Interactive impacts of walkability, social vulnerability, & travel behavior on COVID-19 mortality: A hierarchical Bayesian spatial random parameter approach

Abstract

While existing research highlights the built and social environment impacts on COVID-19 mortality, no empirical evidence exists on how the built and social environments may interact to influence COVID-19 mortality. This study presents a rigorous empirical assessment of the interactive impacts of social vulnerability and walkability on neighborhood-level COVID-19 mortality rates. Based in King County, WA, a unique data infrastructure is created by spatially integrating diverse census tract-level data on COVID-19 mortalities, walkability characteristics, social vulnerability, and travel behavior measures. Advanced Markov Chain Monte Carlo (MCMC) based Full Bayes hierarchical spatial random parameter models are developed to simultaneously capture spatial and unobserved random heterogeneity. Around 46% of the neighborhoods had opposite levels of walkability and social vulnerability. Compared to low walkability and high social vulnerability, neighborhoods with high walkability and low social vulnerability (i.e., best case scenario) had on average 20.2% (95% Bayesian CI: -37.2% to -3.3%) lower COVID-19 mortality rates. Analysis of the interactive impacts when only one of the social and built environment metrics was in a healthful direction revealed significant offsetting effects – suggesting that the underlying structural social vulnerability issues faced by our communities should be addressed first for the infectious disease-related health impacts of walkable urban design to be observed. Concerning travel behavior, the findings indicate that COVID-19 mortality rates may be reduced by discouraging auto use and encouraging active transportation. The study methodologically contributes by simultaneously capturing spatial and unobserved heterogeneity in a holistic Full Bayesian framework.

1. Background

Accelerating the adoption of healthy and active lifestyles is an emerging research priority and is a key to accomplishing sustainable cities and communities (Delso et al., 2019; Wang et al., 2022; Yamasaki & Yamada, 2022). Among other factors, transportation system design influences travel and activity patterns (Handy et al., 2002; Guo & Chen, 2007; Ferdinand et al., 2012), which predict chronic diseases including coronary heart disease, hypertension, and obesity (Sallis et al., 2012; Malambo et al., 2016; Frank et al., 2019). Additionally, with the onset of COVID-19, a rapidly growing body of literature has demonstrated the efficacy of walkable and compact urban environments in reducing morbidity and mortality from infectious diseases (Megahed & Ghoneim, 2020; Frank & Wali, 2021; Khavarian-Garmsir et al., 2021; Wali & Frank, 2021). These impacts have been especially cogent to the existing burden of disease experienced by the most vulnerable and disadvantaged populations (Roberts et al., 2015; Cockerham et al., 2017). In addition to the built environment, social environment factors are also known to influence COVID-19 mortality. Historically, socially vulnerable populations have been at the greatest risk of disease-associated mortality (Karaye & Horney, 2020). In the case of COVID-19, the disproportionate disease burden on socially vulnerable populations (including the elderly, ethnic minorities, low-income individuals, and those with the lowest education) can be partly explained by health inequities in transportation accessibility, housing conditions, nutrition, and health care (Gilbert et al., 2016; Wadhera et al., 2020, Yancy, 2020). Importantly, the physical and social barriers to health collectively shape the social capital of our cities (Bodde & Seo, 2009) and the ability of communities and populations to respond to health disasters (Hasson et al., 2022). As such, the present study is positioned within the built environment-social vulnerability framework to empirically evaluate the nexus between walkability and social vulnerability impacts on COVID-19 mortality.

A broad spectrum of empirical studies has identified built and social environments as key determinants of COVID-19 mortality. Compared to the initial mixed findings on the links between urban infrastructure design and COVID-19 mortality early in the pandemic (Bray et al., 2020; Carozzi, 2020; Kodera et al., 2020), several studies documented a negative relationship between walkable infrastructure design and COVID-19 mortality as more representative and spatially granular data on the rapidly evolving pandemic became available (Frank & Wali, 2021; Oishi et al., 2021; Wali & Frank, 2021; Guan et al., 2022). Besides built environment characteristics, the impacts of the social environment on COVID-19 mortality are also well-elucidated (Harris, 2020; Karaye & Horney, 2020; Freese et al., 2021; Hu et al., 2021, Kim et al., 2021; Akinwumiju et al., 2022). Strong social vulnerability and disparities exist with greater mortality rates for people of color (Hu et al., 2021; Peres et al., 2021), older individuals (Caramelo et al., 2020; Mesas et al., 2020), low income (Drefahl et al., 2020), and less educated individuals (Seligman et al., 2021). Multiple studies have also examined the links between broader social vulnerability measures (e.g., composite social vulnerability index of socioeconomic status, household composition, minority status/language, and housing type) and COVID-19 mortality rates. County-level analyses in the U.S. revealed social vulnerability as an independent predictor of COVID-19 mortality rates (Nayak et al., 2020; Islam et al., 2021; Karmakar et al., 2021). Higher social vulnerability and greater COVID-19 deaths coexisted in over 1 in 4 U.S. counties (Nayak et al., 2020), whereas a 0.1 unit increase in the social vulnerability index was correlated with a 13.7% increase in COVID-19 mortality rates (Karmakar et al., 2021). Results from the above county-level studies have highlighted the need to address social vulnerability and its root causes to lower inequities in the COVID-19 burden faced by communities.

1.1. Research gaps & objective

While previous studies have enhanced our understanding of the social and built environment impacts on COVID-19 mortality, key substantive and methodological knowledge gaps remain. From a substantive perspective, no empirical evidence to our knowledge exists on how walkability and social vulnerability may interact to impact COVID-19 mortality. This is a key knowledge gap because social disparities in the health impacts of walkability and urban design are well documented (Sallis et al., 2009). Additionally, spatial inequity in neighborhood walkability is increasingly becoming known (Sallis et al., 2011) – with disadvantaged and vulnerable neighborhoods exhibiting lower walkability (Bereitschaft, 2017; Su et al., 2017). The inequitable access to walkable infrastructure driven by social vulnerability can offset some of the COVID-19-related benefits of walkable urban designs. While the existing literature highlights the impacts of the built and social environments on COVID-19 outcomes (Nayak et al., 2020; Hu et al., 2021; Karmakar et al., 2021; Kashem et al., 2021), previous studies have not empirically examined the interactions between the two key environmental domains.

From a methodological perspective, two key gaps exist. First, most previous studies have ignored important methodological concerns of spatial and unobserved random heterogeneity in the impacts of social and built environment features on COVID-19 mortality. Precisely, spatial and unobserved random heterogeneity has not been simultaneously addressed. As demonstrated elsewhere (Frank & Wali, 2021; Wali & Frank, 2021), COVID-19 outcomes are influenced by a myriad of behavioral, attitudinal, environmental, and social factors that vary significantly in space. Such factors are often unobserved in the data and are routinely excluded from empirical analyses precluding reliable estimation of the impacts of observed variables (e.g., built/social environment features). Importantly, significant heterogeneity in the impacts of social and built environment features on COVID-19 was observed not only in aggregate (county- and country-level) data (Sannigrahi et al., 2020; Frank & Wali, 2021) but spatially more granular neighborhood-level data as well (Wali & Frank, 2021). Second, most previous studies are based on large geographies (e.g., cities, counties) that cannot capture the substantial variations in social and built environment profiles within cities (Bryan et al., 2021; Wali & Frank, 2021).

Keeping in view the above knowledge gaps, the present study contributes by analyzing the interactive impacts of walkability and social vulnerability on neighborhood-level COVID-19 mortality rates after controlling for travel behavior patterns and the effects of spatially structured and random unobserved factors. An innovative Markov Chain Monte Carlo (MCMC) based Full Bayesian framework is employed to specify and estimate advanced hierarchical spatial random parameter models simultaneously accounting for spatially structured and random unobserved heterogeneity. The advanced methodological framework enables innovative insights critical to the development of evidence- and place-based environmental countermeasures to combat COVID-19 mortality.

2. Methods

2.1. Data

This study was based in King County, WA, and followed an ecological study design harnessing a comprehensive data infrastructure. With a population of over 2.2 million, King County includes 35 cities and is the 13th most populous county in the United States. The county spans over 2300 sq mi. and is comprised of 397 census tracts. The census tract serves as the unit of analysis since it is the highest spatial resolution at which all the relevant geocoded data are publicly available.

A unique data infrastructure is created by spatially integrating diverse neighborhood-level data on COVID-19 outcomes, walkability characteristics, social vulnerability, and travel behavior measures. The four data streams include (1) the King county COVID-19 data dashboard, (2) the 2020 US Environmental Protection Agency Smart Location Database, (3) the US Centers for Disease Control and Prevention (CDC) Social Vulnerability Database, and (4) the American Community Survey (ACS) databases.

2.1.1. COVID-19 fatalities

Census tract-level data on COVID-19 fatalities (as of September 27, 2022) were obtained from the King County COVID-19 dashboard. Neighborhood-specific fatality rates per 1000 individuals were derived by pooling population information from the ACS.

2.1.2. Walkability & built environment data

Objectively assessed data on the built environment were derived from the most recent 2020 release of US EPA's Smart Location Database (https://www.epa.gov/smartgrowth/smart-location-mapping) – which methodologically enhances the previous SLD release versions and encompasses more built environment features. Serving as a comprehensive publicly available repository, the SLD contains over 100 built environment variables characterizing different aspects of the built environment. Guided by the literature, the built environment variables chosen and considered in this study are those that characterize neighborhood walkability levels. Particularly, the built environment measures harnessed in this study capture aspects of the original “5D” environmental model (density, design, diversity, destination accessibility, and distance to transit) (Ewing & Cervero, 2010) predicting activity patterns (Cervero & Kockelman, 1997; Saelens & Handy, 2008; Cervero et al., 2009; Cho et al., 2009), chronic (Frank & Engelke, 2001; Giles-Corti et al., 2015), and infectious disease outcomes (Frank & Wali, 2021; Wali & Frank, 2021; Venerandi et al., 2022). Table 1 summarizes the key built environment variables used in this study representing characteristics related to employment mix, residential and employment land use mix, pedestrian-oriented street connectivity, and transit accessibility. Capturing neighborhood diversity, the employment mix measure characterizes the distribution of eight different employment types (service, office, retail, education, health, industrial, public services, and entertainment) within a neighborhood which serves as a proxy for land-use development configuration patterns. The measure of employment and residential entropy additionally incorporates residential developments to capture the relative mix of residential and employment configuration patterns within a neighborhood. These measures serve as proxies for the original land-use mix measure (Cervero, 1989; Cervero & Kockelman, 1997) and quantify the extent of mixed land use (“live, work, play” environments) that support active and hinder sedentary travel (Cervero, 1991; Frank & Pivo, 1994). The above land-use diversity measures also capture destination accessibility to some extent (Ewing & Cervero, 2010). Capturing urban design, the pedestrian-oriented intersection density measure serves as a proxy for street connectivity. Widely used in the transportation and health literatures (Saelens et al., 2003; Kligerman et al., 2007; Saelens & Handy, 2008; Cho et al., 2009; Ewing & Cervero, 2010), this measure has been shown to predict travel patterns (Ikeda et al., 2018; Le et al., 2018) and health outcomes (including COVID-19 mortality rates) (Frank & Wali, 2021; Wali & Frank, 2021). We used a modified street connectivity measure that does not consider auto-oriented intersections or other intersection types (such as three-way intersections) that could hinder active transportation (Wali & Frank, 2021). While the land-use measures indicate the availability of different activities, the street connectivity measure reflects the provision of adequate pedestrian-oriented infrastructure that vulnerable road users can use to access different activity types. Finally, a distance to transit measure is considered that captures the level of transit accessibility in a neighborhood which is known to hinder sedentary travel (Ewing & Cervero, 2010; Cerin et al., 2017). As noted elsewhere (Ewing & Cervero, 2010), the “5D” environmental model is based on a rough taxonomy and the above measures may capture more than one of the “5Ds” constructs due to overlapping dimensions.

Table 1.

Description of built environment, social vulnerability, and travel behavior measures.

Measure	Description
Built Environment Measures
Employment entropy (D2B_E8MIXA)	A land-use diversity measure measuring 8-tier employment mix on a scale 0 to 1 (higher values indicating more mixed land-use).
Employment & residential entropy (D2A_EPHHM)	A land-use diversity measure capturing the mix of residential and employment activities on a scale 0 to 1 (higher values indicating more distributional evenness of housing and access to jobs).
Street-intersection density (D3B)	A connectivity measure capturing the count of pedestrian-oriented road intersections per sq. kilometer.
Distance to nearest transit stop (D4A)	A transit accessibility measure capturing the distance to nearest transit stop.
Walkability Index	A composite measure of the four environmental measures measuring walkability on a scale 1 to 20 (higher values indicating greater walkability).
Social Vulnerability Measures
Theme 1: Socioeconomic status (RPL_THEME1)	Composite ranking measure of below poverty concentrations, unemployment, income, and less education on a scale of 0 to 1 (higher values indicating greater socioeconomic vulnerability).
Theme 2: Household composition & disability (RPL_THEME2)	Composite ranking measure of old aged and younger population, individuals with disability, and single parent households on a scale of 0 to 1. Higher values indicate greater vulnerability associated with household composition and disability.
Theme 3: Minority status & language (RPL_THEME3)	Composite ranking measure of minority populations and those who cannot speak English well on a scale of 0 to 1. Higher values indicate greater vulnerability associated with minority status and language.
Theme 4: Housing type & transportation (RPL_THEME4)	Composite ranking measure of multi-unit structures, mobile homes, crowding, no vehicle households, and group quarters on a scale of 0 to 1. Higher values indicate greater vulnerability associated with housing type and transportation.
Overall social vulnerability index (RPL_THEMES)	Combined ranking measure of the four themes ranging from 0 to 1 (higher values indicate greater social vulnerability).
Travel Behavior Measures
Drive Alone	Percentage of workers using different travel modes for work commute.
Biking
Walking
Telecommuting

It is well-documented in the literature that built environment features exhibit significant multicollinearity (Frank et al., 2010). To circumvent this issue, a composite walkability index was used that captures the levels of land-use mix/destination accessibility, urban design, and transit accessibility in a single composite measure (Table 1) (Thomas & Reyes, 2021). The national walkability index provided in US EPA's SLD v3.0 serves as a standardized tool that enables community leaders, engineers, and planners to understand walkability levels nationwide and supports a broad spectrum of scenario planning, modeling, and other community analysis efforts (Thomas & Reyes, 2021).

2.1.3. Social vulnerability data

Data on neighborhood social vulnerability was obtained from the US CDC's Social Vulnerability Database (CDC, 2020). The US CDC has established the Social Vulnerability Index (SVI) with nationwide census tract-level coverage that captures the level of community vulnerability across 15 social factors unified into four interrelated themes (CDC, 2020): (1) socioeconomic status, (2) household composition and disability, (3) minority status and language, and (4) housing type and transportation (Table 1) (CDC, 2020). For each of the four themes (Table 1), every census tract is ranked by percentiles for each of the census variables shown and the percentile rankings are summed and ordered across all census tracts nationwide. An overall social vulnerability index combining the four themes is derived by summing the scores for each theme, ordering the census tracts, and then calculating overall percentile rankings nationwide. Ranging between 0 and 1, higher values indicate greater social vulnerability. As a ranked-based percentile methodology was used, an SVI value of 0.5 represents normal vulnerability. Supported by peer-reviewed methods (Flanagan et al., 2011), the SVI database is an ideal social vulnerability index for this study capturing a broad spectrum of social factors known to affect community vulnerability (see Table 1 for the full list of all the 15 variables included in the SVI). The SVI database serves as a premier index characterizing neighborhood social vulnerability profiles nationwide – enabling public health officials to better manage “emergency meteorological and geological events, disease outbreaks, and human-caused incidents.” (Flanagan et al., 2018). Throughout the COVID-19 pandemic, the Geospatial Research, Analysis, and Services Program (GRASP) at the US CDC has collaborated extensively with public health officials and other entities (including the Office of Surgeon General, CDC COVID-19 Taskforce, US National Institutes of Health) using the SVI database to identify vulnerable populations that are at increased risk of becoming affected by the COVID-19 pandemic (CDC, 2021). As a standard measure of social vulnerability in the U.S. endorsed by The National Academy of Science, Engineering, and Medicine (CDC, 2021), several research studies have validated the SVI to predict chronic and infectious disease outcomes (An & Xiang, 2015; Nayak et al., 2020; Rifai et al., 2021; Karmakar et al., 2021; Bevan et al., 2022).

2.1.4. Travel behavior data

To control travel behavior patterns, neighborhood-level commute mode choice proportions were calculated using survey data from the “Detailed Tables” in the ACS. Most recent 5-year estimates (2015–2019) from the ACS were used to enhance statistical reliability. Proportions of workers telecommuting, walking, biking, driving alone, carpooling, and using transit to work were calculated for each of the 397 census tracts in King County (Table 1). These survey-based estimates offer a unique source of key information on travel behavior factors that predict health outcomes. As the present study is at the neighborhood-level, we were limited by the amount of travel behavior data available in the ACS (which is the only national source providing nationwide consistent survey-based census data at the neighborhood level).

2.2. Conceptual framework

Fig. 1 illustrates a quadrant-based conceptual model to examine the interactive impacts of social vulnerability and walkability on COVID-19 mortality rates. The conceptual model classifies the levels of neighborhood walkability (low vs. high) and social vulnerability (low vs. high) into four quadrants. A cut-off of 0.5 (representing normal vulnerability) was used to classify neighborhood social vulnerability into low vs. high vulnerability. The classification of social vulnerability referred to the overall social vulnerability index, which is a combination of the four vulnerability themes discussed earlier and further elaborated in upcoming sections. A cut-off walkability index score of 12.8 (representing average/mean walkability across census tracts) was used to classify high vs. low levels of neighborhood walkability across King County. Our examination of the distribution of the walkability index revealed that the mean and median were not significantly different. The mean walkability index is 12.8 compared to the median walkability index of 13.6.

Fig. 1.

Conceptual model of walkability & social vulnerability interactions.

Quadrant 2 represents the least desirable and least healthy condition containing neighborhoods with low walkability and high social vulnerability. Quadrant 4 represents the best-case scenario capturing neighborhoods exhibiting high walkability and low social vulnerability. More walkable and least socially vulnerable neighborhoods are hypothesized to exhibit lower mortality rates since sociodemographic risk factors known to increase COVID-19 mortality rates would be less prevalent in neighborhoods with lower social vulnerability (Mesas et al., 2020; Hu et al., 2021; Seligman et al., 2021). Likewise, the mortality rates in these neighborhoods are expected to be lower due to the proven health benefits of greater activity levels in more walkable neighborhoods (Frank et al., 2004; Megahed & Ghoneim, 2020; Rojas-Rueda & Morales-Zamora, 2021; Wali & Frank, 2021). Quadrants 1 and 3 represent intermediate scenarios with either of the two metrics (walkability vs. social vulnerability) in the healthful direction. When correlated with COVID-19 mortality outcomes, this framework enables an understanding of the relative health impacts of the two key environmental metrics when only one of them is in a healthful direction. Overall, the quadrant-based conceptual model enables an understanding of the typology of walkability and social vulnerability and the relative impacts of the two on COVID-19 mortality rates (as demonstrated in this study).

2.3. Bayesian modeling framework

We employed a Markov Chain Monte Carlo (MCMC) based Full Bayesian framework for model specification and estimation. For the COVID-19 fatality rate outcome, a series of three models were developed including fixed parameter models (Model A), spatial fixed parameter models (Model B), and spatial random parameter models (Model C). The specification in Model B captures and models spatial heterogeneity in the determinants of COVID-19 mortality, whereas Model C specification simultaneously captures spatial and unobserved random heterogeneity in the determinants of COVID-19 mortality rates. Developed for comparative purposes, the fixed parameter model (Model A) ignores spatial and unobserved random heterogeneity impacts. The model specifications, prior distributions, and Full Bayes estimation are described next.

2.3.1. Model specification

A Full Bayes fixed parameter model can be used at a basic level given the continuous nature of the response outcome (COVID-19 fatalities per 1000 population). The fixed parameter Bayesian model is specified as (Model A):

$$Y_i={\beta }_o+\sum _{k=1}^K{\beta }_k{x}_i^k+{\epsilon }_i$$ (1)

Where: $Y_i$ is a vector of COVID-19 fatality rates in census tract $i$ and $x_i^k$ is the vector of an exogenous variable for the $k^{th}$ covariate across census tract $i=1,2,\dots ,N$. ${\beta }_o$ is the intercept term and ${\beta }_k$ is the estimable parameter for the $k^{th}$ covariate. ${\epsilon }_i$ is a vector of latent factors (unstructured errors) specified as a normally distributed variate with zero mean and standard deviation $\sigma$:

$${\epsilon }_i=normal\left(0,{\sigma }^2\right)$$ (2)

Spatially structured heterogeneity: fixed parameter spatial models (Model B)

The basic fixed parameter Bayesian model assumes that COVID-19 fatality rates are independent across census tracts. However, the neighborhood fatality rates can exhibit spatial dependencies across neighborhoods due to the presence of common observed (e.g., built environmental profiles) and unobserved (e.g., weather characteristics) factors. By modeling the potential autocorrelations in geo-referenced neighborhood-level data (Lawson, 2018), the spatial dependencies in neighborhood fatality rates can be captured leading to more efficient parameter estimates. Also, it helps control for spatially-referenced omitted variable bias that can confound the relationships between observed exogenous factors (e.g., built environment) and COVID-19 fatality rates (Mannering et al., 2016; Lawson, 2018; Wali & Frank, 2021). To address spatially structured heterogeneity, we extend the specification in Eq. (1) as:

$$Y_i={\beta }_o+\sum _{k=1}^K{\beta }_k{x}_i^k+N_i$$ (3)

Where: ${\aleph }_i$ is a census tract-specific vector of random effects capturing the impacts of latent unobserved COVID-19 risk factors. To allow for spatial dependence between the random effects ${\aleph }_i$ in nearby neighborhoods, we implement a Gaussian Conditional Autoregressive (CAR) prior as follows (Besag et al., 1991):

$$N_i|N_{j\ne i}\sim Normal\left(\overline{N_i},{\tau }_i\right)$$ (4)

$$\overline{N_i}={\sum }_{i\ne j}{N}_j{\omega }_{ij}/{\sum }_{i\ne j}{\omega }_{ij}$$ (5)

$${\tau }_i={\tau }_c/{\sum }_{i\ne j}{\omega }_{ij}$$ (6)

Where: ${\tau }_c$ is the precision (inverse of the variance) parameter in the intrinsic CAR prior and ${\omega }_{ij}$ is the entry of proximity matrix W capturing the spatial relationship between neighborhood $i$ and $j$ $\forall$ $i\ne j$. Precisely, ${\omega }_{ij}$ are user-defined spatial dependency parameters defining which census tracts $j$ are neighbors to census tract $i$ (Gelfand et al., 2010). We set ${\omega }_{ii}=0$ and ${\omega }_{ij}=1$ if census tract $i$ is adjacent to census tract $j$ – with adjacency determined using the Queen's definition (Banerjee et al., 2003).

2.3.1.2. Spatial & unobserved heterogeneity: hierarchical random parameter spatial models (Model C)

While the model specification in Section 2.3.1.1 captures spatial dependencies in COVID-19 fatality rates across neighborhoods, it assumes homogeneity in the effects of exogenous variables (e.g., built environment, social vulnerability) on mortality rates. Recent studies have shown significant heterogeneity in the impacts of such variables on COVID-19 outcomes that could arise due to systematic variations in unobserved latent factors (Frank & Wali, 2021; Wali & Frank, 2021). To accommodate the heterogeneous impacts of exogenous factors, the estimable parameters $({\beta }_o,{\beta }_1,\dots ,{\beta }_K)$ underlying the spatial fixed parameter model are now specified as neighborhood-specific random parameters $({\beta }_{io},{\beta }_{i1},\dots ,{\beta }_{iK})$ as (Wali et al., 2018; Boggs et al., 2020; Washington et al., 2020):

$$Y_i={\beta }_{oi}+\sum _{k=1}^K{\beta }_{ki}{x}_i^k+N_i$$ (7)

$${\beta }_{ki}\sim {\beta }_k+{\theta }_{ik},k=0,1,2,\dots ,K$$ (8)

$${\theta }_{ik}\sim normal\left(0,{\delta }^2\right)$$ (9)

Where: ${\beta }_k$ contains the means of the random parameters ${\beta }_{ki}$ and ${\theta }_{ik}$ are normally distributed terms with mean zero and variance ${\delta }^2$. Hierarchical centering is performed with the normal densities for random parameters centered at the population-averaged intercepts or main effects to improve mixing in the Bayesian estimation (Crainiceanu et al., 2005; Congdon, 2007; Wali et al., 2018).

The hierarchical random parameter spatial model is more flexible than the fixed parameter spatial model since it enables the determination of the proportion of heterogeneity due to spatially structured vs. unstructured variations/heterogeneity. To calculate the proportion of heterogeneity in the random parameters due to spatial variations, a $\vartheta$ statistic is calculated as:

$$\vartheta =sd\left(N_i\right)/\left(\sigma +sd\left(N_i\right)+{\delta }_0+\dots +{\delta }_K\right),k=0,1,2,\dots ,K^{th}\text{random}\text{parameter}$$ (10)

Related to the determination of random parameters, the parameter estimates for an independent variable were considered random if it exhibited statistically significant standard deviation and if considering the exogenous factor as a random parameter led to improvements in model goodness of fit compared to a model considering the same independent variable as a fixed parameter (El-Basyouny & Sayed, 2011; Frank & Wali, 2021). All models were derived from a systematic process considering the parsimony of model specification, bivariate associations, and statistical significance. Variance Inflation Factors (VIFs) were monitored for each of the estimable parameters to assure the absence of problematic multicollinearity (Washington et al., 2020).

2.3.2. Prior distributions

The Full Bayesian estimation requires the specification of prior distributions for all stochastic model nodes. For the regression parameters, we use uninformative vague normal priors $\left[N\left(0,{10}^{-5}\right)\right]$ (with the spread of the prior corresponding to the precision (inverse of the variance) term) following the relevant literature (Congdon, 2007; Huang & Abdel-Aty, 2010; Gelman et al., 2013; Gelman et al., 2015; Wali et al., 2018). An exchangeable normal prior is used for all random parameters $\left({\beta }_{i1},\dots ,{\beta }_{iK}\right)$ – with uninformative gamma distribution priors on the heterogeneity parameters (${\sigma }_o^{-2},{\sigma }_k^{-2},{\sigma }^{-2}$) (Congdon, 2007; Gelman et al., 2013; Gelman et al., 2015). The spatial CAR effects are constrained to sum to zero for computational convenience. Thus, a location invariant flat prior is used for the model intercepts in the fixed parameter spatial and random parameter spatial models which is equivalent to the unconstrained parameterization of intrinsic CAR models (Spiegelhalter et al., 2003).

2.3.3. Full bayes estimation

A Gibbs sampler was utilized to construct the posterior distributions of all model parameters. For each of the models (Model A through C), two parallel chains governed by suitably over-dispersed starting values were initiated. Each chain included 105,000 iterations, 75,000 of which were discarded as a burn-in sample after establishing convergence through visual inspection of time-series plots of estimable parameters, Brooks-Gelman-Rubin (BGR) Bayesian model convergence methodology, and evaluation of Monte-Carlo standard errors (MCSE) to the standard deviations of the corresponding posterior distributions (Congdon, 2007; Boggs et al., 2020). The remaining 30,000 draws (60,000 draws for two chains) were used for generating inferences and conducting model evaluation (Yu et al., 2013; Wali et al., 2018). Considering both model complexity and predictive fit, Deviance Information Criterion (DIC) was used to evaluate the competing spatial fixed and random parameter models (Spiegelhalter et al., 2002). A Bayesian model with lower DIC exhibits better goodness of fit (Spiegelhalter et al., 2002).

All the Bayesian models were programmed, specified, and estimated in WinBUGS v14 (Lunn et al., 2000).

3. Results

3.1. Descriptive statistics

Table 2 shows the descriptive statistics for key study variables. On average, there were 7.72 COVID-19 fatalities, equaling an average COVID-19 fatality rate of 1.47 deaths per 1000 residents. Significant variations in COVID-19 fatalities and fatality rates existed across the neighborhoods. The distributions of travel behavior measures suggest that the majority of the workers (around 63%) drove alone for commute purposes, whereas another 6.1% used active travel modes (walk/bike) to work. A sizeable proportion of workers (around 7%) engaged in telecommuting.

Table 2.

Descriptive statistics of key variables.

Variables	Mean /%	SD	Source
COVID-19 Outcome
Deaths / fatalities	7.72	7.50	King county COVID-19 data dashboard (https://kingcounty.gov/depts/health/covid-19/data/download.aspx)
Fatality rate (deaths per 1000 population)	1.47	1.51
Built Environment & Walkability			2020 US Environmental Protection Agency Smart Location Database (https://www.epa.gov/smartgrowth/smart-location-database-technical-documentation-and-user-guide)
Employment entropy	0.56	0.11
Employment & household entropy	0.48	0.15
Street intersection density (count / sq. km)	125.62	81.62
Distance to nearest transit stops (meters)	516.28	292.14
National walkability index	12.82	3.46
Social Vulnerability (on scale 0 to 1)			US CDC's 2018 Social Vulnerability Database (https://www.atsdr.cdc.gov/placeandhealth/svi/data_documentation_download.html)
SVI Theme 1: Socioeconomic status	0.28	0.24
SVI Theme 2: Household composition & disability	0.26	0.23
SVI Theme 3: Minority status & language	0.61	0.21
SVI Theme 4: Housing type & transportation	0.59	0.30
SVI overall theme	0.39	0.28
Walkability × Social Vulnerability (proportion of neighborhoods falling in each quadrant)			Derived from above walkability and social vulnerability variables.
Quadrant 1: High walkability & high vulnerability	22%	—
Quadrant 2: Low walkability & high vulnerability	14%	—
Quadrant 3: Low walkability & low vulnerability	32%	—
Quadrant 4: High walkability & low vulnerability	32%	—
Travel Behavior (workers’ transportation mode to work) (% of workers)			2019 American Community Survey Detailed Tables: 5-year estimates (2015–2019) (https://www.census.gov/acs/www/data/data-tables-and-t ools/american-factfinder/).
Biking	1.51	2.14
Walking	4.64	8.84
Telecommuting	6.97	3.55
Drive alone	63.14	14.71

Notes. N = 397 census tracts; SD is the standard deviation.

3.1.1. Neighborhood walkability & social vulnerability

The neighborhoods in King County exhibited a broad range of employment entropy, employment and household entropy (as indicators of land use mix), pedestrian-oriented street intersection density (as an indicator of urban design), and transit accessibility. With a mean of 125.62 intersections / sq. km., significant variations were observed across the neighborhoods. The average distance to the nearest transit stop was around 516 m. While the average walkability index was 12.82, significant variations were observed across the study census tracts. Referring to Table 2, neighborhood vulnerability was lower based on the constructs of socioeconomic status and household composition and disability, whereas the reverse was true for the vulnerability themes of minority status and language, housing type and transportation. Fig. 2 shows the spatial distributions of neighborhood walkability and social vulnerability (overall theme) revealing discernable differences.

Fig. 2.

Spatial distribution of neighborhood walkability & social vulnerability. (Note: The social vulnerability index values are multiplied by 100 [range of 0 to 100] for plotting purpose.).

While Seattle and surrounding neighborhoods exhibit higher walkability and lower social vulnerability, other areas in the region have lower walkability levels (and higher social vulnerability) and vice versa. Related to the four quadrants, around 22%, 14%, 32%, and 32% of the neighborhoods fell in Quadrant 1 (high walkability and high vulnerability), 2 (low walkability and high vulnerability), 3 (low walkability and low vulnerability), and 4 (high walkability and low vulnerability), respectively. Noteworthy is the fact that around 46% of the neighborhoods had opposite levels of walkability and social vulnerability. The above key differences underscore the need to simultaneously evaluate the built environment and social vulnerability impacts, with a focus on the potential interactive impacts of the two on COVID-19 mortality outcomes.

3.2. Modeling results

Table 3 presents the model evaluation results for the Full Bayes fixed parameter model (Model A), Full Bayes fixed parameter spatial model (Model B), and Full Bayes hierarchical random parameter spatial model (Model C). All the models readily converged with a BGR statistic of less than 1.1 and a ratio of the Monte Carlo Standard Errors to standard deviations less than 0.05 for all estimable model parameters (Table 3).

Table 3.

Evaluation of hierarchical bayesian spatial random parameter models.

Model	Model A: Fixed parameter model	Model B: Hierarchical fixed parameter spatial model	Model C: Hierarchical random parameter spatial model
Heterogeneity treatment
Spatial heterogeneity	×	✓	✓
Unobserved heterogeneity	×	×	✓
# of spatial random parameters	0	1	1
# of random parameters	0	0	3
Bayesian goodness-of-fit statistics
$D_{bar}$	386.739	295.059	−112.462
$D_{hat}$	378.705	223.731	−440.707
$p_d$	8.034	71.328	328.245
DIC	394.773	366.387	215.783
Convergence Diagnostics
Gelman Rubin Statistic (for each estimable parameter)	≈ 1.00	≈ 1.05	≈ 1.08
MCSE / SD (for each estimable parameter)	≤ 0.05	≤ 0.05	≤ 0.05
MCMC Simulation
Sampler	Gibbs sampler	Gibbs sampler	Gibbs sampler
# of chains	2	2	2
Iterations per chain	105,000	105,000	105,000
Burn-in sample per chain	75,000	75,000	75,000
N	397	397	397

Notes. DIC is Deviance Information Criterion. Dbar is the posterior mean of the (unstandardized) deviance of the model D, Dhat is the point estimate when Dbar is substituted in D, and p_d indicates the effective number of parameters (as a measure of model complexity). MCMC is Markov Chain Monte Carlo. MCSE is Monte Carlo Standard Error. N is sample size. The dependent variable is the logarithm of the COVID-19 fatality rate per 1000 individuals in a census tract.

Compared to traditional Model A (Full Bayes fixed parameter model ignoring spatial and unobserved random heterogeneity), addressing spatial heterogeneity in the determinants of COVID-19 mortality rate in Model B led to significant improvements in model goodness of fit. The DIC of Model B was reduced by over 28 points, whereas a difference of over 10 points in the DIC of two competing models rule out the model with higher DIC (Spiegelhalter et al., 2002, 2005). A step further, addressing spatial as well as unobserved random heterogeneity in Model C resulted in even further improvements in model goodness of fit – the DIC of Model C was reduced by around 150 and 179 points compared to Model B (accounting for spatial heterogeneity only) and Model A (ignoring heterogeneity of any kind), respectively.

These results collectively suggest: (1) the presence of common observed and unobserved neighborhood-level factors inducing spatial correlation among mortality rates of nearby neighborhoods, and (2) the presence of significant heterogeneity in the impacts of key risk factors on COVID-19 mortality rates. We present and discuss the substantive interpretations of the heterogeneity-based findings in the next section.

4. Discussion and synthesis

Table 4 shows the estimation results of the best-fit Full Bayes hierarchical random parameter spatial model (Model C). For comparative purposes, the results of the simpler models are also shown. As the dependent variable is log-transformed, the posterior mean β estimates in Table 4 show a 100*β percent change in COVID-19 mortality rates with a unit increase in (continuous independent variable) or a switch from 0 to 1 for dummy indicators. These elasticity transformations and the associated heterogeneity estimates of key exogenous variables are shown in Table 5 .

Table 4.

Parameter estimates & bayesian credible intervals.

Variable	Model A			Model B			Best-Fit Model C
	Mean	95% BCI		Mean	95% BCI		Mean	95% BCI
		2.5%	97.5%		2.5%	97.5%		2.5%	97.5%
Intercept	0.885 a	0.582	1.187	0.908 a	0.567	1.248	0.894 a	0.601	1.159
Walkability & Social Vulnerability
Quadrant 2: Low walkability & high vulnerability (base)	—	—	—	—	—	—	—	—	—
Quadrant 3: Low walkability & low vulnerability	−0.354a	−0.489	−0.217	−0.239 a	−0.385	−0.095	−0.325 a	−0.493	−0.160
Quadrant 4: High walkability & low vulnerability	−0.242a	−0.388	−0.096	−0.114	−0.274	0.044	−0.202 a	−0.372	−0.033
Quadrant 1: High walkability & high vulnerability*	0.106	−0.036	0.246	0.159 a	0.019	0.299	0.112	−0.049	0.265
Scale parameter of random parameter	—	—	—	—	—	—	0.140a	0.020	0.322
Travel Behavior
% of workers driving alone to work*	0.004	−3.2E-05	0.007	7.9E-04b	−0.004	0.006	0.003b	−9.3E-05	0.007
Scale parameter of random parameter	—	—	—	—	—	—	0.006a	0.005	0.006
% of workers biking to work	−0.050 a	−0.073	−0.026	−0.038 a	−0.065	−0.011	−0.055 a	−0.078	−0.031
% of workers telecommuting*	−0.013 a	−0.026	−2.6E-04	−0.005	−0.019	0.008	−0.012	−0.028	0.003
Scale parameter of random parameter	—	—	—	—	—	—	0.019a	0.012	0.027
Spatial Heterogeneity
Scale parameter of spatial heterogeneity (${\aleph }_i$)	—	—	—	0.296 a	0.167	0.426	0.066 a	0.022	0.192
$\vartheta$: Proportion of total heterogeneity attributable to spatial factors	—	—	—	0.453 a	0.308	0.571	0.150 a	0.049	0.381
Residuals
Scale parameter ($\sigma )$: residuals	0.394 a	0.368	0.423	0.350 a	0.311	0.388	0.211 a	0.139	0.273

Notes. BCI is Bayesian Credible Intervals. (*) indicates random parameters. Scale parameters (standard deviations) are provided for the normally distributed random parameters. (---) is Not Applicable. Statistically significant estimates at 95% credible level indicated by ^a. Statistically significant estimates at 90% credible level indicated by ^b. Model A – fixed parameter model. Model B – hierarchical fixed parameter spatial model. Model C – hierarchical random parameter spatial model. The dependent variable is the logarithm of the COVID-19 fatality rate per 1000 individuals in a census tract.

Table 5.

Heterogeneous elasticity estimates.

Variable	Model A		Model B		Best-Fit Model C
	Mean	SD	Mean	SD	Mean	SD
Walkability & Social Vulnerability
Quadrant 2: Low walkability & high vulnerability (base)	—	—	—	—	—	—
Quadrant 3: Low walkability & low vulnerability	−35.40	6.94	−23.90	7.39	−32.50	8.54
Quadrant 4: High walkability & low vulnerability	−24.16	7.43	−11.40	8.08	−20.19	8.65
Quadrant 1: High walkability & high vulnerability*	10.56	7.18	15.92	7.16	11.16	8.21
Travel Behavior
% of workers driving alone to work*	0.37	0.19	0.08	0.24	0.32	0.17
% of workers biking to work	−4.95	1.21	−3.79	1.37	−5.50	1.20
% of workers telecommuting*	−1.32	0.66	−0.59	0.69	−1.24	0.77

Notes. (*) indicates random parameters. (—) is Not Applicable. Model A – fixed parameter model. Model B – hierarchical fixed parameter spatial model. Model C – hierarchical random parameter spatial model. SD is standard deviation. Estimates show the% change in COVID-19 fatality rate associated with each of the independent variables shown.

4.1. Interactive impacts of walkability & social vulnerability on COVID-19 fatality rate

Interactions of neighborhood walkability and social vulnerability were statistically significantly correlated with COVID-19 mortality rates after accounting for the role of travel behavior, spatial, and non-spatial unobserved factors. Referring to Tables 4 and 5, the interactive impacts of neighborhood walkability and social vulnerability are captured by four indicator variables reflecting the four quadrants (Fig. 1). These quadrants include neighborhoods with high walkability and high social vulnerability (1st quadrant), low walkability and high vulnerability (2nd quadrant), low walkability and low vulnerability (3rd quadrant), and high walkability and low vulnerability (4th quadrant) – with neighborhoods in the 2nd quadrant used as a base in model estimation.

Compared to low walkability and high social vulnerability, neighborhoods with high walkability and low vulnerability (i.e., 4th quadrant representing the best-case scenario) had on average 20.2% (95% Bayesian Credible Interval: −37.2% to −3.3%) lower COVID-19 mortality rates. Identifying potential synergies between improvements in walkability and social vulnerability, this new finding highlights the protective role of improving neighborhood walkability and lowering social vulnerability in combating COVID-19. Note that this variable was statistically insignificant in the fixed parameter spatial model counterpart (Model B in Table 4) – highlighting the importance of accounting for unobserved heterogeneity impacts.

The mortality rates in neighborhoods with low walkability but lower social vulnerability as well (3rd quadrant) were on-average lower by 32.5% (95% Bayesian Credible Interval: −49.3% to −16.0%). Interestingly, compared to neighborhoods with low walkability and high social vulnerability, those with high walkability and social vulnerability (1st quadrant) on average had 11.2% higher COVID-19 mortality rates (despite heterogeneity in the impacts discussed later) (Tables 4 and 5).

These findings related to the 1st and 3rd Quadrants collectively highlight the relatively greater impact of the determinants of social vulnerability (e.g., sociodemographic factors) on COVID-19-related outcomes and are in line with previous studies documenting larger elasticity effects for socioeconomic variables compared to built environment features (Hu et al., 2021; Wali et al., 2022). Collectively, the new findings suggest that improvements in neighborhood walkability coupled with reductions in social vulnerability (i.e., the best-case scenario) can lead to significant reductions in COVID-19 mortality. However, between the two environmental metrics (social vulnerability vs. walkability), social vulnerability matters more with greater detrimental impacts on COVID-19 mortality. Precisely, the findings suggest that greater walkability levels can provide the desired COVID-19 health benefits only when it is accompanied by lower social vulnerability levels. This finding is especially important because more vulnerable communities exhibit major structural problems (including socioeconomic/housing disparities and spatial segregation) which are crucial social network barriers that need to be tackled for the impacts of walkability to even matter (Sallis et al., 2011). The built environment layout shapes social capital - with the two determining the magnitude of health inequity. The new results presented herein extend previous results analyzing built (Hamidi et al., 2020; Frank & Wali, 2021) and social environmental (Mesas et al., 2020; Hu et al., 2021) impacts in isolation and address a key knowledge gap by elucidating the interactive impacts of walkability and social vulnerability on COVID-19 associated mortality.

4.2. Correlations of travel behavior with COVID-19 fatality rate

Related to travel behavior, a one percent increase in the proportion of workers driving alone to work was associated with a 0.32% increase in COVID-19 mortality rates (Table 5). Conversely, a percent increase in the proportion of workers telecommuting and biking to work was correlated with a 1.24% (95% Bayesian Credible Interval: −2.8% to −0.3%) and 5.50% (95% Bayesian Credible Interval: −7.8% to −3.1%) reduction in COVID mortality rate, respectively (Tables 4 and 5). These findings highlight the detrimental effects of greater time spent in cars on chronic and infectious diseases (Frank et al., 2004, Dietz & Santos-Burgoa, 2020, Wali & Frank, 2021, Yates et al., 2021). These findings indicate that COVID-19 mortality rates may be reduced by discouraging auto use and encouraging active transportation. Overall, the above heterogeneous elasticity estimates for travel behavior measures are in the expected direction. For example, individuals who spend more time in cars (or conversely have low amounts of active travel such as biking) are more likely to have a greater prevalence of chronic disease (such as obesity) (De Nazelle et al., 2011), which is a key predictor of COVID-19 mortality (Frank & Wali, 2021). Likewise, the negative elasticity estimate of telecommuting on COVID-19 mortality risk is intuitive as telecommuting may lower individuals’ exposures thus lowering the risk of severe COVID-19 outcomes. We tested the proportion of workers using public transport as an exogenous/explanatory variable but found that it was not statistically significantly linked with COVID-19 mortality rates after controlling for the proportions of workers driving alone, biking, telecommuting, unobserved heterogeneity, and spatial heterogeneity. Also, note that the proportions of driving alone and transit exhibited a strong negative correlation (Pearson correlation of −0.83) as expected – thus transit variable was excluded to avoid any problematic multicollinearity. However, the potential impacts of transit use and other factors that are not available in the data would be tracked by the unobserved and spatial heterogeneity contours that are captured and quantified in this study (discussed below).

4.3. Spatially structured & unobserved random heterogeneity

The best-fit Full Bayes hierarchical random parameter spatial model (Model C) unveiled multiple layers of spatially structured and unobserved random heterogeneity. Compared to the traditional model (Model A), the standard deviation of the unstructured errors in the best-fit Model C dropped dramatically by around 44% (from 0.394 to 0.211) (Table 4). Between the two forms of heterogeneity (spatial vs. unobserved), the best-fit Model C implied that spatial heterogeneity accounted for 15% of the variations in COVID-19 mortality (compared to around 45% of heterogeneity attributed to spatial factors in Model B). These findings underscore the importance of simultaneously accounting for spatial and unobserved heterogeneity in the determinants of COVID-19 and that ignoring unobserved heterogeneity may overestimate the extent of spatial heterogeneity. It is noteworthy that even after accounting for unobserved heterogeneity, the scale parameter (standard deviation) of spatial heterogeneity in Model C was statistically significant. The spatially structured heterogeneity is illustrated in Fig. 3A highlighting the impacts of unobserved spatial factors on COVID-19 mortality.

Fig. 3.

Spatially structured & unobserved heterogeneity in impacts of exogenous factors. Notes. All estimates are based on the best-fit hierarchical Bayesian random parameter model (Model C). A shows the spatially structured heterogeneity. B-D shows the heterogeneous impacts of high walkability and high vulnerability, drive-alone population, and telecommuting population, respectively.

Related to unobserved heterogeneity, the impacts of three exogenous variables were found to be normally distributed random parameters. These variables include posterior Bayesian means of the parameter estimates on the indicator variable for high walkability and high social vulnerability, percent of workers driving alone to work, and percent of telecommuting workers. With a posterior mean of 0.112 and a standard deviation of 0.140 (Table 4), the associations between high walkability and high social vulnerability were positive for around 78% of the population and negative for the rest. Likewise, significant heterogeneity in the direction and magnitude of impacts is observed for drive-alone and telecommuting variables (Fig. 3). Positive associations between neighborhoods with a greater proportion of workers driving alone to work and COVID-19 mortality existed for around 70% of the population. Note that the findings on directional heterogeneity do not imply causation but highlight the role of other non-spatial unobserved factors whose impacts might manifest through the observed variables (e.g., travel behavior). As evident, such multifaceted insights into the complex spatial and unobserved heterogeneity contours cannot be obtained from traditional models.

While previous studies have individually examined unobserved heterogeneity (Frank & Wali, 2021; Wali & Frank, 2021) or spatial heterogeneity (Karaye & Horney, 2020; Sannigrahi et al., 2020) in the determinants of COVID-19 mortality, the present study methodologically contributes by simultaneously analyzing the two key sources of heterogeneity in a holistic and parsimonious Full Bayesian framework. Our results demonstrate the need to simultaneously capture spatial and unobserved random heterogeneity in the analysis of COVID-19 mortality outcomes.

4.4. Limitations

Neighborhood-level data from a single diverse county were used since high-resolution spatial COVID-19 data are unavailable for the entire nation or specific regions. We chose King County since up-to-date neighborhood-level (census tract level) COVID-19 data are publicly available and routinely updated by King County. Notably, as discussed earlier, the built environment contours in King County exhibited significant variations and appear to be representative of nationwide built environment distribution as documented in previous studies (Wali & Frank, 2021). However, caution is needed in generalizing the study results despite the similarities between the demographic and socioeconomic profiles nationwide and in King county discussed elsewhere (Wali & Frank, 2021). This study presented cross-sectional insights into the interactive impacts of walkability and social vulnerability. There is a need to validate these findings in a longitudinal framework providing insights into how changes in social vulnerability and walkability levels may predict changes in COVID-19 mortality outcomes. The present study did not control some factors (e.g., government financial aid and assistance actions by NGOs) that may be relevant to COVID-19 mortality outcomes. We were unable to control such factors as data on these variables are not publicly available at the neighborhood (census tract) level. While the present study did not explicitly quantify the associations of government financial aid and NGO assistance, our heterogeneity-based methodological framework accounts for the latent effects of such unobserved factors and are tracked as unobserved and spatial heterogeneity. Finally, this study focused on understanding the interactive impacts of the built and social environment on COVID-19 mortality rates. Future studies can extend the methodology presented in this study to analyze other COVID-19 health outcomes including infection rates.

5. Conclusions

To our knowledge, this is the first study providing a rigorous empirical assessment of the interactive impacts of social vulnerability and walkability on neighborhood-level COVID-19 mortality rates. Methodologically, the study contributed by specifying and developing advanced Full Bayes hierarchical random parameter spatial models to address spatial and unobserved heterogeneity in the determinants of COVID-19 mortality. Our findings suggest that the best-case scenario of greater neighborhood walkability coupled with lower social vulnerability was associated with significant reductions in COVID-19 mortality rates. Analysis of the interactive impacts of the two environmental metrics (social vulnerability vs. walkability) when only one of the two was in a healthful direction revealed significant offsetting effects. Neighborhoods with low walkability and low social vulnerability exhibited significantly lower mortality rates. On the contrary, despite heterogeneity, neighborhoods that had higher walkability coupled with greater social vulnerability on average exhibited greater COVID-19 mortality. These findings suggest that between the two environmental metrics (social vulnerability vs. walkability), social vulnerability matters more with greater detrimental impacts on COVID-19 mortality. Additionally, the evidence suggests that greater walkability levels can provide the desired COVID-19 health benefits only when it is accompanied by lower social vulnerability levels. These findings were robust to the travel behavior patterns and other spatial and non-spatial unobserved factors. The Full Bayes hierarchical random parameter spatial models unveiled significant spatial and unobserved heterogeneity in the determinants of COVID-19 mortality.

The study findings present methodological/academic and practical contributions. From a substantive viewpoint, the present study offers empirical evidence on how the built and social environments may interact to influence COVID-19 mortality. Methodologically, the study contributes by simultaneously analyzing two key sources of heterogeneity in a parsimonious Full Bayesian framework – with results demonstrating the exigency to capture spatial and unobserved random heterogeneity to obtain accurate and unbiased insights into the determinants of COVID-19 mortality outcomes. The research methodology presented in this study can be transferred to other regions nationwide as neighborhood-level COVID-19 data becomes publicly available for other regions. Spatial and unobserved heterogeneity contours are highly localized in nature, and the application of the study methodology in other regions can help develop place-based COVID-19 interventions. Finally, from a practical standpoint, the study findings have key implications for infectious disease prevention and control. An important finding for engineers and planners is that the underlying structural social vulnerability issues faced by our communities must be addressed first for the health impacts of more compact and walkable urban design to be realized and observed. It is increasingly important to simultaneously consider the physical and social barriers to health as urban design features continue to shape the social capital of our cities.

Declaration of Competing Interest

None.

Data availability

• Data will be made available on request.