextual exposure on a health outcome. Methodologically, extending multilevel models to allow intercepts and slopes to vary spatially is straightforward. The purpose of this paper, therefore, is to show how multilevel spatial models can be extended to include spatially varying covariate effects. We provide an empirical example on the effect of agriculture on malaria risk in children under 5 years of age in the Democratic Republic of Congo.

A mixed-effects, spatially varying coefficients model with application to multi-resolution functional magnetic resonance imaging data.

Spatial resolution plays an important role in functional magnetic resonance imaging studies as the signal-to-noise ratio increases linearly with voxel volume. In scientific studies, where functional magnetic resonance imaging is widely used, the standard spatial resolution typically used is relatively low which ensures a relatively high signal-to-noise ratio. However, for pre-surgical functional magnetic resonance imaging analysis, where spatial accuracy is paramount, high-resolution functional magnetic resonance imaging may play an important role with its greater spatial resolution. High spatial resolution comes at the cost of a smaller signal-to-noise ratio. This begs the question as to whether we can leverage the higher signal-to-noise ratio of a standard functional magnetic resonance imaging study with the greater spatial accuracy of a high-resolution functional magnetic resonance imaging study in a pre-operative patient. To answer this question, we propose to regress the statistic image from a high resolution scan onto the statistic image obtained from a standard resolution scan using a mixed-effects model with spatially varying coefficients. We evaluate our model via simulation studies and we compare its performance with a recently proposed model that operates at a single spatial resolution. We apply and compare the two models on data from a patient awaiting tumor resection. Both simulation study results and the real data analysis demonstrate that our newly proposed model indeed leverages the larger signal-to-noise ratio of the standard spatial resolution scan while maintaining the advantages of the high spatial resolution scan.

A Statistical Model to Analyze Clinician Expert Consensus on Glaucoma Progression using Spatially Correlated Visual Field Data.

PURPOSE: We developed a statistical model to improve the detection of glaucomatous visual field (VF) progression as defined by the consensus of expert clinicians. METHODS: We developed new methodology in the Bayesian setting to properly model the progression status of a patient (as determined by a group of expert clinicians) as a function of changes in spatially correlated sensitivities at each VF location jointly. We used a spatial probit regression model that jointly incorporates all highly correlated VF changes in a single framework while accounting for structural similarities between neighboring VF regions. RESULTS: Our method had improved model fit and predictive ability compared to competing models as indicated by the deviance information criterion (198.15 vs. 201.29-213.38), a posterior predictive model selection metric (130.08 vs. 142.08-155.59), area under the receiver operating characteristic curve (0.80 vs. 0.59-0.72; all P values < 0.018), and optimal sensitivity (0.92 vs. 0.28-0.82). Simulation study results suggest that estimation (reduction of mean squared errors) and inference (correct coverage of 95% credible intervals) for the model parameters are improved when spatial modeling is incorporated. CONCLUSIONS: We developed a statistical model for the detection of VF progression defined by clinician expert consensus that accounts for spatially correlated changes in visual sensitivity over time, and showed that it outperformed competing models in a number of areas. TRANSLATIONAL RELEVANCE: This model may easily be incorporated into routine clinical practice and be useful for detecting glaucomatous VF progression defined by clinician expert consensus.

Spatially Modelling the Association Between Access to Recreational Facilities and Exercise: The 'Multi-Ethnic Study of Atherosclerosis'.

Numerous studies have investigated the relationship between the built environment and physical activity. However these studies assume that these relationships are invariant over space. In this study, we introduce a novel method to analyze the association between access to recreational facilities and exercise allowing for spatial heterogeneity. In addition, this association is studied before and after controlling for crime, a variable that could explain spatial heterogeneity of associations. We use data from the Chicago site of the Multi-Ethnic Study of Atherosclerosis of 781 adults aged 46 years and over. A spatially varying coefficient Tobit regression model is implemented in the Bayesian setting to allow for the association of interest to vary over space. The relationship is shown to vary over Chicago, being positive in the south but negative or null in the north. Controlling for crime weakens the association in the south with little change observed in northern Chicago. The results of this study indicate that spatial heterogeneity in associations of environmental factors with health may vary over space and deserve further exploration.

ANALYSIS OF MULTIPLE SCLEROSIS LESIONS VIA SPATIALLY VARYING COEFFICIENTS.

Magnetic resonance imaging (MRI) plays a vital role in the scientific investigation and clinical management of multiple sclerosis. Analyses of binary multiple sclerosis lesion maps are typically "mass univariate" and conducted with standard linear models that are ill suited to the binary nature of the data and ignore the spatial dependence between nearby voxels (volume elements). Smoothing the lesion maps does not entirely eliminate the non-Gaussian nature of the data and requires an arbitrary choice of the smoothing parameter. Here we present a Bayesian spatial model to accurately model binary lesion maps and to determine if there is spatial dependence between lesion location and subject specific covariates such as MS subtype, age, gender, disease duration and disease severity measures. We apply our model to binary lesion maps derived from T2-weighted MRI images from 250 multiple sclerosis patients classified into five clinical subtypes, and demonstrate unique modeling and predictive capabilities over existing methods.