Healthcare resources are crucial but limited, requiring careful consideration and informed allocation based on population needs. In the US, healthcare spending has consistently exceeded that of 38 other high-income countries, reaching 12.5% of GDP in 2000 and 17.8% in 2021 (1). Despite this substantial investment, the performance of the US health care system has been comparatively poor, ranking last among 11 high-income countries (2). The emergence of infectious diseases, such as COVID-19, further strains healthcare systems by escalating the demand for resources. In such challenging circumstances, maximizing access to healthcare services becomes paramount.

Barriers associated with access to healthcare have commonly been grouped into five dimensions: availability, accessibility, affordability, acceptability, and accommodation (3). Availability is often defined as the number of service or supply points, such as clinics or hospitals, while accessibility concerns the travel impedance between points of demand and points of service. In resource allocation settings, particularly during unprecedented events such as the COVID-19 pandemic or to address chronic priority health problems, availability and accessibility should be considered simultaneously. This combined measure is often referred to as spatial accessibility. In 2000, Radke and Mu (4) proposed the two-step floating catchment area (2SFCA) methodology to evaluate spatial accessibility to social services, building upon previous work by Shen (5) and Weibull (6). This method, later refined by Luo and Wang (7, 8), employs two core steps to measure spatial accessibility based on a travel impedance measurement, such as travel distance or time. Compared to previous methods, the 2SFCA utilizes a floating “catchment” that is not restricted by county or other geographical delineations. Since its inception, the methodology has been expanded, refined, and adjusted to create a family of spatial accessibility methods defined broadly as the floating catchment area (FCA) family. FCA methods have been used to assess spatial accessibility to health care facilities and primary care physicians (7, 9–13), care facilities for older adults (14), cancer care (15), pharmacies (16), parks and green spaces (17), and food stores (18). Since the COVID-19 pandemic, the FCA methods have gained substantial popularity, and have been utilized to assess access to testing sites, vaccination centers, and other services related to pandemic response (19–22). These analyses have aided in evaluating pandemic response strategies and guided decisions for optimizing resource allocation during such crises.

Despite the FCA family's popularity, there remains a significant knowledge gap in comprehensive comparisons between various FCA method parameters through the public health lens. One study compared the relative importance of distance decay (travel impedance) function selection and catchment area thresholds, but it lacked a public health focus and perspective (23). Another study by Wang et al. (24), compared three GIS-based accessibility approaches, including the gravity model from which the FCA is derived, to urban parks in Australia and the Netherlands. A recent study by Luan et al. (25), compared multiple measures of accessibility in New York City using the 2SFCA and Gaussian 2SFCA approaches, emphasizing health-related shortage areas. To our knowledge, no study has provided a comprehensive comparison of FCA accessibility parameters across Texas from a public health perspective. Therefore, our objectives were to compare county-level accessibility patterns from the 2SFCA approach across (i) two kernel density functions for travel impedance and (ii) 10 different catchment thresholds, indicating the maximum travel time or distance.

We used an early sample of data on clinics participating in a telehealth program designed to provide community-based Texas primary care physicians (PCPs) and pediatricians with mental health consultation services from child psychiatrists and other mental health professionals to meet the behavioral health needs of children and adolescents (26). We chose these data to illustrate a public health response to the ongoing rise in mental health problems in the US, especially among adolescents. According to a recent survey by the Centers for Disease Control and Prevention (CDC), the proportion of emergency department visits related to mental health issues increased by 24% among children aged 5–11, and by 31% among adolescents aged 12–17 from 2019 to 2020 (27). Further, social and economic factors, including socioeconomic status, insurance coverage, and stigma, have been previously shown to be barriers to mental health services and may further decrease access for vulnerable and underserved children and adolescents (28–31). With the dual objective of performing a comparative analysis and addressing the need for refined spatial evaluation methods to guide equitable allocation of scarce mental health resources for children and adolescents, our study contributes to the field of spatial accessibility research and its relevance in tackling critical healthcare challenges.

We applied the 2SFCA method with a continuous kernel density distance decay function to the Texas clinic dataset described above and ADHD prevalence data provided by Zgodic et al. (37). The estimated county-level ADHD prevalence among children and adolescents aged 5–17 presented substantial geographical variation, ranging from 2.28% in Kenedy County to 35.26% in Galveston County (median [IQR]: 14.94 [11.93, 17.40]) (Figure 2A). The estimated ADHD count, reflecting pediatric demand, was highly skewed (median [IQR]: 476.5 [143, 1485]) with urban areas such as Houston, Dallas, Austin, and San Antonio showing higher counts compared to rural areas.

At the time of analysis, clinics enrolled in the 1st year of the program were present in 193 of the 254 Texas counties. However, the number of enrolled clinics per county varied substantially and was highly skewed with 73.06% (141 of 193) of counties having 1–5 enrolled clinics, while 2.59% (5 of 193) had over 100 (Supplementary Figure 1C). Moreover, urban counties had more clinics compared to rural counties (Urban: 6 [1, 18.75]; Rural: 1 [0, 2]), with clinics heavily clustered around urban centers (Supplementary Figure 2). We also calculated the number of enrolled clinics per 100,000 population aged 5–17 at the county level, which ranged from 0 to 854.7 (median [IQR]: 40.48 [9.69, 74.90]) (Figure 2B). Accounting for the study population size, rural counties tended to have a higher, but more variable, enrolled clinic count per 100,000 (Urban: 29.09 [11.56, 54.01]; Rural: 47.62 [0, 85.21]).

For the kernel density 2SFCA, we compared accessibility across two kernel distance decay functions, the Epanechnikov and Quartic, and across a selection of maximum catchment areas (d_max) based on travel time thresholds (30, 45, 60, 90, and 120 min) and thresholds determined by the percent of the population with access to at least one point of supply (80%, 85%, 90%, 95%, and 100%). SPAR values, representing spatial accessibility scores, ranged from 0 to 15.88 (SD: 1.62) for a 30-min travel time catchment. As travel time increased to 90 min, the geographic spread and variability of SPAR reduced to a range of 0.022–11.20 (SD: 0.98) (Figure 3). Urban counties had lower average SPAR values (30 min: 0.48 [0.25, 0.79]; 90 min: 0.89 [0.63, 1.20]) compared to rural counties at the same catchment criteria (30 min: 0.70 [0.20, 1.45]; 90 min: 0.83 [0.50, 1.21]), though this difference was less pronounced at larger catchments. Between the 30- and 90-min catchments, specific regions in West Texas, including Jeff Davis, Presidio, and Brewster counties, exhibited the greatest change in SPAR, transitioning from the very low accessibility category (SPAR values between 0.0 and 0.5) at 30 min to the highest accessibility (SPAR values above 5) at 90 min (Figure 3). In contrast, portions of central and southern Texas consistently fell within the lowest accessibility category across all specified catchments and distance decay functions (Supplementary Figures 3–6). Highly populated counties such as Harris (including Houston), Dallas, and Tarrant (including Fort Worth) had an improvement regarding access category between 30- and 90-min (Figure 3), while Travis County, which includes Austin, remained within the same access category between both catchment selections. Changing the maximum catchment area by travel time resulted in distinct variations in the SPAR values across Texas, presenting noticeable geographic patterns. When holding the travel time constant but varying the decay functions in defining the catchment areas, SPAR values were highly correlated (Pearson's correlation coefficient r: 0.92–0.99) between the Epanechnikov and Quartic kernel distance decay functions (Supplementary Figures 7, 8 and Supplementary Table 1) Finally, achieving 80% access for the demand population required a catchment of 26.15 min, while 100% access required 72.66 min (Figure 3).

Bivariate mapping is a useful approach to visually investigate the association of the SPAR with another relevant areal characteristic using a color scale to highlight areas potentially in need of new resource implementation. To illustrate this method, Figure 4 presents the bivariate map of estimated ADHD prevalence and county-level SPAR values for four selected catchments of 30-min or 90-min travel time, and 80% or 100% population with access. We categorized SPAR into terciles representing low, medium, and high access, for each of the four catchments. Estimated ADHD prevalence was also divided into equal-sized terciles of low, moderate, and high groups. Counties with high prevalence, but very low access, represent potential areas to prioritize for future program outreach and enrollment efforts. With a catchment of 30- and 90-min, 29 and 33 counties had high prevalence but very low access to enrolled clinics, respectively. Additionally, Figure 5 presents the bivariate map of county-level SVI and SPAR values for the same selected catchments. SVI was categorized into terciles, representing low, medium, and high vulnerability. Counties with low access, but high vulnerability may also be suitable areas to prioritize for future program allocation. For both 30- and 90-min catchments, 27 counties had high vulnerability, but very low access to enrolled clinics. Among these counties, several urban and highly vulnerable areas were identified, including Nueces, Polk, and Trinity counties, suggesting these counties may be suitable areas for future priority enrollment efforts.

In this study, we compared the relative impact of key 2SFCA method inputs, specifically the distance decay function and catchment area. We then assessed the resulting spatial accessibility measures for clinics enrolled in a statewide child and adolescent psychiatric consultation program, specifically noting regions in Texas that consistently had poor access across method inputs. Pockets of low access were observed in central and southern Texas paired with high vulnerability. Further, a more spatially granular investigation of large urban centers will be required for a complete picture of access to pediatric mental health services. While we use this Texas clinic data, this study is not intended as an evaluation of the program, but as guidance for selecting spatial methods to evaluate future program enrollment or other intervention efforts.

The inclusion of distance decay functions in spatial accessibility analysis has been explored to account for travel impedance within the catchment. We considered the Epanechnikov and Quartic decay functions previously used to assess spatial accessibility (10, 18), and found that county-level SPAR were similar and highly correlated between both distance functions for the same catchment area value (Supplementary Table 1). This consistency aligns with previous studies (23, 41), suggesting that the specific choice of distance decay may be less critical in practice. Conversely, the selection of the catchment area exhibited a more significant impact on accessibility trends, as evidenced by the notable increase in SPAR values in counties like Jeff Davis, Presidio, and Brewster when the catchment was increased from 30- to 90-min. Smaller catchments (e.g., 30 min) displayed more discrete and local geographic variability, while larger catchments (e.g., 90 min) produced geographically smoother patterns of SPAR, as expected (see Figure 3). However, despite changes in the state-wide accessibility patterns, clusters of counties in central and southern Texas consistently remained in the lowest SPAR category, indicating low accessibility across all catchments.

While some general benchmarks exist in the FCA literature, catchment area specification is often arbitrary (12) and loosely grounded in empirical data on care-seeking behavior (12, 45, 46). Certain population characteristics have been previously investigated in relation to care-seeking behavior. Previous work has shown that residents of rural counties are often more willing to travel further for care than their urban counterparts (50, 51). Further, car ownership is not universal and urban residents in particular may utilize alternative modes of transportation, such as public transport, cycling, or walking (11, 13, 52, 53). Various catchments and multi-modal transportation have been proposed in the 2SFCA approach to address differences in supply capacity and care-seeking behavior. For example, Tao et al. (20) used facility size to inform supply catchments and Bauer and Groneberg (45) integrated different distance decay and catchments, to capture consumer behavior variations.

However, determining the optimal catchment area to accurately represent the “true” accessibility pattern remains a challenge since care-seeking behavior is often tied to specific healthcare needs of the study population and region. Data on specific care-seeking behavior to define the optimal catchment is often not available. For example, one study compared the realized and acceptable access to primary and specialist care (54). Various demographic factors influenced acceptable differences including age and town size for primary care and income for specialist care. To the best of our knowledge, no such study exists for Texas; factors influencing realized and acceptable access to primary and specialist services are likely to differ. Other dimensions of accessibility, notably affordability (e.g., out-of-pocket costs, insurance coverage), are also likely to influence realized access, but are not incorporated into the FCA framework. Programs like CPAN may help to overcome other accessibility barriers by linking primary care providers with specialist consultations, which may directly improve patient care and help to build PCP capacity to manage future similar cases (55).

Comparing the resulting SPAR values to estimated ADHD prevalence patterns (Figure 4) and SVI (Figure 5) revealed a more nuanced pattern across counties. Assessing SPAR alone, central and southern Texas counties fell within the lowest accessibility category. Priority counties may further be specified by identifying which counties have particularly low access and/or high social vulnerability, but relatively higher demand. Most counties in southern Texas had low access coupled with low demand. By contrast, counties such as Bandera, Kerr, Kimble, and Neuces may be higher priority counties for future CPAN enrollment as they exhibit very low access but fall within the highest tercile of ADHD prevalence across multiple applied catchment areas. However, the observed bivariate patterns may be misleading, particularly in large urban areas (e.g., Harris County), as we were unable to account for clinic capacity. Further, consideration for varying levels of ADHD diagnosis could have affected the findings. A complete discussion on patterns of diagnosis for ADHD is beyond the scope of this paper, as ADHD prevalence was one example measure selected among various other mental health conditions that affect children and adolescents.

Our study has a few limitations of note. First, we were unable to incorporate a measure of supply capacity (e.g., the number of primary care physicians, pediatric patient load) due to data limitations and restrictions, whereby only the location of the clinics was available. This may have had the strongest impact on urban clinics, which may be equipped to handle a larger influx of patients than their rural counterparts. The lack of supply capacity may explain why some urban areas like Houston, where the Texas Medical Center is located, received lower accessibility scores. Second, the 2SFCA method provides a simplification of travel behavior complexity. Improving data availability on care-seeking behavior, including the relative importance of distance impedance versus other barriers to care such as out-of-pocket costs, is crucial to inform the catchment parameters of the FCA methodology and better guide policy. Travel distance has been shown to reflect a significant barrier to care, especially for rural regions (51, 56); however, with the rise of Telemedicine as a popular alternative for seeking health services (particularly in mental health services), the role of distance as a barrier to care may shift, necessitating a reevaluation of FCA and other accessibility approaches. Finally, our analysis only provides a broad, state-wide assessment of accessibility. The 2SFCA approach assumes a uniform population distribution within the catchment area, which may not reflect the actual population distribution, particularly for catchment areas that include large urban areas and small rural counties. The realized accessibility of more granular units, such as neighborhoods, may be obscured by county-level patterns.