Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing

Childhood stunting in Indonesia: assessing the performance of Bayesian spatial conditional autoregressive models

Stunting continues to be a significant health issue, particularly in developing nations, with Indonesia ranking third in prevalence in Southeast Asia. This research examined the risk of stunting and influencing factors in Indonesia by implementing various Bayesian spatial conditional autoregressive (CAR) models that include covariates. A total of 750 models were run, including five different Bayesian spatial CAR models (Besag-York-Mollie (BYM), CAR Leroux and three forms of localised CAR), with 30 covariate combinations and five different hyperprior combinations for each model. The Poisson distribution was employed to model the counts of stunting cases. After a comprehensive evaluation of all model selection criteria utilized, the Bayesian localised CAR model with three covariates were preferred, either allowing up to 2 clusters with a variance hyperprior of inverse-gamma (1, 0.1) or allowing 3 clusters with a variance hyperprior of inverse-gamma (1, 0.01). Poverty and recent low birth weight (LBW) births are significantly associated with an increased risk of stunting, whereas child diet diversity is inversely related to the risk of stunting. Model results indicated that Sulawesi Barat Province has the highest risk of stunting, with DKI Jakarta Province the lowest. These areas with high stunting require interventions to reduce poverty, LBW births and increase child diet diversity.

Relation of prenatal and postnatal PM2.5 exposure with cognitive and motor function among preschool-aged children

The literature informing susceptible periods of exposure on children's neurodevelopment is limited. We evaluated the impacts of pre- and postnatal fine particulate matter (PM2.5) exposure on children's cognitive and motor function among 1303 mother-child pairs in the Spanish INMA (Environment and Childhood) Study. Random forest models with temporal back extrapolation were used to estimate daily residential PM2.5 exposures that we averaged across 1-week lags during the prenatal period and 4-week lags during the postnatal period. The McCarthy Scales of Children's Abilities (MSCA) were administered around 5 years to assess general cognitive index (GCI) and several subscales (verbal, perceptual-performance, memory, fine motor, gross motor). We applied distributed lag nonlinear models within the Bayesian hierarchical framework to explore periods of susceptibility to PM2.5 on each MSCA outcome. Effect estimates were calculated per 5 μg/m3 increase in PM2.5 and aggregated across adjacent statistically significant lags using cumulative β (βcum) and 95% Credible Intervals (95%CrI). We evaluated interactions between PM2.5 with fetal growth and child sex. We did not observe associations of PM2.5 exposure with lower GCI scores. We found a period of susceptibility to PM2.5 on fine motor scores in gestational weeks 1-9 (βcum = -2.55, 95%CrI = -3.53,-1.56) and on gross motor scores in weeks 7-17 (βcum = -2.27,95%CrI = -3.43,-1.11) though the individual lags for the latter were only borderline statistically significant. Exposure in gestational week 17 was weakly associated with verbal scores (βcum = -0.17, 95%CrI = -0.26,-0.09). In the postnatal period (from age 0.5-1.2 years), we observed a window of susceptibility to PM2.5 on lower perceptual-performance (β = -2.42, 95%CrI = -3.37,-1.46). Unexpected protective associations were observed for several outcomes with exposures in the later postnatal period. We observed no evidence of differences in susceptible periods by fetal growth or child sex. Preschool-aged children's motor function may be particularly susceptible to PM2.5 exposures experienced in utero whereas the first year of life was identified as a period of susceptibility to PM2.5 for children's perceptual-performance.

Susceptible windows of prenatal and postnatal fine particulate matter exposures and attention-deficit hyperactivity disorder symptoms in early childhood

Few prior studies have explored windows of susceptibility to fine particulate matter (PM2.5) in both the prenatal and postnatal periods and children's attention-deficit/hyperactivity disorder (ADHD) symptoms. We analyzed data from 1416 mother-child pairs from the Spanish INMA (INfancia y Medio Ambiente) Study (2003-2008). Around 5 years of age, teachers reported the number of ADHD symptoms (i.e., inattention, hyperactivity/impulsivity) using the ADHD Diagnostic and Statistical Manual of Mental Disorders. Around 7 years of age, parents completed the Conners' Parent Rating Scales, from which we evaluated the ADHD index, cognitive problems/inattention, hyperactivity, and oppositional subscales, reported as age- and sex-standardized T-scores. Daily residential PM2.5 exposures were estimated using a two-stage random forest model with temporal back-extrapolation and averaged over 1-week periods in the prenatal period and 4-week periods in the postnatal period. We applied distributed lag non-linear models within the Bayesian hierarchical model framework to identify susceptible windows of prenatal or postnatal exposure to PM2.5 (per 5-μg/m3) for ADHD symptoms. Models were adjusted for relevant covariates, and cumulative effects were reported by aggregating risk ratios (RRcum) or effect estimates (βcum) across adjacent susceptible windows. A similar susceptible period of exposure to PM2.5 (1.2-2.9 and 0.9-2.7 years of age, respectively) was identified for hyperactivity/impulsivity symptoms assessed ~5 years (RRcum = 2.72, 95% credible interval [CrI] = 1.98, 3.74) and increased hyperactivity subscale ~7 years (βcum = 3.70, 95% CrI = 2.36, 5.03). We observed a susceptibility period to PM2.5 on risk of hyperactivity/impulsivity symptoms ~5 years in gestational weeks 16-22 (RRcum = 1.36, 95% CrI = 1.22, 1.52). No associations between PM2.5 exposure and other ADHD symptoms were observed. We report consistent evidence of toddlerhood as a susceptible window of PM2.5 exposure for hyperactivity in young children. Although mid-pregnancy was identified as a susceptible period of exposure on hyperactivity symptoms in preschool-aged children, this association was not observed at the time children were school-aged.

Habitat and climatic associations of climate-sensitive species along a southern range boundary

Climate change and habitat loss are recognized as important drivers of shifts in wildlife species' geographic distributions. While often considered independently, there is considerable overlap between these drivers, and understanding how they contribute to range shifts can predict future species assemblages and inform effective management. Our objective was to evaluate the impacts of habitat, climatic, and anthropogenic effects on the distributions of climate-sensitive vertebrates along a southern range boundary in Northern Michigan, USA. We combined multiple sources of occurrence data, including harvest and citizen-science data, then used hierarchical Bayesian spatial models to determine habitat and climatic associations for four climate-sensitive vertebrate species (American marten [Martes americana], snowshoe hare [Lepus americanus], ruffed grouse [Bonasa umbellus] and moose [Alces alces]). We used total basal area of at-risk forest types to represent habitat, and temperature and winter habitat indices to represent climate. Marten associated with upland spruce-fir and lowland riparian forest types, hares with lowland conifer and aspen-birch, grouse with lowland riparian hardwoods, and moose with upland spruce-fir. Species differed in climatic drivers with hares positively associated with cooler annual temperatures, moose with cooler summer temperatures and grouse with colder winter temperatures. Contrary to expectations, temperature variables outperformed winter habitat indices. Model performance varied greatly among species, as did predicted distributions along the southern edge of the Northwoods region. As multiple species were associated with lowland riparian and upland spruce-fir habitats, these results provide potential for efficient prioritization of habitat management. Both direct and indirect effects from climate change are likely to impact the distribution of climate-sensitive species in the future and the use of multiple data types and sources in the modelling of species distributions can result in more accurate predictions resulting in improved management at policy-relevant scales.

A Systematic Review of Joint Spatial and Spatiotemporal Models in Health Research

With the advancement of spatial analysis approaches, methodological research addressing the technical and statistical issues related to joint spatial and spatiotemporal models has increased. Despite the benefits of spatial modelling of several interrelated outcomes simultaneously, there has been no published systematic review on this topic, specifically when such models would be useful. This systematic review therefore aimed at reviewing health research published using joint spatial and spatiotemporal models. A systematic search of published studies that applied joint spatial and spatiotemporal models was performed using six electronic databases without geographic restriction. A search with the developed search terms yielded 4077 studies, from which 43 studies were included for the systematic review, including 15 studies focused on infectious diseases and 11 on cancer. Most of the studies (81.40%) were performed based on the Bayesian framework. Different joint spatial and spatiotemporal models were applied based on the nature of the data, population size, the incidence of outcomes, and assumptions. This review found that when the outcome is rare or the population is small, joint spatial and spatiotemporal models provide better performance by borrowing strength from related health outcomes which have a higher prevalence. A framework for the design, analysis, and reporting of such studies is also needed.

Susceptible windows of exposure to fine particulate matter and fetal growth trajectories in the Spanish INMA (INfancia y Medio Ambiente) birth cohort

While prior studies report associations between fine particulate matter (PM2.5) exposure and fetal growth, few have explored temporally refined susceptible windows of exposure. We included 2328 women from the Spanish INMA Project from 2003 to 2008. Longitudinal growth curves were constructed for each fetus using ultrasounds from 12, 20, and 34 gestational weeks. Z-scores representing growth trajectories of biparietal diameter, femur length, abdominal circumference (AC), and estimated fetal weight (EFW) during early (0-12 weeks), mid- (12-20 weeks), and late (20-34 weeks) pregnancy were calculated. A spatio-temporal random forest model with back-extrapolation provided weekly PM2.5 exposure estimates for each woman during her pregnancy. Distributed lag non-linear models were implemented within the Bayesian hierarchical framework to identify susceptible windows of exposure for each outcome and cumulative effects [βcum, 95% credible interval (CrI)] were aggregated across adjacent weeks. For comparison, general linear models evaluated associations between PM2.5 averaged across multi-week periods (i.e., weeks 1-11, 12-19, and 20-33) and fetal growth, mutually adjusted for exposure during each period. Results are presented as %change in z-scores per 5 μg/m3 in PM2.5, adjusted for covariates. Weeks 1-6 [βcum = -0.77%, 95%CrI (-1.07%, -0.47%)] were identified as a susceptible window of exposure for reduced late pregnancy EFW while weeks 29-33 were positively associated with this outcome [βcum = 0.42%, 95%CrI (0.20%, 0.64%)]. A similar pattern was observed for AC in late pregnancy. In linear regression models, PM2.5 exposure averaged across weeks 1-11 was associated with reduced late pregnancy EFW and AC; but, positive associations between PM2.5 and EFW or AC trajectories in late pregnancy were not observed. PM2.5 exposures during specific weeks may affect fetal growth differentially across pregnancy and such associations may be missed by averaging exposure across multi-week periods, highlighting the importance of temporally refined exposure estimates when studying the associations of air pollution with fetal growth.

Methods Used in the Spatial and Spatiotemporal Analysis of COVID-19 Epidemiology: A Systematic Review

The spread of the COVID-19 pandemic was spatially heterogeneous around the world; the transmission of the disease is driven by complex spatial and temporal variations in socioenvironmental factors. Spatial tools are useful in supporting COVID-19 control programs. A substantive review of the merits of the methodological approaches used to understand the spatial epidemiology of the disease is hardly undertaken. In this study, we reviewed the methodological approaches used to identify the spatial and spatiotemporal variations of COVID-19 and the socioeconomic, demographic and climatic drivers of such variations. We conducted a systematic literature search of spatial studies of COVID-19 published in English from Embase, Scopus, Medline, and Web of Science databases from 1 January 2019 to 7 September 2021. Methodological quality assessments were also performed using the Joanna Briggs Institute (JBI) risk of bias tool. A total of 154 studies met the inclusion criteria that used frequentist (85%) and Bayesian (15%) modelling approaches to identify spatial clusters and the associated risk factors. Bayesian models in the studies incorporated various spatial, temporal and spatiotemporal effects into the modelling schemes. This review highlighted the need for more local-level advanced Bayesian spatiotemporal modelling through the multi-level framework for COVID-19 prevention and control strategies.

Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data

Bayesian empirical likelihood (BEL) models are becoming increasingly popular as an attractive alternative to fully parametric models. However, they have only recently been applied to spatial data analysis for small area estimation. This study considers the development of spatial BEL models using two popular conditional autoregressive (CAR) priors, namely BYM and Leroux priors. The performance of the proposed models is compared with their parametric counterparts and with existing spatial BEL models using independent Gaussian priors and generalised Moran basis priors. The models are applied to two benchmark spatial datasets, simulation study and COVID-19 data. The results indicate promising opportunities for these models to capture new insights into spatial data. Specifically, the spatial BEL models outperform the parametric spatial models when the underlying distributional assumptions of data appear to be violated.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Genetic architecture of divergence: the selfing syndrome in Ipomoea lacunosa

PREMISE

Highly selfing plant species frequently display a distinctive suite of traits termed the selfing syndrome. Here we tested the hypothesis that these traits are grouped into correlated evolutionary modules and determined the degree of independence between such modules.

METHODS

We evaluated phenotypic correlations and QTL overlaps in F2 offspring of a cross between the morning glories Ipomoea lacunosa and I. cordatotriloba and investigated how traits clustered into modules at both the phenotypic and genetic level. We then compared our findings to other QTL studies of the selfing syndrome.

RESULTS

In the I. lacunosa selfing syndrome, traits grouped into modules that displayed correlated evolution within but not between modules. QTL overlap predicted phenotypic correlations, and QTLs affecting the same trait module were significantly physically clustered in the genome. The genetic architecture of the selfing syndrome varied across systems, but the pattern of stronger within- than between-module correlation was widespread.

CONCLUSIONS

The genetic architecture we observe in the selfing syndrome is consistent with a growing understanding of floral morphological integration achieved via pleiotropy in clustered traits. This view of floral evolution is consistent with resource limitation or predation driving the evolution of the selfing syndrome, but invites further research into both the selective causes of the selfing syndrome and how genetic architecture itself evolves in response to changes in mating system.

A comparison of multiple neighborhood matrix specifications for spatio-temporal model fitting: a case study on COVID-19 data

Establishing proper neighbor relations between a set of spatial units under analysis is essential when carrying out a spatial or spatio-temporal analysis. However, it is usual that researchers choose some of the most typical (and simple) neighborhood structures, such as the first-order contiguity matrix, without exploring other options. In this paper, we compare the performance of different neighborhood matrices in the context of modeling the weekly relative risk of COVID-19 over small areas located in or near Valencia, Spain. Specifically, we construct contiguity-based, distance-based, covariate-based (considering mobility flows and sociodemographic characteristics), and hybrid neighborhood matrices. We evaluate the goodness of fit, the overall predictive quality, the ability to detect high-risk spatio-temporal units, the capability to capture the spatio-temporal autocorrelation in the data, and the goodness of smoothing for a set of spatio-temporal models based on each of the neighborhood matrices. The results show that contiguity-based matrices, some of the distance-based matrices, and those based on sociodemographic characteristics perform better than the matrices based on k-nearest neighbors and those involving mobility flows. In addition, we test the linear combination of some of the constructed neighborhood matrices and the reweighting of these matrices after eliminating weak neighbor relations, without any model improvement.

Beyond standardized mortality ratios; some uses of smoothed age-specific mortality rates on small areas studies

Background

Most epidemiological risk indicators strongly depend on the age composition of populations, which makes the direct comparison of raw (unstandardized) indicators misleading because of the different age structures of the spatial units of study. Age-standardized rates (ASR) are a common solution for overcoming this confusing effect. The main drawback of ASRs is that they depend on age-specific rates which, when working with small areas, are often based on very few, or no, observed cases for most age groups. A similar effect occurs with life expectancy at birth and many more epidemiological indicators, which makes standardized mortality ratios (SMR) the omnipresent risk indicator for small areas epidemiologic studies.

Methods

To deal with this issue, a multivariate smoothing model, the M-model, is proposed in order to fit the age-specific probabilities of death (PoDs) for each spatial unit, which assumes dependence between closer age groups and spatial units. This age–space dependence structure enables information to be transferred between neighboring consecutive age groups and neighboring areas, at the same time, providing more reliable age-specific PoDs estimates.

Results

Three case studies are presented to illustrate the wide range of applications that smoothed age specific PoDs have in practice . The first case study shows the application of the model to a geographical study of lung cancer mortality in women. This study illustrates the convenience of considering age–space interactions in geographical studies and to explore the different spatial risk patterns shown by the different age groups. Second, the model is also applied to the study of ischaemic heart disease mortality in women in two cities at the census tract level. Smoothed age-standardized rates are derived and compared for the census tracts of both cities, illustrating some advantages of this mortality indicator over traditional SMRs. In the latest case study, the model is applied to estimate smoothed life expectancy (LE), which is the most widely used synthetic indicator for characterizing overall mortality differences when (not so small) spatial units are considered.

Conclusion

Our age–space model is an appropriate and flexible proposal that provides more reliable estimates of the probabilities of death, which allow the calculation of enhanced epidemiological indicators (smoothed ASR, smoothed LE), thus providing alternatives to traditional SMR-based studies of small areas.