The use of sampling weights in Bayesian hierarchical models for small area estimation

Bayesian modeling of spatial ordinal data from health surveys

Health surveys allow exploring health indicators that are of great value from a public health point of view and that cannot normally be studied from regular health registries. These indicators are usually coded as ordinal variables and may depend on covariates associated with individuals. In this article, we propose a Bayesian individual-level model for small-area estimation of survey-based health indicators. A categorical likelihood is used at the first level of the model hierarchy to describe the ordinal data, and spatial dependence among small areas is taken into account by using a conditional autoregressive distribution. Post-stratification of the results of the proposed individual-level model allows extrapolating the results to any administrative areal division, even for small areas. We apply this methodology to describe the geographical distribution of a self-perceived health indicator from the Health Survey of the Region of Valencia (Spain) for the year 2016.

Inferring Population HIV Viral Load From a Single HIV Clinic's Electronic Health Record: Simulation Study With a Real-World Example

BACKGROUND

Population viral load (VL), the most comprehensive measure of the HIV transmission potential, cannot be directly measured due to lack of complete sampling of all people with HIV.

OBJECTIVE

A given HIV clinic's electronic health record (EHR), a biased sample of this population, may be used to attempt to impute this measure.

METHODS

We simulated a population of 10,000 individuals with VL calibrated to surveillance data with a geometric mean of 4449 copies/mL. We sampled 3 hypothetical EHRs from (A) the source population, (B) those diagnosed, and (C) those retained in care. Our analysis imputed population VL from each EHR using sampling weights followed by Bayesian adjustment. These methods were then tested using EHR data from an HIV clinic in Delaware.

RESULTS

Following weighting, the estimates moved in the direction of the population value with correspondingly wider 95% intervals as follows: clinic A: 4364 (95% interval 1963-11,132) copies/mL; clinic B: 4420 (95% interval 1913-10,199) copies/mL; and clinic C: 242 (95% interval 113-563) copies/mL. Bayesian-adjusted weighting further improved the estimate.

CONCLUSIONS

These findings suggest that methodological adjustments are ineffective for estimating population VL from a single clinic's EHR without the resource-intensive elucidation of an informative prior.

Assessing and attenuating the impact of selection bias on spatial cluster detection studies

Spatial cluster analyses are commonly used in epidemiologic studies of case-control data to detect whether certain areas in a study region have an excess of disease risk. Case-control studies are susceptible to potential biases including selection bias, which can result from non-participation of eligible subjects in the study. However, there has been no systematic evaluation of the effects of non-participation on the findings of spatial cluster analyses. In this paper, we perform a simulation study assessing the effect of non-participation on spatial cluster analysis using the local spatial scan statistic under a variety of scenarios that vary the location and rates of study non-participation and the presence and intensity of a zone of elevated risk for disease for simulated case-control studies. We find that geographic areas of lower participation among controls than cases can greatly inflate false-positive rates for identification of artificial spatial clusters. Additionally, we find that even modest non-participation outside of a true zone of elevated risk can decrease spatial power to identify the true zone. We propose a spatial algorithm to correct for potentially spatially structured non-participation that compares the spatial distributions of the observed sample and underlying population. We demonstrate its ability to markedly decrease false positive rates in the absence of elevated risk and resist decreasing spatial sensitivity to detect true zones of elevated risk. We apply our method to a case-control study of non-Hodgkin lymphoma. Our findings suggest that greater attention should be paid to the potential effects of non-participation in spatial cluster studies.

A situational assessment of treatments received for childhood diarrhea in the Federal Republic of Nigeria

We assess progress towards improved case management of childhood diarrhea in Nigeria over a period of targeted health systems reform from 2013 to 2018. Individual and community data from three Demographic and Health Survey rounds are leveraged in a geospatial model designed for stratified estimation by venue of treatment seeking and State. Our analysis reveals a highly regionalised health system undergoing rapid change. Nationally, there have been substantial increases in the proportion of children under 5 years old with diarrhea receiving the recommended oral rehydration therapy after seeking treatment at either a health clinic (0.57 [0.44-0.69; 95% CI] in 2008; 0.70 [0.54-0.83] in 2018) or chemist/pharmacy (0.28 [0.17-0.42] in 2008; 0.48 [0.31-0.64] in 2018). Yet State-level variations in venue attendance and performance by venue have conspired to hold the overall proportion receiving this potentially life-saving therapy (0.45 [0.35-0.55] in 2018) to well-below ideal coverage levels. High performing states that have demonstrated significant improvements include Kano, Jigawa and Borno, while under-performing states that have suffered declines in coverage include Kaduna and Taraba. The use of antibiotics is not recommended for mild cases of childhood diarrhea yet remains concerningly high nationally (0.27 [0.19-0.36] in 2018) with negligible variation between venues. Antibiotic use rates are particularly high in Enugu, Kaduna, Taraba, Kano, Niger and Kebbi, yet welcome reductions were identified in Jigawa, Adamawa and Osun. These results support the conclusions of previous studies and build the strength of evidence that urgent action is needed throughout the multi-tiered health system to improve the quality and equity of care for common childhood illnesses in Nigeria.

Substantial but spatially heterogeneous progress in male circumcision for HIV prevention in South Africa

BACKGROUND

Voluntary medical male circumcision (VMMC) reduces the risk of male HIV acquisition by 60%. Programmes to provide VMMCs for HIV prevention have been introduced in sub-Saharan African countries with high HIV burden. Traditional circumcision is also a long-standing male coming-of-age ritual, but practices vary considerably across populations. Accurate estimates of circumcision coverage by age, type, and time at subnational levels are required for planning and delivering VMMCs to meet targets and evaluating their impacts on HIV incidence.

METHODS

We developed a Bayesian competing risks time-to-event model to produce region-age-time-type specific probabilities and coverage of male circumcision with probabilistic uncertainty. The model jointly synthesises data from household surveys and health system data on the number of VMMCs conducted. We demonstrated the model using data from five household surveys and VMMC programme data to produce estimates of circumcision coverage for 52 districts in South Africa between 2008 and 2019.

RESULTS

Nationally, in 2008, 24.1% (95% CI: 23.4-24.8%) of men aged 15-49 were traditionally circumcised and 19.4% (18.9-20.0%) were medically circumcised. Between 2010 and 2019, 4.25 million VMMCs were conducted. Circumcision coverage among men aged 15-49 increased to 64.0% (63.2-64.9%) and medical circumcision coverage to 42% (41.3-43.0%). Circumcision coverage varied widely across districts, ranging from 13.4 to 86.3%. The average age of traditional circumcision ranged between 13 and 19 years, depending on local cultural practices.

CONCLUSION

South Africa has made substantial, but heterogeneous, progress towards increasing medical circumcision coverage. Detailed subnational information on coverage and practices can guide programmes to identify unmet need to achieve national and international targets.

Impact of ignoring sampling design in the prediction of binary health outcomes through logistic regression: evidence from Malawi demographic and health survey under-five mortality data; 2000-2016

The birth and death rates of a population are among the crucial vital statistics for socio-economic policy planning in any country. Since the under-five mortality rate is one of the indicators for monitoring the health of a population, it requires regular and accurate estimation. The national demographic and health survey data, that are readily available to the puplic, have become a means for answering most health-related questions among African populations, using relevant statistical methods. However, many of such applications tend to ignore survey design effect in the estimations, despite the availability of statistical tools that support the analyses. Little is known about the amount of inaccurate information that is generated when predicting under-five mortality rates. This study estimates and compares the bias encountered when applying unweighted and weighted logistic regression methods to predict under-five mortality rate in Malawi using nationwide survey data. The Malawi demographic and health survey data of 2004, 2010, and 2015-16 were used to determine the bias. The analyses were carried out in R software version 3.6.3 and Stata version 12.0. A logistic regression model that included various bio- and socio-demographic factors concerning the child, mother and households was used to estimate the under-five mortality rate. The results showed that accuracy of predicting the national under-five mortality rate hinges on cluster-weighting of the overall predicted probability of child-deaths, regardless of whether the model was weighted or not. Weighting the model caused small positive and negative changes in various fixed-effect estimates, which diffused the result of weighting in the fitted probabilities of deaths. In turn, there was no difference between the overall predicted mortality rate obtained using the weighted model and that obtained in the unweighted model. We recommend considering survey cluster-weights during the computation of overall predicted probability of events for a binary health outcome. This can be done without worrying about the weights during model fitting, whose aim is prediction of the population parameter.

Subnational HIV incidence trends in Malawi: large, heterogeneous declines across space

The rate of new HIV infections globally has decreased substantially from its peak in the late 1990s, but the epidemic persists and remains highest in many countries in eastern and southern Africa. Previous research hypothesised that, as the epidemic recedes, it will become increasingly concentrated among sub-populations and geographic areas where transmission is the highest and that are least effectively reached by treatment and prevention services. However, empirical data on subnational HIV incidence trends is sparse, and the local transmission rates in the context of effective treatment scale-up are unknown. In this work, we developed a novel Bayesian spatio-temporal epidemic model to estimate adult HIV prevalence, incidence and treatment coverage at the district level in Malawi from 2010 through the end of 2021. We found that HIV incidence decreased in every district of Malawi between 2010 and 2021 but the rate of decline varied by area. National-level treatment coverage more than tripled between 2010 and 2021 and more than doubled in every district. Large increases in treatment coverage were associated with declines in HIV transmission, with 12 districts having incidence-prevalence ratios of 0.03 or less (a previously suggested threshold for epidemic control). Across districts, incidence varied more than HIV prevalence and ART coverage, suggesting that the epidemic is becoming increasingly spatially concentrated. Our results highlight the success of the Malawi HIV treatment programme over the past decade, with large improvements in treatment coverage leading to commensurate declines in incidence. More broadly, we demonstrate the utility of spatially resolved HIV modelling in generalized epidemic settings. By estimating temporal changes in key epidemic indicators at a relatively fine spatial resolution, we were able to directly assess, for the first time, whether the ART scaleup in Malawi resulted in spatial gaps or hotspots. Regular use of this type of analysis will allow HIV program managers to monitor the equity of their treatment and prevention programmes and their subnational progress towards epidemic control.

A Novel Bayesian Spatial-Temporal Approach to Quantify SARS-CoV-2 Testing Disparities for Small Area Estimation

Objectives. To propose a novel Bayesian spatial-temporal approach to identify and quantify severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) testing disparities for small area estimation. Methods. In step 1, we used a Bayesian inseparable space-time model framework to estimate the testing positivity rate (TPR) at geographically granular areas of the census block groups (CBGs). In step 2, we adopted a rank-based approach to compare the estimated TPR and the testing rate to identify areas with testing deficiency and quantify the number of needed tests. We used weekly SARS-CoV-2 infection and testing surveillance data from Cameron County, Texas, between March 2020 and February 2022 to demonstrate the usefulness of our proposed approach. Results. We identified the CBGs that had experienced substantial testing deficiency, quantified the number of tests that should have been conducted in these areas, and evaluated the short- and long-term testing disparities. Conclusions. Our proposed analytical framework offers policymakers and public health practitioners a tool for understanding SARS-CoV-2 testing disparities in geographically small communities. It could also aid COVID-19 response planning and inform intervention programs to improve goal setting and strategy implementation in SARS-CoV-2 testing uptake. (Am J Public Health. 2023;113(1):40-48. https://doi.org/10.2105/AJPH.2022.307127).

Neighbourhood income inequalities in mental health in Barcelona 2001-2016: a Bayesian smoothed estimate

OBJECTIVE

Obtaining reliable health estimates at the small area level (such as neighbourhoods) using survey data usually poses the problem of small sample sizes. To overcome this limitation, we explored smoothing techniques in order to estimate poor mental health prevalence at the neighbourhood level and analyse its profile by income in Barcelona city (Spain).

METHOD

A Bayesian smoothing model with a logit-normal transformation was applied to four repeated cross-sectional waves of the Barcelona health survey for 2001, 2006, 2011 and 2016. Mental health status was identified from the 12-item General Health Questionnaire. Income inequalities were analysed with neighbourhood income in quantiles for each year and trends in the pooled analysis.

RESULTS

The prevalence of poor mental health ranged from 14.6% in 2001 to 18.9% in 2016. The yearly difference between neighbourhoods was 12.4% in 2001, 16.7% in 2006, 14.2% in 2011, and 20.0% in 2016. The odds ratio and 95% credible interval (95%CI) of experiencing poor mental health was 1.40 times higher (95%CI: 1.02-1.91) in less advantaged neighbourhoods than in more advantaged neighbourhoods in 2001, 1.61 times higher (95%CI: 1.01-2.59) in 2006 and 2.31 times higher (95%CI: 1.57-3.40) in 2016.

CONCLUSIONS

This study shows that the Bayesian smoothed techniques allows detection of inequalities in health in neighbourhoods and monitoring of interventions against them. In Barcelona, mental health problems are more prevalent in low-income neighbourhoods and raised in 2016.

Accounting for Sampling Weights in the Analysis of Spatial Distributions of Disease Using Health Survey Data, with an Application to Mapping Child Health in Malawi and Mozambique

Most analyses of spatial patterns of disease risk using health survey data fail to adequately account for the complex survey designs. Particularly, the survey sampling weights are often ignored in the analyses. Thus, the estimated spatial distribution of disease risk could be biased and may lead to erroneous policy decisions. This paper aimed to present recent statistical advances in disease-mapping methods that incorporate survey sampling in the estimation of the spatial distribution of disease risk. The methods were then applied to the estimation of the geographical distribution of child malnutrition in Malawi, and child fever and diarrhoea in Mozambique. The estimation of the spatial distributions of the child disease risk was done by Bayesian methods. Accounting for sampling weights resulted in smaller standard errors for the estimated spatial disease risk, which increased the confidence in the conclusions from the findings. The estimated geographical distributions of the child disease risk were similar between the methods. However, the fits of the models to the data, as measured by the deviance information criteria (DIC), were different.

Geographic Variation in HIV Testing Among Transgender and Nonbinary Adults in the United States

BACKGROUND

Transgender and nonbinary (TNB) populations are disproportionately affected by HIV and few local health departments or HIV surveillance systems collect/report data on TNB identities. Our objective was to estimate the prevalence of HIV testing among TNB adults by US county and state, with a focus on the Ending the HIV Epidemic (EHE) geographies.

METHODS

We applied a Bayesian hierarchical spatial small area estimation model to data from the 2015 US Transgender Survey, a large national cross-sectional Internet-based survey. We estimated the county- and state-level proportion of TNB adults who ever tested or tested for HIV in the last year by gender identity, race/ethnicity, and age.

RESULTS

Our analysis included 26,100 TNB participants with valid zip codes who resided in 1688 counties (54% of all 3141 counties that cover 92% of the US population). The median county-level proportion of TNB adults who ever tested for HIV was 44% (range 10%-80%) and who tested in the last year was 17% (range 4%-44%). Within most counties, testing was highest among transgender women, black respondents, and people aged ≥25 years. HIV testing was lowest among nonbinary people and young adults aged <25 years. The proportion of TNB adults who tested within the last year was very low in most EHE counties and in all 7 rural states.

CONCLUSIONS

HIV testing among TNB adults is likely below national recommendations in the majority of EHE geographies. Geographic variation in HIV testing patterns among TNB adults indicates that testing strategies need to be tailored to local settings.

Finding gaps in routine TB surveillance activities in Bangladesh

BACKGROUND :

TB was the leading cause of death from a single infectious pathogen globally between 2014 and 2019. Fine-scale estimates of TB prevalence and case notifications can be combined to guide priority-setting for strengthening routine surveillance activities in high-burden countries. We produce policy-relevant estimates of the TB epidemic at the second administrative unit in Bangladesh.

METHODS :

We used a Bayesian spatial framework and the cross-sectional National TB Prevalence Survey from 2015–2016 in Bangladesh to estimate prevalence by district. We used case notifications to calculate prevalence-to-notification ratio, a key metric of under-diagnosis and under-reporting.

RESULTS :

TB prevalence rates were highest in the north-eastern districts and ranged from 160 cases per 100,000 (95% uncertainty interval [UI] 80–310) in Jashore to 840 (UI 690–1020) in Sunamganj. Despite moderate prevalence rates, the Rajshahi and Dhaka Divisions presented the highest prevalence-to-notification ratios due to low case notifications. Resolving subnational disparities in case detection could lead to 26,500 additional TB cases (UI 8,500–79,400) notified every year.

CONCLUSION :

This study is the first to produce and map subnational estimates of TB prevalence and prevalence-to-notification ratios, which are essential to target prevention and treatment efforts in high-burden settings. Reaching TB cases currently missing from care will be key to ending the TB epidemic.

Spatial epidemiology: An empirical framework for syndemics research

Syndemics framework describes two or more co-occurring epidemics that synergistically interact with each other and the complex structural social forces that sustain them leading to excess disease burden. The term syndemic was first used to describe the interaction between substance abuse, violence, and AIDS by Merrill Singer. A broader range of syndemic studies has since emerged describing the framework's applicability to other public health scenarios. With syndemic theory garnering significant attention, the focus is shifting towards developing robust empirical analytical approaches. Unfortunately, the complex nature of the disease-disease interactions nested within several social contexts complicates empirical analyses. In answering the call to analyze syndemics at the population level, we propose the use of spatial epidemiology as an empirical framework for syndemics research. Spatial epidemiology, which typically relies on geographic information systems (GIS) and statistics, is a discipline that studies spatial variations to understand the geographic landscape and the risk environment within which disease epidemics occur. GIS maps provide visualization aids to investigate the spatial distribution of disease outcomes, the associated social factors, and environmental exposures. Analytical inference, such as estimation of disease risks and identification of spatial disease clusters, can provide a detailed statistical view of spatial distributions of diseases. Spatial and spatiotemporal models can help us to understand, measure, and analyze disease syndemics as well as the social, biological, and structural factors associated with them in space and time. In this paper, we present a background on syndemics and spatial epidemiological theory and practice. We then present a case study focused on the HIV and HCV syndemic in West Virginia to provide an example of the use of GIS and spatial analytical methods. The concepts described in this paper can be considered to enhance understanding and analysis of other syndemics for which space-time data are available.

A Bayesian approach to combining multiple information sources: Estimating and forecasting childhood obesity in Thailand

We estimate and forecast childhood obesity by age, sex, region, and urban-rural residence in Thailand, using a Bayesian approach to combining multiple source of information. Our main sources of information are survey data and administrative data, but we also make use of informative prior distributions based on international estimates of obesity trends and on expectations about smoothness. Although the final model is complex, the difficulty of building and understanding the model is reduced by the fact that it is composed of many smaller submodels. For instance, the submodel describing trends in prevalences is specified separately from the submodels describing errors in the data sources. None of our Thai data sources has more than 7 time points. However, by combining multiple data sources, we are able to fit relatively complicated time series models. Our results suggest that obesity prevalence has recently starting rising quickly among Thai teenagers throughout the country, but has been stable among children under 5 years old.

A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa

Despite making significant progress in tackling its HIV epidemic, South Africa, with 7.7 million people living with HIV, still has the biggest HIV epidemic in the world. The Government, in collaboration with developmental partners and agencies, has been strengthening its responses to the HIV epidemic to better target the delivery of HIV care, treatment strategies and prevention services. Population-based household HIV surveys have, over time, contributed to the country’s efforts in monitoring and understanding the magnitude and heterogeneity of the HIV epidemic. Local-level monitoring of progress made against HIV and AIDS is increasingly needed for decision making. Previous studies have provided evidence of substantial subnational variation in the HIV epidemic. Using HIV prevalence data from the 2016 South African Demographic and Health Survey, we compare three spatial smoothing models, namely, the intrinsically conditionally autoregressive normal, Laplace and skew-t (ICAR-normal, ICAR-Laplace and ICAR-skew-t) in the estimation of the HIV prevalence across 52 districts in South Africa. The parameters of the resulting models are estimated using Bayesian approaches. The skewness parameter for the ICAR-skew-t model was not statistically significant, suggesting the absence of skewness in the HIV prevalence data. Based on the deviance information criterion (DIC) model selection, the ICAR-normal and ICAR-Laplace had DIC values of 291.3 and 315, respectively, which were lower than that of the ICAR-skewed t (348.1). However, based on the model adequacy criterion using the conditional predictive ordinates (CPO), the ICAR-skew-t distribution had the lowest CPO value. Thus, the ICAR-skew-t was the best spatial smoothing model for the estimation of HIV prevalence in our study.

What is the place for space in epidemiology?

At the heart of spatial epidemiology is the need to describe and understand variation in population health. In this review and introduction to the themed issue on "Spatial Analysis and GIS in Epidemiology," we present theoretical foundations and methodological developments in spatial epidemiology, discuss spatial analytical techniques and their public health applications, and identify novel data sources and applications with the potential to make epidemiology more consequential. Challenges with using georeferenced data are also explored, including dealing with small sample sizes, missingness, generalizability, and geographic scale. Given the increasing availability of spatial data and visualization tools, we have an opportunity to overcome traditionally siloed fields and practice settings to advance knowledge and more appropriately respond to emerging public health crises.

Model building and assessment of the impact of covariates for disease prevalence mapping in low-resource settings: to explain and to predict

This paper provides statistical guidance on the development and application of model-based geostatistical methods for disease prevalence mapping. We illustrate the different stages of the analysis, from exploratory analysis to spatial prediction of prevalence, through a case study on malaria mapping in Tanzania. Throughout the paper, we distinguish between predictive modelling, whose main focus is on maximizing the predictive accuracy of the model, and explanatory modelling, where greater emphasis is placed on understanding the relationships between the health outcome and risk factors. We demonstrate that these two paradigms can result in different modelling choices. We also propose a simple approach for detecting over-fitting based on inspection of the correlation matrix of the estimators of the regression coefficients. To enhance the interpretability of geostatistical models, we introduce the concept of domain effects in order to assist variable selection and model validation. The statistical ideas and principles illustrated here in the specific context of disease prevalence mapping are more widely applicable to any regression model for the analysis of epidemiological outcomes but are particularly relevant to geostatistical models, for which the separation between fixed and random effects can be ambiguous.

District-level estimation of vaccination coverage: Discrete vs continuous spatial models

Health and development indicators (HDIs) such as vaccination coverage are regularly measured in many low- and middle-income countries using household surveys, often due to the unreliability or incompleteness of routine data collection systems. Recently, the development of model-based approaches for producing subnational estimates of HDIs using survey data, particularly cluster-level data, has been an active area of research. This is mostly driven by the increasing demand for estimates at certain administrative levels, for example, districts, at which many development goals are set and evaluated. In this study, we explore spatial modeling approaches for producing district-level estimates of vaccination coverage. Specifically, we compare discrete spatial smoothing models which directly model district-level data with continuous Gaussian process (GP) models that utilize geolocated cluster-level data. We adopt a fully Bayesian framework, implemented using the INLA and SPDE approaches. We compare the predictive performance of the models by analyzing vaccination coverage using data from two Demographic and Health Surveys (DHS), namely the 2014 Kenya DHS and the 2015-16 Malawi DHS. We find that the continuous GP models performed well, offering a credible alternative to traditional discrete spatial smoothing models. Our analysis also revealed that accounting for between-cluster variation in the continuous GP models did not have any real effect on the district-level estimates. Our results provide guidance to practitioners on the reliability of these model-based approaches for producing estimates of vaccination coverage and other HDIs.

Individual and Community Social Determinants of Health Associated With Diabetes Management in a Mexican American Population

Background: Diabetes is a major health burden in Mexican American populations, especially among those in the Lower Rio Grande Valley (LRGV) in the border region of Texas. Understanding the roles that social determinants of health (SDOH) play in diabetes management programs, both at the individual and community level, may inform future intervention strategies.

Methods: This study performed a secondary data analysis on 1,568 individuals who participated in Salud y Vida (SyV), a local diabetes and chronic disease management program, between October 2013 and September 2018 recruited from a local clinic. The primary outcome was the reduction of hemoglobin A1C (HbA1C) at the last follow-up visit compared to the baseline. In addition to age, gender, insurance status, education level and marital status, we also investigated 15 community (census tract) SDOH using the American Community Survey. Because of the high correlation in the community SDOH, we developed the community-level indices representing different domains. Using Bayesian multilevel spatial models that account for the geographic dependency, we were able to simultaneously investigate the individual- and community-level SDOH that may impact HbA1C reduction.

Results: After accounting for the diabetes self-management education classes taken by the participants and their length of stay in the program, we found that older age at baseline, being married (compared to being widowed or divorced) and English speaking (compared to Spanish) were significantly associated with greater HbA1C reduction. Moreover, we found that the community level SDOH were also highly associated with HbA1C reduction. With every percentile rank decrease in the socioeconomic advantage index, we estimated an additional 0.018% reduction in HbA1C [95% CI (−0.028, −0.007)]. Besides the socioeconomic advantage index, urban core opportunity and immigrant's cohesion and accessibility indices were also statistically associated with HbA1C reduction.

Conclusion: To our knowledge, our study is the first to utilize Bayesian multilevel spatial models and simultaneously investigate both individual- and community-level SDOH in the context of diabetes management. Our findings suggest that community SDOH play an important role in diabetes control and management, and the need to consider community and neighborhood context in future interventions programs to maximize their overall effectiveness.

Bayesian estimation of SARS-CoV-2 prevalence in Indiana by random testing

From 25 to 29 April 2020, the state of Indiana undertook testing of 3,658 randomly chosen state residents for the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, the agent causing COVID-19 disease. This was the first statewide randomized study of COVID-19 testing in the United States. Both PCR and serological tests were administered to all study participants. This paper describes statistical methods used to address nonresponse among various demographic groups and to adjust for testing errors to reduce bias in the estimates of the overall disease prevalence in Indiana. These adjustments were implemented through Bayesian methods, which incorporated all available information on disease prevalence and test performance, along with external data obtained from census of the Indiana statewide population. Both adjustments appeared to have significant impact on the unadjusted estimates, mainly due to upweighting data in study participants of non-White races and Hispanic ethnicity and anticipated false-positive and false-negative test results among both the PCR and antibody tests utilized in the study.

Models for Small Area Estimation for Census Tracts

This study examines issues of Small Area Estimation (SAE) that are raised by reliance on the American Community Survey (ACS), which reports tract-level data based on much smaller samples than the decennial census long-form that it replaced. We demonstrate the problem using a 100% transcription of microdata from the 1940 census. By drawing many samples from two major cities, we confirm a known pattern: random samples yield unbiased point estimates of means or proportions, but estimates based on smaller samples have larger average errors in measurement and greater risk of large error. Sampling variability also inflates estimates of measures of variation across areas (reflecting segregation or spatial inequality). This variation is at the heart of much contemporary spatial analysis (Sampson 2012). We then evaluate possible solutions. For point estimates, we examine three Bayesian models, all of which reduce sampling variation, and we encourage use of such models to correct ACS small area estimates. However, the corrected estimates cannot be used to calculate estimates of variation, because smoothing toward local or grand means artificially reduces variation. We note that there are potential Bayesian approaches to this problem, and we demonstrate an efficacious alternative that uses the original sample data.

A Scoping Review of Spatial Analysis Approaches Using Health Survey Data in Sub-Saharan Africa

Spatial analysis has become an increasingly used analytic approach to describe and analyze spatial characteristics of disease burden, but the depth and coverage of its usage for health surveys data in Sub-Saharan Africa are not well known. The objective of this scoping review was to conduct an evaluation of studies using spatial statistics approaches for national health survey data in the SSA region. An organized literature search for studies related to spatial statistics and national health surveys was conducted through PMC, PubMed/Medline, Scopus, NLM Catalog, and Science Direct electronic databases. Of the 4,193 unique articles identified, 153 were included in the final review. Spatial smoothing and prediction methods were predominant (n = 108), followed by spatial description aggregation (n = 25), and spatial autocorrelation and clustering (n = 19). Bayesian statistics methods and lattice data modelling were predominant (n = 108). Most studies focused on malaria and fever (n = 47) followed by health services coverage (n = 38). Only fifteen studies employed nonstandard spatial analyses (e.g., spatial model assessment, joint spatial modelling, accounting for survey design). We recommend that for future spatial analysis using health survey data in the SSA region, there must be an improve recognition and awareness of the potential dangers of a naïve application of spatial statistical methods. We also recommend a wide range of applications using big health data and the future of data science for health systems to monitor and evaluate impacts that are not well understood at local levels.

Multi-Scale Multivariate Models for Small Area Health Survey Data: A Chilean Example

Background: We propose a general approach to the analysis of multivariate health outcome data where geo-coding at different spatial scales is available. We propose multiscale joint models which address the links between individual outcomes and also allow for correlation between areas. The models are highly novel in that they exploit survey data to provide multiscale estimates of the prevalences in small areas for a range of disease outcomes. Results The models incorporate both disease specific, and common disease spatially structured components. The multiple scales envisaged is where individual survey data is used to model regional prevalences or risks at an aggregate scale. This approach involves the use of survey weights as predictors within our Bayesian multivariate models. Missingness has to be addressed within these models and we use predictive inference which exploits the correlation between diseases to provide estimates of missing prevalances. The Case study we examine is from the National Health Survey of Chile where geocoding to Province level is available. In that survey, diabetes, Hypertension, obesity and elevated low-density cholesterol (LDL) are available but differential missingness requires that aggregation of estimates and also the assumption of smoothed sampling weights at the aggregate level. Conclusions: The methodology proposed is highly novel and flexibly handles multiple disease outcomes at individual and aggregated levels (i.e., multiscale joint models). The missingness mechanism adopted provides realistic estimates for inclusion in the aggregate model at Provincia level. The spatial structure of four diseases within Provincias has marked spatial differentiation, with diabetes and hypertension strongly clustered in central Provincias and obesity and LDL more clustered in the southern areas.

Spatial Modelling to Inform Public Health Based on Health Surveys: Impact of Unsampled Areas at Lower Geographical Scale

Small area estimation is an important tool to provide area-specific estimates of population characteristics for governmental organizations in the context of education, public health and care. However, many demographic and health surveys are unrepresentative at a small geographical level, as often areas at a lower level are not included in the sample due to financial or logistical reasons. In this paper, we investigated (1) the effect of these unsampled areas on a variety of design-based and hierarchical model-based estimates and (2) the benefits of using auxiliary information in the estimation process by means of an extensive simulation study. The results showed the benefits of hierarchical spatial smoothing models towards obtaining more reliable estimates for areas at the lowest geographical level in case a spatial trend is present in the data. Furthermore, the importance of auxiliary information was highlighted, especially for geographical areas that were not included in the sample. Methods are illustrated on the 2008 Mozambique Poverty and Social Impact Analysis survey, with interest in the district-specific prevalence of school attendance.

Estimating under-five mortality in space and time in a developing world context

Accurate estimates of the under-five mortality rate in a developing world context are a key barometer of the health of a nation. This paper describes a new model to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is wishing to estimate under-five mortality rate across regions and years and to investigate the association between the under-five mortality rate and spatially varying covariate surfaces. We illustrate the methodology by producing yearly estimates for subnational areas in Kenya over the period 1980-2014 using data from the Demographic and Health Surveys, which use stratified cluster sampling. We use a binomial likelihood with fixed effects for the urban/rural strata and random effects for the clustering to account for the complex survey design. Smoothing is carried out using Bayesian hierarchical models with continuous spatial and temporally discrete components. A key component of the model is an offset to adjust for bias due to the effects of HIV epidemics. Substantively, there has been a sharp decline in Kenya in the under-five mortality rate in the period 1980-2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. In exploratory work, we examine whether a variety of spatial covariate surfaces can explain the variability in under-five mortality rate. Temperature, precipitation, a measure of malaria infection prevalence, and a measure of nearness to cities were candidates for inclusion in the covariate model, but the interplay between space, time, and covariates is complex.

Incidence estimation from sentinel surveillance data; a simulation study and application to data from the Belgian laboratory sentinel surveillance

Background

Inverse probability weighting (IPW) methods can be used to estimate the total number of cases from the sample collected through sentinel surveillance. Central to these methods are the inverse weights which can be derived in several ways and, in this case, represent the probability that laboratory (lab) sentinel surveillance detects a lab-confirmed case.

Methods

We compare different weights in a simulation study. Weights are obtained from the proportion of participating labs over all labs. We adjust these weights for attractiveness and density of labs over population. The market share of sentinel labs, as estimated by the econometric Huff-model, is also considered. Additionally, we investigate the effect of not recognizing sentinel labs as sentinel labs when they report no cases. We estimate the bias associated with the different weights as the difference between the simulated number of cases and the estimate of this total from the sentinel sample.

As motivating data examples, we apply an extended Huff-model to four pathogens under laboratory sentinel surveillance in Belgium between 2010 and 2015 and discuss the model fit. We estimate the total number of lab-confirmed cases associated with Rotavirus, influenza virus, Y. enterocolitica and Campylobacter spp.. The extended Huff-model takes the lab-concept, the number of reimbursements and the number of departments, lab-density, regional borders, distance and competition between labs in account.

Results

Estimates obtained with the Huff-model were most accurate in the more complex simulation scenarios as compared to other weights. In the data examples, several significant coefficients are identified, but the fit of the Huff-model to the Belgian sentinel surveillance data leaves much variability in market shares unexplained.

Conclusion

The Huff-model allows for estimation of the spatial and population coverage of sentinel surveillance and through IPW-methods also for the estimation of the total number of cases. The Huff-model‘s gravity function allows us to differentiate inside an area while estimating from the full dataset. Our data examples show that additional data on the participation to surveillance and practices of labs is necessary for a more accurate estimation.

Spatial smoothing models to deal with the complex sampling design and nonresponse in the Florida BRFSS survey

Public health and governmental organizations have acknowledged the importance of obtaining information of various characteristics for small areas, such as counties. Spatial smoothing models have been developed to gain reliable information on the geographical distribution of the outcome of interest. When the geographical analysis is based on survey data, two issues pose challenges: (1) the complex design of the survey and (2) the presence of missing data due to non-response. We investigate the influence of missing data and the adjustment thereof in the context of the 2013 Florida Behavioral Risk Factor Surveillance System (BRFSS) health survey. We focus on the application and comparison of the Hajek ratio estimator and two model-based approaches for estimation of the spatial trend of the prevalence of having no health insurance coverage. The model-based methods are compared using the Deviance Information Criterion which show the benefits of modeling the weights as flexibly as possible. Methods are extended towards subgroup analyses and the estimation of area-specific standardized rates, where household incomes was identified as an important factor to include in the analysis.

Building a Data Platform for Cross-Country Urban Health Studies: the SALURBAL Study

Studies examining urban health and the environment must ensure comparability of measures across cities and countries. We describe a data platform and process that integrates health outcomes together with physical and social environment data to examine multilevel aspects of health across cities in 11 Latin American countries. We used two complementary sources to identify cities with ≥ 100,000 inhabitants as of 2010 in Argentina, Brazil, Chile, Colombia, Costa Rica, El Salvador, Guatemala, Mexico, Nicaragua, Panama, and Peru. We defined cities in three ways: administratively, quantitatively from satellite imagery, and based on country-defined metropolitan areas. In addition to "cities," we identified sub-city units and smaller neighborhoods within them using census hierarchies. Selected physical environment (e.g., urban form, air pollution and transport) and social environment (e.g., income, education, safety) data were compiled for cities, sub-city units, and neighborhoods whenever possible using a range of sources. Harmonized mortality and health survey data were linked to city and sub-city units. Finer georeferencing is underway. We identified 371 cities and 1436 sub-city units in the 11 countries. The median city population was 234,553 inhabitants (IQR 141,942; 500,398). The systematic organization of cities, the initial task of this platform, was accomplished and further ongoing developments include the harmonization of mortality and survey measures using available sources for between country comparisons. A range of physical and social environment indicators can be created using available data. The flexible multilevel data structure accommodates heterogeneity in the data available and allows for varied multilevel research questions related to the associations of physical and social environment variables with variability in health outcomes within and across cities. The creation of such data platforms holds great promise to support researching with greater granularity the field of urban health in Latin America as well as serving as a resource for the evaluation of policies oriented to improve the health and environmental sustainability of cities.

Changes in the spatial distribution of the under-five mortality rate: Small-area analysis of 122 DHS surveys in 262 subregions of 35 countries in Africa

The under-five mortality rate (U5MR) is a critical and widely available population health indicator. Both the MDGs and SDGs define targets for improvement in the U5MR, and the SDGs require spatial disaggregation of indicators. We estimate trends in the U5MR for Admin-1 subnational areas using 122 DHS surveys in 35 countries in Africa and assess progress toward the MDG target reductions for each subnational region and each country as a whole. In each country, direct weighted estimates of the U5MR from each survey are calculated and combined into a single estimate for each Admin-1 region across five-year periods. Our method fully accounts for the sample design of each survey. The region-time-specific estimates are smoothed using a Bayesian, space-time model that produces more precise estimates (when compared to the direct estimates) at a one-year scale that are consistent with each other in both space and time. The resulting estimated distributions of the U5MR are summarized and used to assess subnational progress toward the MDG 4 target of two-thirds reduction in the U5MR during 1990–2015. Our space-time modeling approach is tractable and can be readily applied to a large collection of sample survey data. Subnational, regional spatial heterogeneity in the levels and trends in the U5MR vary considerably across Africa. There is no generalizable pattern between spatial heterogeneity and levels or trends in the U5MR. Subnational, small-area estimates of the U5MR: (i) identify subnational regions where interventions are still necessary and those where improvement is well under way; and (ii) countries where there is very little spatial variation and others where there are important differences between subregions in both levels and trends. More work is necessary to improve both the data sources and methods necessary to adequately measure subnational progress toward the SDG child survival targets.

A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

The contribution of area-level walkability to geographic variation in physical activity: a spatial analysis of 95,837 participants from the 45 and Up Study living in Sydney, Australia

BACKGROUND

Individual-level studies support a positive relation between walkable built environments and participation in moderate-intensity walking. However, the utility of this evidence for population-level planning is less clear as it is derived at much finer spatial scales than those used for regional programming. The aims of this study were to: evaluate if individual-level relations between walkability and walking to improve health manifest at population-level spatial scales; assess the specificity of area-level walkability for walking relative to other moderate and vigorous physical activity (MVPA); describe geographic variation in walking and other MVPA; and quantify the contribution of walkability to this variation.

METHODS

Data on sufficient walking, sufficient MVPA, and high MVPA to improve health were analyzed for 95,837 Sydney respondents to the baseline survey of the 45 and Up Study between January 2006 and April 2010. We used conditional autoregressive models to create smoothed MVPA "disease maps" and assess relations between sufficient MVPA to improve health and area-level walkability adjusted for individual-level demographic, socioeconomic, and health factors, and area-level relative socioeconomic disadvantage.

RESULTS

Within-cohort prevalence of meeting recommendations for sufficient walking, sufficient MVPA, and high MVPA were 31.7 (95% CI 31.4-32.0), 69.4 (95% CI 69.1-69.7), and 56.1 (95% CI 55.8-56.4) percent. Prevalence of sufficient walking was increased by 1.20 (95% CrI 1.12-1.29) and 1.07 (95% CrI 1.01-1.13) for high and medium-high versus low walkability postal areas, and for sufficient MVPA by 1.05 (95% CrI 1.01-1.08) for high versus low walkability postal areas. Walkability was not related to high MVPA. Postal area walkability explained 65.8 and 47.4 percent of residual geographic variation in sufficient walking and sufficient MVPA not attributable to individual-level factors.

CONCLUSIONS

Walkability is associated with area-level prevalence and geographic variation in sufficient walking and sufficient MVPA to improve health in Sydney, Australia. Our study supports the use of walkability indexes at multiple spatial scales for informing population-level action to increase physical activity and the utility of spatial analysis for walkability research and planning.

Spatial small area smoothing models for handling survey data with nonresponse

Spatial smoothing models play an important role in the field of small area estimation. In the context of complex survey designs, the use of design weights is indispensable in the estimation process. Recently, efforts have been made in these spatial smoothing models, in order to obtain reliable estimates of the spatial trend. However, the concept of missing data remains a prevalent problem in the context of spatial trend estimation as estimates are potentially subject to bias. In this paper, we focus on spatial health surveys where the available information consists of a binary response and its associated design weight. Furthermore, we investigate the impact of nonresponse as missing data on a range of spatial models for different missingness mechanisms and different degrees of missingness by means of an extensive simulation study. The computations were performed in R, using INLA and other existing packages. The results show that weight adjustment to correct for missingness has a beneficial effect on the bias in the missing at random setting for all models. Furthermore, we estimate the geographical distribution of perceived health at the district level based on the Belgian Health Interview Survey (2001). Copyright © 2017 John Wiley & Sons, Ltd.

Model-based inference for small area estimation with sampling weights

Obtaining reliable estimates about health outcomes for areas or domains where only few to no samples are available is the goal of small area estimation (SAE). Often, we rely on health surveys to obtain information about health outcomes. Such surveys are often characterised by a complex design, stratification, and unequal sampling weights as common features. Hierarchical Bayesian models are well recognised in SAE as a spatial smoothing method, but often ignore the sampling weights that reflect the complex sampling design. In this paper, we focus on data obtained from a health survey where the sampling weights of the sampled individuals are the only information available about the design. We develop a predictive model-based approach to estimate the prevalence of a binary outcome for both the sampled and non-sampled individuals, using hierarchical Bayesian models that take into account the sampling weights. A simulation study is carried out to compare the performance of our proposed method with other established methods. The results indicate that our proposed method achieves great reductions in mean squared error when compared with standard approaches. It performs equally well or better when compared with more elaborate methods when there is a relationship between the responses and the sampling weights. The proposed method is applied to estimate asthma prevalence across districts.

Spatial and socio-economic effects on malaria morbidity in children under 5 years in Malawi in 2012

BACKGROUND

Malaria is a major health challenge in sub-Saharan Africa with children under 5 being most vulnerable. Identifying regions of greater malarial burden is vital in targeting interventions.

METHODS

This study analysed malaria morbidity using data from the Malawi 2012 Malaria Indicator Survey that were obtained from Demographic and Health Survey (DHS) program website. These data captured malaria related information on children under 5. Poisson regression was done to determine associations between outcome (number of children under 5 with malaria in household) and explanatory variables. A Bayesian smoothing approach was employed to adjust for spatial random effects on child related variables.

RESULTS

There were 1878 households in 140 clusters. The number of children under five was 1900. Spatially structured effects accounted for more than 90% of random effects as these had a mean of 1.32 (95% Credible Interval (CI)=0.37, 2.50) whilst spatially unstructured had a mean of 0.10 (CI=9.0 × 10(-4), 0.38). Spatially adjusted significant variables were; type of place of residence (urban or rural) [posterior odds ratio (POR)=2.06; CI= 1.27, 3.34], not owning land [POR=1.77; CI=1.19, 2.64], not staying in a slum [POR=0.52; CI=0.33, 0.83] and enhanced vegetation index [POR=0.02; CI=0.00, 1.08]. A trend was observed on usage of insecticide treated mosquito nets [POR=0.80; CI=0.63, 1.03].

CONCLUSION

This study showed that malaria is a disease of poverty. Enhanced vegetation index was an important factor in malaria morbidity. The central region was identified as the area with greatest disease burden.

A comparison of spatial smoothing methods for small area estimation with sampling weights

Small area estimation (SAE) is an important endeavor in many fields and is used for resource allocation by both public health and government organizations. Often, complex surveys are carried out within areas, in which case it is common for the data to consist only of the response of interest and an associated sampling weight, reflecting the design. While it is appealing to use spatial smoothing models, and many approaches have been suggested for this endeavor, it is rare for spatial models to incorporate the weighting scheme, leaving the analysis potentially subject to bias. To examine the properties of various approaches to estimation we carry out a simulation study, looking at bias due to both non-response and non-random sampling. We also carry out SAE of smoking prevalence in Washington State, at the zip code level, using data from the 2006 Behavioral Risk Factor Surveillance System. The computation times for the methods we compare are short, and all approaches are implemented in R using currently available packages.