Bayesian penalized spline models for the analysis of spatio-temporal count data

Does mobility restriction significantly control infectious disease transmission? Accounting for non-stationarity in the impact of COVID-19 based on Bayesian spatially varying coefficient models

COVID-19 is the most severe health crisis of the 21st century. COVID-19 presents a threat to almost all countries worldwide. The restriction of human mobility is one of the strategies used to control the transmission of COVID-19. However, it has yet to be determined how effective this restriction is in controlling the rise in COVID-19 cases, particularly in small areas. Using Facebook's mobility data, our study explores the impact of restricting human mobility on COVID-19 cases in several small districts in Jakarta, Indonesia. Our main contribution is showing how the restriction of human mobility data can give important information about how COVID-19 spreads in different small areas. We proposed modifying a global regression model into a local regression model by accounting for the spatial and temporal interdependence of COVID-19 transmission across space and time. We applied Bayesian hierarchical Poisson spatiotemporal models with spatially varying regression coefficients to account for non-stationarity in human mobility. We estimated the regression parameters using an Integrated Nested Laplace Approximation. We found that the local regression model with spatially varying regression coefficients outperforms the global regression model based on DIC, WAIC, MPL, and R2 criteria for model selection. In Jakarta's 44 districts, the impact of human mobility varies significantly. The impacts of human mobility on the log relative risk of COVID-19 range from -4.445 to 2.353. The prevention strategy involving the restriction of human mobility may be beneficial in some districts but ineffective in others. Therefore, a cost-effective strategy had to be adopted.

Small Area Forecasting of Opioid-Related Mortality: Bayesian Spatiotemporal Dynamic Modeling Approach

BACKGROUND

Opioid-related overdose mortality has remained at crisis levels across the United States, increasing 5-fold and worsened during the COVID-19 pandemic. The ability to provide forecasts of opioid-related mortality at granular geographical and temporal scales may help guide preemptive public health responses. Current forecasting models focus on prediction on a large geographical scale, such as states or counties, lacking the spatial granularity that local public health officials desire to guide policy decisions and resource allocation.

OBJECTIVE

The overarching objective of our study was to develop Bayesian spatiotemporal dynamic models to predict opioid-related mortality counts and rates at temporally and geographically granular scales (ie, ZIP Code Tabulation Areas [ZCTAs]) for Massachusetts.

METHODS

We obtained decedent data from the Massachusetts Registry of Vital Records and Statistics for 2005 through 2019. We developed Bayesian spatiotemporal dynamic models to predict opioid-related mortality across Massachusetts' 537 ZCTAs. We evaluated the prediction performance of our models using the one-year ahead approach. We investigated the potential improvement of prediction accuracy by incorporating ZCTA-level demographic and socioeconomic determinants. We identified ZCTAs with the highest predicted opioid-related mortality in terms of rates and counts and stratified them by rural and urban areas.

RESULTS

Bayesian dynamic models with the full spatial and temporal dependency performed best. Inclusion of the ZCTA-level demographic and socioeconomic variables as predictors improved the prediction accuracy, but only in the model that did not account for the neighborhood-level spatial dependency of the ZCTAs. Predictions were better for urban areas than for rural areas, which were more sparsely populated. Using the best performing model and the Massachusetts opioid-related mortality data from 2005 through 2019, our models suggested a stabilizing pattern in opioid-related overdose mortality in 2020 and 2021 if there were no disruptive changes to the trends observed for 2005-2019.

CONCLUSIONS

Our Bayesian spatiotemporal models focused on opioid-related overdose mortality data facilitated prediction approaches that can inform preemptive public health decision-making and resource allocation. While sparse data from rural and less populated locales typically pose special challenges in small area predictions, our dynamic Bayesian models, which maximized information borrowing across geographic areas and time points, were used to provide more accurate predictions for small areas. Such approaches can be replicated in other jurisdictions and at varying temporal and geographical levels. We encourage the formation of a modeling consortium for fatal opioid-related overdose predictions, where different modeling techniques could be ensembled to inform public health policy.

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).

Modeling latent spatio-temporal disease incidence using penalized composite link models

Epidemiological data are frequently recorded at coarse spatio-temporal resolutions to protect confidential information or to summarize it in a compact manner. However, the detailed patterns followed by the source data, which may be of interest to researchers and public health officials, are overlooked. We propose to use the penalized composite link model (Eilers PCH (2007)), combined with spatio-temporal P-splines methodology (Lee D.-J., Durban M (2011)) to estimate the underlying trend within data that have been aggregated not only in space, but also in time. Model estimation is carried out within a generalized linear mixed model framework, and sophisticated algorithms are used to speed up computations that otherwise would be unfeasible. The model is then used to analyze data obtained during the largest outbreak of Q-fever in the Netherlands.

Census Tract Patterns and Contextual Social Determinants of Health Associated With COVID-19 in a Hispanic Population From South Texas: A Spatiotemporal Perspective

BACKGROUND

Previous studies have shown that various social determinants of health (SDOH) may have contributed to the disparities in COVID-19 incidence and mortality among minorities and underserved populations at the county or zip code level.

OBJECTIVE

This analysis was carried out at a granular spatial resolution of census tracts to explore the spatial patterns and contextual SDOH associated with COVID-19 incidence from a Hispanic population mostly consisting of a Mexican American population living in Cameron County, Texas on the border of the United States and Mexico. We performed age-stratified analysis to identify different contributing SDOH and quantify their effects by age groups.

METHODS

We included all reported COVID-19-positive cases confirmed by reverse transcription-polymerase chain reaction testing between March 18 (first case reported) and December 16, 2020, in Cameron County, Texas. Confirmed COVID-19 cases were aggregated to weekly counts by census tracts. We adopted a Bayesian spatiotemporal negative binomial model to investigate the COVID-19 incidence rate in relation to census tract demographics and SDOH obtained from the American Community Survey. Moreover, we investigated the impact of local mitigation policy on COVID-19 by creating the binary variable "shelter-in-place." The analysis was performed on all COVID-19-confirmed cases and age-stratified subgroups.

RESULTS

Our analysis revealed that the relative incidence risk (RR) of COVID-19 was higher among census tracts with a higher percentage of single-parent households (RR=1.016, 95% posterior credible intervals [CIs] 1.005, 1.027) and a higher percentage of the population with limited English proficiency (RR=1.015, 95% CI 1.003, 1.028). Lower RR was associated with lower income (RR=0.972, 95% CI 0.953, 0.993) and the percentage of the population younger than 18 years (RR=0.976, 95% CI 0.959, 0.993). The most significant association was related to the "shelter-in-place" variable, where the incidence risk of COVID-19 was reduced by over 50%, comparing the time periods when the policy was present versus absent (RR=0.506, 95% CI 0.454, 0.563). Moreover, age-stratified analyses identified different significant contributing factors and a varying magnitude of the "shelter-in-place" effect.

CONCLUSIONS

In our study, SDOH including social environment and local emergency measures were identified in relation to COVID-19 incidence risk at the census tract level in a highly disadvantaged population with limited health care access and a high prevalence of chronic conditions. Results from our analysis provide key knowledge to design efficient testing strategies and assist local public health departments in COVID-19 control, mitigation, and implementation of vaccine strategies.

A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data

Spatiotemporal models for count data are required in a wide range of scientific fields, and they have become particularly crucial today because of their ability to analyze COVID-19-related data. The main objective of this paper is to present a review describing the most important approaches, and we monitor their performance under the same dataset. For this review, we focus on the three R-packages that can be used for this purpose, and the different models assessed are representative of the two most widespread methodologies used to analyze spatiotemporal count data: the classical approach and the Bayesian point of view. A COVID-19-related case study is analyzed as an illustration of these different methodologies. Because of the current urgent need for monitoring and predicting data in the COVID-19 pandemic, this case study is, in itself, of particular importance and can be considered the secondary objective of this work. Satisfactory and promising results have been obtained in this second goal. With respect to the main objective, it has been seen that, although the three models provide similar results in our case study, their different properties and flexibility allow us to choose the model depending on the application at hand.

Population Mobility Trends, Deprivation Index and the Spatio-Temporal Spread of Coronavirus Disease 2019 in Ireland

Like most countries worldwide, the coronavirus disease (COVID-19) has adversely affected Ireland. The aim of this study was to (i) investigate the spatio-temporal trend of COVID-19 incidence; (ii) describe mobility trends as measured by aggregated mobile phone records; and (iii) investigate the association between deprivation index, population density and COVID-19 cases while accounting for spatial and temporal correlation. Standardised incidence ratios of cases were calculated and mapped at a high spatial resolution (electoral division level) over time. Trends in the percentage change in mobility compared to a pre-COVID-19 period were plotted to investigate the impact of lockdown restrictions. We implemented a hierarchical Bayesian spatio-temporal model (Besag, York and Mollié (BYM)), commonly used for disease mapping, to investigate the association between covariates and the number of cases. There have been three distinct "waves" of COVID-19 cases in Ireland to date. Lockdown restrictions led to a substantial reduction in human movement, particularly during the 1st and 3rd wave. Despite adjustment for population density (incidence ratio (IR) = 1.985 (1.915-2.058)) and the average number of persons per room (IR = 10.411 (5.264-22.533)), we found an association between deprivation index and COVID-19 incidence (IR = 1.210 (CI: 1.077-1.357) for the most deprived quintile compared to the least deprived). There is a large range of spatial heterogeneity in COVID-19 cases in Ireland. The methods presented can be used to explore locally intensive surveillance with the possibility of localised lockdown measures to curb the transmission of infection, while keeping other, low-incidence areas open. Our results suggest that prioritising densely populated deprived areas (that are at increased risk of comorbidities) during vaccination rollout may capture people that are at risk of infection and, potentially, also those at increased risk of hospitalisation.

A Bayesian joint model for zero-inflated integers and left-truncated event times with a time-varying association: Applications to senior health care

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time-to-event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject-specific responses are handled by a zero-inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age-dependent, with an unspecified association structure. This is well-approximated through a flexible functional specification provided by penalized B-splines. The parameter estimation of the joint model is derived under a Bayesian scheme.

An R package for an integrated evaluation of statistical approaches to cancer incidence projection

Background

Projection of future cancer incidence is an important task in cancer epidemiology. The results are of interest also for biomedical research and public health policy. Age-Period-Cohort (APC) models, usually based on long-term cancer registry data (> 20 yrs), are established for such projections. In many countries (including Germany), however, nationwide long-term data are not yet available. General guidance on statistical approaches for projections using rather short-term data is challenging and software to enable researchers to easily compare approaches is lacking.

Methods

To enable a comparative analysis of the performance of statistical approaches to cancer incidence projection, we developed an R package (incAnalysis), supporting in particular Bayesian models fitted by Integrated Nested Laplace Approximations (INLA). Its use is demonstrated by an extensive empirical evaluation of operating characteristics (bias, coverage and precision) of potentially applicable models differing by complexity. Observed long-term data from three cancer registries (SEER-9, NORDCAN, Saarland) was used for benchmarking.

Results

Overall, coverage was high (mostly > 90%) for Bayesian APC models (BAPC), whereas less complex models showed differences in coverage dependent on projection-period. Intercept-only models yielded values below 20% for coverage. Bias increased and precision decreased for longer projection periods (> 15 years) for all except intercept-only models. Precision was lowest for complex models such as BAPC models, generalized additive models with multivariate smoothers and generalized linear models with age x period interaction effects.

Conclusion

The incAnalysis R package allows a straightforward comparison of cancer incidence rate projection approaches. Further detailed and targeted investigations into model performance in addition to the presented empirical results are recommended to derive guidance on appropriate statistical projection methods in a given setting.

A Bayesian spatiotemporal statistical analysis of out-of-hospital cardiac arrests

We propose a Bayesian spatiotemporal statistical model for predicting out-of-hospital cardiac arrests (OHCAs). Risk maps for Ticino, adjusted for demographic covariates, are built for explaining and forecasting the spatial distribution of OHCAs and their temporal dynamics. The occurrence intensity of the OHCA event in each area of interest, and the cardiac risk-based clustering of municipalities are efficiently estimated, through a statistical model that decomposes OHCA intensity into overall intensity, demographic fixed effects, spatially structured and unstructured random effects, time polynomial dependence, and spatiotemporal random effect. In the studied geography, time evolution and dependence on demographic features are robust over different categories of OHCAs, but with variability in their spatial and spatiotemporal structure. Two main OHCA incidence-based clusters of municipalities are identified.

A modelling approach for correcting reporting delays in disease surveillance data

One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistical problems, infrastructure difficulties, and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast due to the use of the integrated nested Laplace approximation. The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and severe acute respiratory infection data in the state of Paraná, Brazil.

Spatially varying auto-regressive models for prediction of new human immunodeficiency virus diagnoses

In demand of predicting new HIV diagnosis rates based on publicly available HIV data that is abundant in space but has few points in time, we propose a class of spatially varying autoregressive (SVAR) models compounded with conditional autoregressive (CAR) spatial correlation structures. We then propose to use the copula approach and a flexible CAR formulation to model the dependence between adjacent counties. These models allow for spatial and temporal correlation as well as space-time interactions and are naturally suitable for predicting HIV cases and other spatio-temporal disease data that feature a similar data structure. We apply the proposed models to HIV data over Florida, California and New England states and compare them to a range of linear mixed models that have been recently popular for modeling spatio-temporal disease data. The results show that for such data our proposed models outperform the others in terms of prediction.

Evaluation of spatio-temporal Bayesian models for the spread of infectious diseases in oil palm

In the field of epidemiology, studies are often focused on mapping diseases in relation to time and space. Hierarchical modeling is a common flexible and effective tool for modeling problems related to disease spread. In the context of oil palm plantations infected by the fungal pathogen Ganoderma boninense, we propose and compare two spatio-temporal hierarchical Bayesian models addressing the lack of information on propagation modes and transmission vectors. We investigate two alternative process models to study the unobserved mechanism driving the infection process. The models help gain insight into the spatio-temporal dynamic of the infection by identifying a genetic component in the disease spread and by highlighting a spatial component acting at the end of the experiment. In this challenging context, we propose models that provide assumptions on the unobserved mechanism driving the infection process while making short-term predictions using ready-to-use software.

Flexible Bayesian P-splines for smoothing age-specific spatio-temporal mortality patterns

In this paper age-space-time models based on one and two-dimensional P-splines with B-spline bases are proposed for smoothing mortality rates, where both fixed relative scale and scale invariant two-dimensional penalties are examined. Model fitting and inference are carried out using integrated nested Laplace approximations, a recent Bayesian technique that speeds up computations compared to McMC methods. The models will be illustrated with Spanish breast cancer mortality data during the period 1985-2010, where a general decline in breast cancer mortality has been observed in Spanish provinces in the last decades. The results reveal that mortality rates for the oldest age groups do not decrease in all provinces.

Spatial-Temporal Epidemiology of Tuberculosis in Mainland China: An Analysis Based on Bayesian Theory

OBJECTIVE

To explore the spatial-temporal interaction effect within a Bayesian framework and to probe the ecological influential factors for tuberculosis.

METHODS

Six different statistical models containing parameters of time, space, spatial-temporal interaction and their combination were constructed based on a Bayesian framework. The optimum model was selected according to the deviance information criterion (DIC) value. Coefficients of climate variables were then estimated using the best fitting model.

RESULTS

The model containing spatial-temporal interaction parameter was the best fitting one, with the smallest DIC value (-4,508,660). Ecological analysis results showed the relative risks (RRs) of average temperature, rainfall, wind speed, humidity, and air pressure were 1.00324 (95% CI, 1.00150-1.00550), 1.01010 (95% CI, 1.01007-1.01013), 0.83518 (95% CI, 0.93732-0.96138), 0.97496 (95% CI, 0.97181-1.01386), and 1.01007 (95% CI, 1.01003-1.01011), respectively.

CONCLUSIONS

The spatial-temporal interaction was statistically meaningful and the prevalence of tuberculosis was influenced by the time and space interaction effect. Average temperature, rainfall, wind speed, and air pressure influenced tuberculosis. Average humidity had no influence on tuberculosis.