Disparities in Spatial Access to Emergency Surgical Services in the US

Key Points Question How does spatial access to emergency surgical services vary across the US, and what community characteristics are associated with low access to care? Findings In this cross-sectional study using advanced geospatial metrics that capture distance, hospital capacity, and population demand for all 320 million US residents in 2015, an estimated 1 in 10 residents experienced low access to any hospital with emergency surgical capabilities, and 1 in 4 experienced low access to hospitals with advanced clinical resources. Communities with high proportions of uninsured, publicly insured, and racial and ethnic minority groups in micropolitan and rural regions were at the greatest risk of being in low-access areas. Meaning Substantial disparities exist in spatial access to emergency surgical care across the US; comprehensive metrics of spatial access, such as enhanced 2-step floating catchment models, should be adopted to identify targets for surgical health system development.


eMethods: Gravity-based spatial access model
Realizing the limitations of both travel impedance (cost) measures and provider-population ratios in modeling spatial access to healthcare, researchers have adopted gravity models to account for the complicated interactions among healthcare supply, population demand for healthcare, and travel impedance between population locations and healthcare sites. [1][2][3][4] Gravity-based spatial access models estimate spatial access to medical services based on the law of gravitation. 5 Specifically, gravity models assume a population site's spatial access to a medical site decreases with the increase of travel distance to that medical site. A distance impedance function, f(d), is generally used to model the influence of travel distance d on the spatial access.
One of the most commonly used and widely validated gravity models is the enhanced 2-step floating catchment area (E2SFCA) method. 2,3,6-8 Given m population sites (e.g., CBG centroids) and n medical sites (e.g., hospitals) in a study area, E2SFCA works in two steps. The first step calculates the supply-demand ratio of each medical site, j. Specifically, it generates a 60-minute driving zone (also called a catchment area) around j, divides the catchment into four contiguous zones based on predefined driving time intervals (e.g., 0-10 min, 10-20 min, 20-30 min, 30-60), searches all population sites within each zone, and calculates the supply-demand ratio for j by where is the medical capacity (estimated by number of inpatient beds) of medical site j, is the population size of the kth population site within the catchment, is the travel cost between j and k, is the rth sub-zone, and is a distance-based weight for . Following previous studies 1,3,4 , we used the Gaussian function (i.e., ( ) = − 2 ⁄ where d represents a distance and represents an impedance parameter) to calculate . More details on the Gaussian function and the calculation of can be found in Wan et al. 2012 4 .
The second step of E2SFCA is to calculate a Spatial Access Index (SPAI) for each population site i. Specifically, a 60-min catchment and four driving zones (i.e., 0-10 min, 10-20 min, 20-30 min, 30-60 min) are generated for i, following the same procedures in the first step. Then it summarizes the supply-demand ratios of all medical sites within the catchment using the following formula: where is the SPAI for i, is the supply-to-demand ratio (calculated in step 1) of medical site k that falls inside the catchment of i, and is the travel time between k and i. is the same distance-based weight calculated in step 1.
The E2SFCA implements the idea of gravity assumption, as a shorter distance denotes a higher population demand for a hospital (realized by function f(d) in step 1) and better spatial access for a population site (realized by function f(d) in the second demand). Therefore, a higher denotes a better spatial access, and vice versa.
The above mentioned E2SFCA method will be used to examine spatial access to emergency surgical services (for both all hospitals with emergency surgical capabilities and advanced-resource centers) in the United States in this study. Specifically, the population size of each CBG is used to approximate demand and number of inpatient beds at each hospital is used to represent the relative capacity of each hospital. CBG population size is the most direct measure of population demand, as CBG-level estimates of EGS disease are not available. Hospital bed number is commonly used as a marker of facility size and capacity and is frequently used in health care research and planning. Both CBG population size and number of hospital beds are standard measures used in other studies of spatial access to hospital care using E2SCA models. [9][10][11] To minimize the influence of the infamous distance impedance problem (i.e., the selection of the impedance parameter could influence the spatial access results), we used a weighted spatial access index, Spatial Access Ratio (SPAR) 4 , to represent the eventual result. SPAR for a population site is calculated as the ratio between that population site's SPAI and the average of SPAI among all population sites in the study area. The higher the SPAR, the better the spatial access. And SPAR values great than one means better-than-state-average spatial access, and vice versa. SPAR has been proved effective in overcoming the distance impedance problem in multiple studies and has been used to explore spatial access to a variety of healthcare services 1,12-14 . eTable 2: Regional variation in proportion of population living in CBGs with low access to any EGS-capable hospital

Multinomial
Model aRR (95% CI) ±Logistic regression model adjusts for spatial autocorrelation using an exponential spatial covariance structure, where covariance between observations is based on Euclidian distance between centroids ^p<0.05; *p<0.001