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Introduction HIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small‐area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five‐year age groups. Methods Small‐area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district‐level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016–2018. Results Adult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty‐eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city. Conclusions The Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data.

Cardiovascular diseases (CVDs) remain a leading cause of mortality globally, with environmental risk factors playing a significant role in their prevalence. This review aims to critically evaluate the current methodologies employed in spatiotemporal analyses of CVDs and provides recommendations to enhance the accuracy and practical application of these models. A systematic search of the literature was conducted using Scopus, PubMed, and Embase databases. Studies were selected based on their use of spatiotemporal models to assess the relationship between environmental factors and CVDs. We evaluated the methodological quality of included studies using the Spatial Methodology Appraisal of Research Tool (SMART). Significant challenges were noted, including the need for higher spatial resolution data sets and improved methods for addressing the modifiable areal and temporal unit problems and ecological bias. Additionally, the visualization of spatiotemporal data remains underutilized and underdeveloped, limiting the practical utility of the findings. We also discuss combining parameters to form an indicator that better represents environmental conditions, as well as cases where ground, satellite, or modeled data products are suitable. These recommendations could extend to other acquired chronic diseases and their relationship with environmental risk factors to improve the utility of spatiotemporal models. While spatiotemporal modeling holds considerable promise in understanding and mitigating CVD risks associated with environmental factors, appropriate data selection, addressing methodological pitfalls and reporting spatial and temporal model outcomes are necessary to enhance their reliability and impact. Plain Language Summary Cardiovascular diseases (CVDs), like heart attacks and strokes, are major causes of death worldwide, with environmental factors such as air pollution and temperature linked to their occurrence. The occurrence of CVDs and environmental factors are closely linked to the geographical location, as well as changes over time. This review looks at how researchers are using models that track changes over space and time to study these links. Our review highlights key challenges in these models, such as the need for more precise data on where people live and better methods to account for the way different time periods and regions are grouped. We also found that tools for visualizing this data are often underdeveloped, making it harder for researchers and policymakers to apply the findings in real‐world settings. We provide recommendations on choosing the best data sources to reflect environmental conditions accurately and combining several factors into one indicator to better represent environmental risks. These recommendations could improve the way we model and understand how CVDs and environmental factors are connected, benefiting research into other chronic diseases as well. By enhancing the data and methods used in these models, we can better understand and ultimately reduce CVD risks related to environmental factors. Key Points Spatiotemporal models provide a robust understanding of the relationship between health effects and environmental risk factors Current applications require improvements in spatial and temporal resolution of data sets to reduce generalization of exposure levels Advanced visualization tools are needed to interpret spatiotemporal data for improving their utility in a public health setting

Small domain estimation (SDE) research outside of the United States has been centered in Canada and Europe—both in transnational organizations, such as the European Union, and in the national statistics offices of individual countries. Support for SDE research is driven by government policy-makers responsible for core national statistics across domains. Examples include demographic information about provision of health care or education (a social domain) or business data for a manufacturing sector (economic domain). Small area estimation (SAE) research on forest statistics has typically studied a subset of core environmental statistics for a limited geographic domain. The statistical design and sampling intensity of national forest inventories (NFIs) provide population estimates of acceptable precision at the national level and sometimes for broad sub-national regions. But forest managers responsible for smaller areas—states/provinces, districts, counties—are facing changing market conditions, such as emerging forest carbon markets, and budgetary pressures that limit local forest inventories. They need better estimates of conditions and trends for small sub-sets of a national-scale domain than can be provided at acceptable levels of precision from NFIs. Small area estimation research is how forest biometricians at the science-policy interface build bridges to inform decisions by forest managers, landowners, and investors.

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one-point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area-level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson-gamma and the binomial-beta, and the normal-normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well-known expectation-maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second-order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.

Most important large-scale surveys carried out by national statistical institutes are the repeated survey type, typically intended to produce estimates for several parameters of the whole population, as well as parameters related to some subpopulations. Small area estimation techniques are becoming more and more important for the production of official statistics where direct estimators are not able to produce reliable estimates. In order to exploit data from different survey cycles, unit-level linear mixed models with area and time random effects can be considered. However, the large amount of data to be processed may cause computational problems. To overcome the computational issues, a reformulation of predictors and the correspondent mean cross product estimator is given. The R code based on the new formulation enables the elaboration of about 7.2 millions of data records in a matter of minutes.

Extreme heat is the leading weather-related cause of death in the United States. Many individuals, however, fail to perceive this risk, which will be exacerbated by global warming. Given that awareness of one’s physical and social vulnerability is a critical precursor to preparedness for extreme weather events, understanding Americans’ perceptions of heat risk and their geographic variability is essential for promoting adaptive behaviors during heat waves. Using a large original survey dataset of 9,217 respondents, we create and validate a model of Americans’ perceived risk to their health from extreme heat in all 50 US states, 3,142 counties, and 72,429 populated census tracts. States in warm climates (e.g., Texas, Nevada, and Hawaii) have some of the highest heatrisk perceptions, yet states in cooler climates often face greater health risks from heat. Likewise, places with older populations who have increased vulnerability to health effects of heat tend to have lower risk perceptions, putting them at even greater risk since lack of awareness is a barrier to adaptive responses. Poorer neighborhoods and those with larger minority populations generally have higher risk perceptions than wealthier neighborhoods with more white residents, consistent with vulnerability differences across these populations. Comprehensive models of extreme weather risks, exposure, and effects should take individual perceptions, which motivate behavior, into account. Understanding risk perceptions at fine spatial scales can also support targeting of communication and education initiatives to where heat adaptation efforts are most needed.

Background Human immunodeficiency virus (HIV) remains a public health priority in Latin America. While the burden of HIV is historically concentrated in urban areas and high-risk groups, subnational estimates that cover multiple countries and years are missing. This paucity is partially due to incomplete vital registration (VR) systems and statistical challenges related to estimating mortality rates in areas with low numbers of HIV deaths. In this analysis, we address this gap and provide novel estimates of the HIV mortality rate and the number of HIV deaths by age group, sex, and municipality in Brazil, Colombia, Costa Rica, Ecuador, Guatemala, and Mexico. Methods We performed an ecological study using VR data ranging from 2000 to 2017, dependent on individual country data availability. We modeled HIV mortality using a Bayesian spatially explicit mixed-effects regression model that incorporates prior information on VR completeness. We calibrated our results to the Global Burden of Disease Study 2017. Results All countries displayed over a 40-fold difference in HIV mortality between municipalities with the highest and lowest age-standardized HIV mortality rate in the last year of study for men, and over a 20-fold difference for women. Despite decreases in national HIV mortality in all countries—apart from Ecuador—across the period of study, we found broad variation in relative changes in HIV mortality at the municipality level and increasing relative inequality over time in all countries. In all six countries included in this analysis, 50% or more HIV deaths were concentrated in fewer than 10% of municipalities in the latest year of study. In addition, national age patterns reflected shifts in mortality to older age groups—the median age group among decedents ranged from 30 to 45 years of age at the municipality level in Brazil, Colombia, and Mexico in 2017. Conclusions Our subnational estimates of HIV mortality revealed significant spatial variation and diverging local trends in HIV mortality over time and by age. This analysis provides a framework for incorporating data and uncertainty from incomplete VR systems and can help guide more geographically precise public health intervention to support HIV-related care and reduce HIV-related deaths.

Many people living in low-and middle-income countries are not covered by civil registration and vital statistics systems. Consequently, a wide variety of other types of data, including many household sample surveys, are used to estimate health and population indicators. In this paper we combine data from sample surveys and demographic surveillance systems to produce small area estimates of child mortality through time. Small area estimates are necessary to understand geographical heterogeneity in health indicators when full-coverage vital statistics are not available. For this endeavor spatiotemporal smoothing is beneficial to alleviate problems of data sparsity. The use of conventional hierarchical models requires careful thought since the survey weights may need to be considered to alleviate bias due to nonrandom sampling and nonresponse. The application that motivated this work is an estimation of child mortality rates in five-year time intervals in regions of Tanzania. Data come from Demographic and Health Surveys conducted over the period 1991-2010 and two demographic surveillance system sites. We derive a variance estimator of under five years child mortality that accounts for the complex survey weighting. For our application, the hierarchical models we consider include random effects for area, time and survey and we compare models using a variety of measures including the conditional predictive ordinate (CPO). The method we propose is implemented via the fast and accurate integrated nested Laplace approximation (INLA).

Collecting data using probability samples can be expensive, and response rates for many household surveys are decreasing. The increasing availability of large data sources opens new opportunities for statisticians to use the information in survey data more efficiently by combining survey data with information from these other sources. We review some of the work done to date on statistical methods for combining information from multiple data sources, discuss the limitations and challenges for different methods that have been proposed, and describe research that is needed for combining survey estimates.