Quantifying Disparities in Accessibility and Availability of Pediatric Primary Care across Multiple States with Implications for Targeted Interventions

Abstract

Objective

To quantify disparities in accessibility and availability of pediatric primary care by modeling interventions across multiple states that compare publicly insured versus privately insured children, and urban versus rural communities.

Data Sources

Secondary data sources include 2013 National Plan and Provider Enumeration System, 2009 MAX Medicaid claims, 2012 American Community Survey.

Study Design

The study models accessibility and availability of care for all children in seven states.

Methods

Optimization modeling with access constraints is used to estimate access. Statistical hypothesis testing is used to quantify systematic disparities.

Principal Findings

California has the best accessibility for privately insured children and Minnesota for publicly insured children. Mississippi has the lowest availability for both populations. Overall, the disparities in availability for pediatric primary care are not as significant as in accessibility. Both rural and urban communities are in need of improvement in accessibility to primary care for publicly insured children, although at varying levels across states.

Conclusions

Disparities in availability are not as significant as disparities in accessibility. Opportunities to improve access to pediatric primary care vary by state. Generating specific recommendations for small areas is critical to enabling health policy decision makers to improvement access.

Access to preventive health care is a major determinant of health among children (Marmot et al. 2008). Along with social and environmental factors, appropriate access to primary care for children can result in fewer missed days of school, lower emergency room utilization to treat ambulatory sensitive conditions, and better lifelong health (Starfield, Shi, and Macinko 2005; Macinko, Starfield, and Shi 2007).

Despite these benefits, children enrolled in either state Medicaid programs or state Children's Health Insurance Programs (CHIP) have historically received less primary care than children not eligible for public insurance (Berman, Wasserman, and Grimm 1991; Berman et al. 2002; Sebelius 2011). Reducing disparities and increasing access to person‐ and family‐centered care, including primary care for children, were identified as priorities for all federally funded insurance programs, including Medicaid and CHIP in the federal National Quality Strategy (2011 Report to Congress: National Strategy for Quality Improvement in Health Care; Burwell 2014).

The aim of this study was to understand differences in spatial access to pediatric primary across and within states. Spatial access has two substantive dimensions: (1) accessibility and (2) availability (Guagliardo 2004). Similar to Penchansky and Thomas (1981), for the purposes of this study, we define availability as providers’ patient volume or time available for health care delivery that patients would experience when seeking care and accessibility as the time and/or distance barriers that patients would experience in reaching their providers.

The study outcomes include quantification of systematic disparities of accessibility and availability measured at the census tract level accompanied by a systematic geographic analysis within states and between states in order to suggest interventions and to identify communities in need for improvement of pediatric primary care access. The states piloted in this analysis include southeastern states (Georgia, Louisiana, Mississippi, North Carolina, and Tennessee) and comparative states (California and Minnesota). The seven selected states vary significantly in implementation of Medicaid/CHIP programs, as well as in population size, population distribution, and demographics as detailed in Web‐Supplement A.

Specific research questions include the following:

• Are there systematic disparities in spatial access to pediatric primary care between states and within states?

• Are there systematic disparities in spatial access between publicly insured and privately insured children?

• Are there systematic disparities between children living in urban versus rural communities?

• Which communities are in need of improvement and which spatial access dimensions need to be targeted by policy makers?

The approach to addressing these questions introduces a comprehensive framework for studying disparities in spatial access. The modeling approach is data “rich,” mathematically rigorous, and computationally scalable, integrating large data and health policy in a systematic manner. As more data become available, the approach has the potential to provide even more specific information to target community or state‐specific interventions.

Methods

Modeling Overview

This paper uses a modeling approach to estimate access. It estimates assignments between patients and providers accounting for locations of each, the underlying need (using wellness visits by age as a proxy), patient trade‐offs between distance and crowding, and some limits in the system. This modeling approach has been found to be superior to catchment approaches, which underestimate access in dense areas (Li, Serban, and Swann 2015) and to simple ratios of providers and population by area (Gentili et al. 2015), which inaccurately portray access, especially at lower geographic granularity. The matching model also has the advantage over both catchment methods and simple ratios of accounting for specific types of barriers to access that are of significant concern in states with high poverty rates like the southeastern states, including the willingness of providers to accept Medicaid, and the limited transportation options of some participants.

Data and Estimation Approach: Supply of Pediatric Primary Care

The primary care supply consists of family medicine (Bazemore et al. 2012), internal medicine physicians (Freed et al. 2005), and general pediatricians and nurse practitioners specializing in pediatrics. Registered nurses and public health nurses were excluded. Providers’ practice location addresses are obtained from the 2013 National Plan and Provider Enumeration System (NPPES). A maximum provider caseload of 7,500 visits/year (approximately 2,500 patients/year) is assumed (Altschuler et al. 2012). Caseloads of general pediatricians and pediatric nurse practitioners are assumed to be completely devoted to pediatric care, while family and general physicians are assumed to devote 13.6 percent and internal medicine are assumed to devote 1.6 percent of their caseload to children provided by the National Ambulatory Medical Care Survey. Sensitivity analysis examined other variations on these percentages.

The 2009 MAX Medicaid claims data obtained from the Centers for Medicare and Medicaid Services are used to determine what providers have seen Medicaid patients. We further used the approach in Nobles, Serban, and Swann (2014) to inform the constraints on provider Medicaid acceptance by considering the aggregated count of providers accepting Medicaid at the county level and using a sampling technique to specify whether a provider accepts Medicaid.

Data and Estimation Approach: Need for Pediatric Primary Care

We focus on wellness visits and, thus, we apply the recommendations by the American Academy of Pediatrics to calculate the type and frequency of wellness visits/year by age with an average number of visits/year equal to 8, 1.6, and 1 for 0–1, 1–5, and 6–18 age groups, respectively. The patient population is aggregated at the census tract level, using the 2010 SF2 100 percent census data and the 2012 American Community Survey data to compute the number of children in each census tract by age class along with information on poverty and ownership of cars, to estimate access to private transportation means.

An estimation of the population of children at or below the minimum income‐eligibility threshold for public coverage according to federal law is derived using the thresholds in table 1 in Appendix SA2 (CMS 2014). We refer to this population as eligible to be publicly insured and those above the threshold as likely to be privately insured. We recognize the distinction is imperfect, including that some children may have both insurance types, some neither, and additional variations in coverage eligibility exist (e.g., medically needy).

We assume patients do not travel to excessively distant providers (i.e., more than 25 miles) as recommended by the Health Resources Services Administration and that those without private transportation in their household will travel a maximum distance of 10 miles. Street‐network distances are computed using the ArcGIS Network Analyst (Environmental Systems Research Institute, NY, USA).

Accessibility and Availability Measures

We apply the optimization model introduced in Gentili et al. (2015) to estimate served need for pediatric primary care by matching the available supply and the population‐based need of services under a series of access and system constraints. The model is applied to each of the seven states separately.

The model assumes that patients prefer to visit nearby and less congested/busy physicians; however, when a provider office has a high patient volume, families prefer providers or/and mid‐level providers farther away (Dill et al. 2013). Under these assumptions, the objective function of the optimization model is a weighted sum of the total distance travelled and of the provider preference contingent upon availability of the providers. The balance between these two components is controlled by a trade‐off parameter defining their relative importance. Experiments are run on the value of the trade‐off parameter to select a reasonable range. Thus, the overall model maximizes spatial access given the limitations of capacity and preferences (see Appendix SA3 for details).

The output of the model is the number of patients in each census tract of a given age matched to each provider in the network. While it is desirable to have all children matched, it is not feasible given the access standard of 25 miles or less and other constraints as above. Thus, we assume at least 90 percent of the population should be matched, where the specific value was obtained by experimentation.

Accessibility and availability measures of primary care at the census tract level are derived from the optimization model for all children, children eligible for public insurance, and children likely to be privately insured. Accessibility is quantified as the average distance a child in a census tract must travel for each visit to his/her matched provider; thus, smaller values of the measure indicate better accessibility. Availability is quantified by the congestion a child experiences for each visit at his/her matched provider, where patient congestion is measured as the ratio between all assigned visits to a provider and his/her maximum caseload; thus, smaller values indicate better availability. Children experiencing a distance of 25 miles or greater are assumed to be “unserved” by the existing network. Hence, the output represents the served need, which may be smaller than the need itself.

Extensive analysis was conducted to assess the sensitivity of the access estimates to variations in input data. For provider workload, 50 different parameter settings of the model are considered by varying the workload for each provider, differentiated by clinician type and gender. Thus, our output consists of 50 values of accessibility and availability measures for each census tract. We summarize the results based on all 50 settings.

We varied parameters for the provider workload of family/general practitioners and internists in specific ranges. We also tested the sensitivity of the model with respect to the percentage of providers’ caseload devoted to children eligible for public insurance by varying such a parameter within a specific range.

Details about the experimental settings are provided in Appendix SA3.

Systematic Disparities: Measures and Statistical Inference

Statistical Inference: Between‐State Disparities

To evaluate whether between‐state disparities in accessibility and availability are systematic, we apply the one‐sided hypothesis test of difference in the medians using the Wilcoxon signed‐ranked test, for each pair of states and for each population group. This hypothesis test applies under the independence assumption, which does not hold since the access measures are spatially dependent. Because of this limitation, the test is more conservative in detecting differences between states.

Most papers in disparities compare whether any difference exists (i.e., $\mathit{\delta }=0$). We consider multiple levels of differences to gain understanding of how large differences are, if they exist. The null hypothesis difference in medians thus takes three different levels for both accessibility and spatial availability:

• $\mathit{\delta }=0$, $\mathit{\delta }=1,$ or $\mathit{\delta }=2$ miles for the accessibility measure; and

• $\mathit{\delta }=0.0$, $\mathit{\delta }=0.1,$ or $\mathit{\delta }=0.2$ patient‐to‐provider caseload ratio for the availability measure.

Statistical Inference: Within‐State Disparities

We group census tracts into three categories according to their rural–urban commuting area code (RUCA; Morrill, Cromartie, and Hart 1999). We classify the census tracts as Large Urban Areas (RUCA = 1–3), Small Urban Areas (RUCA = 4–6), and Rural Areas (RUCA = 7–10). We then compare disparities in accessibility and availability between publicly eligible children and children likely to be privately insured.

Intervention Maps

We identify served, underserved, and unserved census tracts if the percentage of served need is at least 80 percent, between 50 and 80 percent, and less than 50 percent, respectively; these levels can be adjusted depending on the coverage targeted. The results are displayed as choropleth maps in Appendix SA5 and summarized in Table 3.

Using the method described in Serban (2011), we identify the specific tracts where the difference in either accessibility or availability between the children eligible for public insurance and those who are likely to be privately insured is statistically significant. Specifically, we consider the difference process $Z\left(s\right)=M\left(s\right)-O\left(s\right)$ for each spatial unit $s$ (i.e., census tract) within a geographic domain (e.g., state). We decompose $Z\left(s\right)=f\left(s\right)+{\mathit{\epsilon }}_s$, with $f\left(s\right)$ the regression function assumed unknown and estimated using nonparametric regression. Subsequently, we use the existing methods proposed by Serban (2011) and Krivobokova, Kneib, and Claeskens (2010) to estimate simultaneous confidence bands $\left[l\left(s\right),u\left(s\right)\right]$ for the regression function $f\left(s\right)$. For those spatial units $s$ or regions such that $u\left(s\right)<0$, the difference is significantly negative, while for those spatial units $s$ such that $l\left(s\right)>0$, the difference is significantly positive. The results are displayed as point maps, where the points correspond to the centroids of the census tracts where the difference process $Z\left(s\right)$ is significantly negative or positive, defined as significance maps. A significance level of 0.01 is used (see Appendix SA4).

Results

The study population represents more than 9 million children across approximately 16,500 census tracts served by a network of more than 17,000 unique provider locations representing around 76,000 individual and group providers.

Statistical Inference: Between‐State Disparities

Figure 1 displays the boxplots of the median of the access measures computed at the census tract level across all 50 settings for all census tracts in each of the seven states and for each population group. Table 1 in Appendix SA5 (Part 1) provides statistical summaries of the two measures. The median state‐level distance to care for children eligible for public insurance ranges from 7.54 to 9.79 miles. For children likely to be privately insured, it ranges from 4.78 to 8.50 miles. The median state‐level congestion for children eligible for public insurance ranges from 0.40 to 0.74. For children likely to be privately insured, it ranges from 0.39 to 0.70.

Figure 1.

Distribution of Median of the Distance (in miles) a Child Must Travel for Visits to Matched Providers, and of the Congestion, Measured as the Ratio between All Assigned Visits to a Provider and His/Her Maximum Caseload, for Different Population Groups

• Note. Each boxplot represents the distribution across census tracts after taking the median across the 50 runs for each census tract.

Table 1 summarizes the results of the statistical comparison of the median distance for children eligible for public insurance and children likely to be privately insured for each pair of states. The comparisons between congestion medians at the state‐level are summarized in table 2 in Appendix SA5 (Part 1) for both population groups. Table 3a and b in Appendix SA5 (Part 1) reports the p‐values for the comparison.

Table 1.

Between‐State Differences in Median Distance (in miles) a Child Must Travel for Visits to Matched Providers, by Insurance Type, Averaged across Fifty Runs

States	CA		GA		LA		MN
	Public	Private	Public	Private	Public	Private	Public	Private
CA			−0.8082	−2.3116	0.8931	0.5933	−0.6064	−2.9870
GA	0.8082*	2.3116*		−1.0000	1.7013*	2.9049*	0.2018*	−0.6754
LA	−0.8931	−0.5933*	−1.7013	−2.9049		−1.0000	−1.4996	−3.5804
MN	0.6064*	2.9870*	−0.2018	0.6754	1.4996	3.5804*
MS	2.4092**	4.7211***	1.6010*	2.4095*	3.3024**	5.3144**	1.8028**	1.7341*
NC	0.8453*	3.2631***	0.0371*	0.9515*	1.7384*	3.8564**	0.2389*	0.2761*
TN	1.1832*	2.4998**	0.3750	0.1882	2.0763*	3.0931*	0.5768*	−0.4872

States	MS		NC		TN
	Public	Private	Public	Private	Public	Private
CA	−2.4092	−4.7211	−0.8453	−3.2631	−1.1832	−2.4998
GA	−1.6010	−2.4095	−0.0371	−0.9515	−0.3750	−0.1882
LA	−3.3024	−5.3144	−1.7384	−3.8564	−2.0763	−3.0931
MN	−1.8028	−1.7341	−0.2389	−0.2761	−0.5768	0.4872
MS			1.5639*	1.4580	1.2260*	2.2213*
NC	−1.5639	−1.4580			−0.3379	0.7633*
TN	−1.2260	−2.2213	0.3379	−0.7633

For each run, we apply the one‐sided Wilcoxon test for comparison of medians of distance (in miles) for each pair of states for the children eligible for public insurance (Public) and children above the income threshold for public insurance (Private). The test compares H0: ${\mathit{\mu }}_{\mathrm{State}1}-{\mathit{\mu }}_{\mathrm{State}2}\le \mathit{\delta }$ vs. H1: ${\mathit{\mu }}_{\mathrm{State}1}-{\mathit{\mu }}_{\mathrm{State}2}>\mathit{\delta }$ (State 1 is specified by the row, and State 2 is specified by the column). A symbol “*,” “**,” and “***” in the cell indicates a p‐value ≤.01 in at least 75% of the runs for null difference in medians $\mathit{\delta }=0$, $\mathit{\delta }=1$, and $\mathit{\delta }=2$, respectively.

Comparing accessibility (Table 1, null value $\mathit{\delta }=0$), each state except Louisiana has a higher median distance than California for the eligible population, and all states have a higher median distance than California for the population likely to be privately insured; some differences remain significant at distance $\mathit{\delta }\le 2$ miles for the population likely to be privately insured. Mississippi has higher median distance than all the other states for the eligible population, and it has a higher distance than all the other states, except North Carolina, for the population likely to be privately insured. Several states have higher median distance than Louisiana or Minnesota ($\mathit{\delta }=0$ miles) for both population groups. There are no comparisons between pairs of states where the difference is statistically significant for $\mathit{\delta }\ge 2$ miles.

Comparing availability (table 2 in Appendix SA5 [Part 1], null value $\mathit{\delta }=0$), Mississippi has a higher median congestion for both the population groups than all the other states. Minnesota has a higher median congestion for both the population groups than all the other states except Mississippi. All states except North Carolina have a higher median congestion than Louisiana for children eligible for public insurance insured. And all states except North Carolina and Tennessee have higher median congestion for children likely to be privately insured. All differences in medians are not statistically significant for $\mathit{\delta }\ge 0.1$.

Statistical Inference: Within‐State Disparities

Table 2 shows that the median distance for the eligible children is statistically significantly higher than for children likely to be privately insured in each state and for all three urbanicity classes for a difference of $\mathit{\delta }=0$ miles. The differences remain statistically significant at $\mathit{\delta }\le 2$ miles for California for areas all urbanicity classes. These differences are not statistically significant for $\mathit{\delta }\ge 2$ for all the other states.

Table 2.

Within‐State Differences in Median Distance (in miles) a Child Must Travel for Visits to Matched Providers, and Median Congestion, Measured as the Ratio between All Assigned Visits to a Provider and His/Her Maximum Caseload

	Distance—Medians				Congestion—Medians
	State	Large Urban	Small Urban	Rural	State	Large Urban	Small Urban	Rural
California	3.3381***	5.8216***	2.3172***	9.7767***	0.0133*	0.0064*	0.1217*	0.3611*
Georgia	1.8348*	2.2379*	1.2642*	1.6948*	0.0504*	0.0474*	0.0509*	0.0842*
Louisiana	3.0383*	2.6598*	1.0970*	1.9829*	0.0424*	0.0591*	0.0394*	0.0497*
Minnesota	0.9575*	0.5092*	1.0071*	1.2097*	0.0012*	−0.0188	0.0333*	0.0424*
Mississippi	1.0263*	1.3521*	0.9263*	1.2245*	0.0233*	0.0048	0.0545*	0.0316
North Carolina	0.9203*	0.5494*	0.6730*	1.3608*	0.0436*	0.0000*	0.0327*	0.0858*
Tennessee	2.0216*	2.2643*	1.9465*	2.4214**	0.0605*	0.0504*	0.1124*	0.0671*

Difference in the median distance (in miles) and median congestion of children eligible for public insurance versus children above the income threshold for public insurance, averaged across the 50 runs. For each run, we apply the Wilcoxon paired statistical test H0: ${\mathit{\mu }}_{\mathrm{MED}}-{\mathit{\mu }}_{\mathrm{OTH}}\le \mathit{\delta }$; H1: ${\mathit{\mu }}_{\mathrm{MED}}-{\mathit{\mu }}_{\mathrm{OTH}}>\mathit{\delta }$ for each state for three different values of the hypothesized difference $\mathit{\delta }$ for the three different urbanicity classifications of the census tracts with respect to their RUCA category. Census tracts are classified as Large Urban Areas (RUCA = 1–3), Small Urban Areas (RUCA = 4–6), and Rural Areas (RUCA = 7–10). A symbol “*,” “**,” or “***” in the cell indicates a median p‐value over the 50 runs less than or equal to $\frac{\mathit{\alpha }}{4}$ ($\mathit{\alpha }=0.01)$, as specified in Bonferroni's method (Miller 1981) for correcting for multiple hypothesis tests, for null difference δ = 0, δ = 1, or δ = 2, respectively.

The eligible population has higher congestion in each state and for each urbanicity level with few exceptions at the null value $\mathit{\delta }=0.0$. These differences are not statistically significant for $\mathit{\delta }\ge 0.1$.

Comparisons of medians of distance and congestion of children likely to be privately insured versus children eligible for public insurance across urban and rural areas and across the 50 runs are shown in table 1 in Appendix SA5 (Part 1). The corresponding box plots are shown in figure 1 in Appendix SA5 (Part 1). The median distances for children eligible for public insurance range from 6.13 (large urban areas in Minnesota) to the maximum of 17.91 miles (rural areas in California). The median distances for children likely to be privately insured range from 4.44 (large urban areas in California) to 13.49 (rural areas in California) miles. The median congestion values for children eligible for public insurance range from 0.35 in large urban areas in North Carolina to the maximum of 0.79 in rural areas in California. The median congestion values for children likely to be privately insured range from 0.35 in large urban areas in North Carolina to 0.77 in rural areas in Mississippi.

Intervention Analysis

The number of served, underserved, and unserved census tracts in each state for different urbanicity areas is provided in Table 3. Table 4 and figure 2 in Appendix SA5 (Part 2) show the corresponding percentages at the state level and the corresponding maps.

Table 3.

Number of Census Tracts in Each State That Are Served, Underserved, and Unserved

State	Service Level	Entire State	Large Urban	Small Urban	Rural
CA	Served	7046 [7041, 7051]	6795 [6790, 6800]	195 [193, 196]	56 [54, 57]
	Underserved	576 [567, 583]	481 [474, 488]	44 [43, 47]	51 [49, 54]
	Unserved	378 [375, 382]	222 [219, 225]	54 [53, 55]	102 [101, 104]
GA	Served	1595 [1593, 1597]	1365 [1363, 1367]	152 [151, 152]	79 [78, 79]
	Underserved	234 [231, 236]	153 [151, 156]	40 [39, 41]	41 [39, 42]
	Unserved	126 [125, 128]	72 [71, 73]	28 [27, 28]	27 [26, 28]
LA	Served	959 [957, 960]	818 [817, 819]	78 [77, 78]	63 [62, 64]
	Underserved	98 [96, 100]	58 [57, 59]	18 [18, 19]	22 [20, 23]
	Unserved	68 [66, 69]	42 [42, 42]	4 [4, 4]	22 [20, 23]
MN	Served	1118 [1116, 1120]	866 [865, 868]	116 [115, 117]	136 [135, 137]
	Underserved	122 [120, 124]	43 [41, 44]	22 [22, 23]	57 [55, 59]
	Unserved	94 [93, 95]	14 [14, 15]	15 [15, 15]	65 [64, 66]
MS	Served	558 [556, 560]	258 [257, 259]	194 [193, 195]	106 [104, 107]
	Underserved	76 [74, 78]	27 [26, 28]	20 [19, 21]	29 [28, 31]
	Unserved	21 [21, 22]	6 [6, 6]	9 [9, 9]	6 [6, 6]
NC	Served	1828 [1825, 1831]	1439 [1437, 1442]	280 [278, 283]	108 [106, 109]
	Underserved	222 [218, 225]	129 [126, 132]	50 [47, 52]	43 [41, 46]
	Unserved	120 [118, 121]	62 [61, 64]	23 [22, 24]	35 [34, 36]
TN	Served	1215 [1213, 1217]	963 [961, 964]	156 [154, 157]	97 [95, 98]
	Underserved	174 [170, 177]	91 [88, 92]	48 [47, 50]	35 [33, 37]
	Unserved	91 [89, 92]	35 [34, 36]	24 [23, 25]	32 [30, 33]

A served census tract is such that at least 80% of the population in the census tract is assigned to a provider on average across the 50 runs. An underserved census tract is such that the percentage of the population in the census tract assigned to a provider is between 50% and 80% on average across the 50 runs. An unserved census tract is such that less than 50% of the population of the census tract is assigned to a provider on average across the 50 runs.

The average percentage of served census tracts across the 50 settings ranges from 82 percent (Georgia and Tennessee) to 88 percent (California); the average percentage of underserved census tracts ranges from 7 percent (California) to 12 percent (Georgia, Mississippi, and Tennessee); the average percentage of unserved census tracts ranges from 3 percent (Mississippi) to 7 percent (Minnesota).

Census tracts identified as served or unserved tend to be located in a subset of counties, while those identified as underserved are in many counties dispersed around the state. The served tracts tend to be located in large urban areas. The percentage of large urban census tracts among the served census tracts ranges between 46 percent (Mississippi) and 96 percent (California). The unserved census tracts are located in large urban areas in all the states except Minnesota where they are mostly located in rural areas (69 percent) and Mississippi where they are located in small urban tracts (43 percent).

Figure 2 shows the significance maps of Georgia as an example, with summary values in tables 5 and 6 in Appendix SA5 (Part 2). Significance maps for the remaining states are shown in figure 3 in Appendix SA5 (Part 2). The results are also summarized in tables 7–8 in Appendix SA5 (Part 2), which show the number of census tracts where the difference is statistically significantly positive, negative, or with no change, for three levels of the difference. The percentage of census tracts where children eligible for public insurance need to travel further to access care than the children likely to be privately insured ranges from 22 percent (North Carolina) to 71 percent (California). For δ = 2 miles, the percentage varies from 0 percent (Mississippi and Minnesota) to 35 percent (California) including many in large urban areas.

Figure 2.

Significance Maps for the State of Georgia for Distance and Congestion Measures, and the Urbanicity Map of the Census Tracts [Color figure can be viewed at wileyonlinelibrary.com]

• Note. Each dot on the map corresponds to a census tract where children eligible for public insurance has a statistically significantly greater distance (lower accessibility) or greater congestion (lower availability) than the children likely to be privately insured, at $\mathit{\alpha }=0.01$ significance level in at least 75% of the runs. The gray‐shaded regions on the maps correspond to counties where the children eligible for public insurance do not experience a significantly worse accessibility or availability in at least 75% of the runs. The map on the bottom shows the urbanicity classifications of census tracts in the state according to their rural–urban commuting area code (RUCA). We classify the census tracts as Large Urban Areas (RUCA = 1–3), Small Urban Areas (RUCA = 4–6), and Rural Areas (RUCA = 7–10).

There are relatively fewer census tracts where children eligible for public insurance have lower availability than the other children. The percentage of census tracts where the public insurance eligible experience higher congestion than the children likely to be privately insured ranges from 7 percent in Minnesota, Mississippi, and North Carolina to 24 percent in California. At $\mathit{\delta }$ = 0.0, the tracts where availability is lowest for the public insurance eligible tend to be more concentrated in small urban and rural areas in Minnesota and Mississippi and more concentrated in large urban areas in the other states.

Discussion

This study uncovers systematic differences and disparities in accessibility and availability of pediatric primary care across seven states for public insurance eligible and children above the income threshold for public insurance. Disparities are quantified between states and within states, comparing public insurance eligible versus likely to be privately insured children and across three urbanicity levels.

The paper also introduces a framework that can be used to help support policy making. The objective is to identify where the communities with the greatest need for improvement are and which spatial access dimensions need to be targeted by policy makers in order to increase access to primary care for children. This framework will be especially useful if local data are available and the model assumptions adjust to fit the data.

The between‐state pairwise comparisons reveal that children above the income threshold for public insurance have the best median accessibility in California, and public insurance eligible children have the best median accessibility in California, Minnesota, and Louisiana. The median availability is the lowest in Louisiana for both population groups. While disparities between states exist, they are not significant for pairwise comparisons when considering intervention levels of a difference ≥1 mile in travel distance (except for comparisons with California) or a difference ≥0.1 in experienced congestion (except for comparison with Minnesota and Mississippi). This is an important finding as many disparity studies have only drawn inferences at zero absolute differences between states or between population groups (Regidor 2004a, b; Harper and Lynch 2006; Harper et al. 2008). While there are disparities between states, they are significant at low comparison levels, suggesting that within‐state disparities are more relevant than those between states.

The within‐state systematic disparities are more nuanced when comparing accessibility and availability for the two population groups and across urbanicity levels. In general, we do find that public insurance eligible children experience lower access than children above the income threshold for public insurance. However, the difference in accessibility is >1 mile only for California, and for rural areas in Tennessee. The differences in availability are less systematic, with significant differences only for the level equal to 0.

The intervention analysis shows that the areas of lower spatial access can be found throughout a state across all urbanicity levels. Eligible children have worse spatial access than children likely to be privately insured across all the urbanicity levels. These findings highlight the importance of identifying specific areas where interventions are needed, with interventions targeted to the type of spatial access in need of improvement.

The findings for specific states may offer some guidance on where and how to target resources. For example, California has the greatest opportunity to improve accessibility for the public insurance eligible children as it has the largest percentage of communities (~53 percent) where the eligible children need to travel more than 1 mile further than the other children, in contrast to all other states for which the percentage ranges between 0 percent in Minnesota and 24 percent in Tennessee.

For other states such as Georgia and Minnesota, census tracts with high accessibility are geographically clustered, especially in urban areas, while being significantly worse for publicly insured children in some of those same areas. For the same states, communities with low availability are spread throughout the state; thus, interventions to improve availability are more challenging to implement as the communities in need are spread throughout the state as compared to interventions for improving accessibility. These findings suggest interventions need to be targeted to the local need, combining both policy interventions for improving public insurance acceptance by providers already in practice and network interventions that add providers to some areas (e.g., telehealth, school‐based health centers, and mobile clinics).

In states such as Tennessee, North Carolina, and Louisiana, public insurance eligible children experience lower accessibility and availability throughout the state, indicating that investments in multiple types of statewide interventions would be needed, particularly policy interventions targeting access for publicly insured children. In states such as Mississippi, spatial access is systematically low both populations; thus, targeting network interventions that would lead to an increase in the primary care providers, both physician and mid‐level providers, will have the highest impact.

Limitations

This study has several limitations, many of which stemming primarily from the limited availability of detailed data. First, we used income thresholds for public insurance programs to estimate the numbers of children who are publicly insured. Because the ACS data used to estimate household income are not the same as the units of measure for insurance eligibility and low‐income populations are more likely to live in multifamily households, the model may underestimate the number of children eligible for public insurance.

Second, because no single data source exists that identifies all providers who provide primary care to children or that quantifies caseload, we have used multiple data sources and a series of assumptions; thus, supply and locations of service may have been under‐ or overestimated. To know the supply of health care providers, we used the NPEES database for information on geolocation for each provider and on provider type. NPPES provides provider‐level data on both specialty and location; however, it has limitations. As some nurse practitioners bill under physician's national provide index (NPI), the supply of pediatric primary care may be underestimated. This may be offset by the fact some physicians spent significant time in supervising mid‐level providers as well as residents, interns, and fellows. Moreover, some providers may practice from different offices, while only the business address is provided with the provider's NPI. We also use the MAX files for obtaining information on the Medicaid acceptance rates, although Medicaid MAX files can have data quality issues, especially for states with large populations on managed care (Byrd and Dodd 2012). We did not capture the differences among states of the variation of providers’ caseload devoted to the publicly insured. It is also possible that there are some providers who would see patients on CHIP but not patients on Medicaid, and this is not captured in our data.

Third, household level data on transportation options by income thresholds for eligibility for public insurance were not available, so we compare the estimated income derived from census data with the federal net‐income thresholds instead of modified adjusted‐gross income (MAGI)‐equivalent minimum thresholds as defined in federal public insurance coverage laws and regulations.

A final limitation is the set of assumptions specifying some of the system constraints. We assume the maximum provider capacity is the same across all providers. We assume the same maximum willingness to travel for populations in both rural and urban areas. We do not account for changes in the percentage of physicians practicing pediatric primary care after 2013. We are also estimating need for pediatric care using recommendations for wellness visits for children. We do not include visits for minor illnesses or more intensive care for children with chronic or complex conditions. Thus, we underestimate the level of access for some children. We assume that the disutility of crowding is linear, although in other papers we have shown how the model can incorporate nonlinear functions. We also estimate matches between patients and providers assuming a centralized framework; in other papers, we have shown how the model can incorporate decentralized decision making with patients maximizing their own individual welfare.

Overall, most of the above stated assumptions can be relaxed with the acquisition of local‐level, detailed data. This would be paired with minor modifications to the model used to account for the provider‐specific or geographic‐specific data.

Conclusions

Even though this study has limitations, it has potential implications for public health and health care policy. While concerns about the availability of primary care providers have been expressed within recent health policy, this study finds that across states the disparities in availability for pediatric primary care are not as significant as the disparities in accessibility. Moreover, contrary to some beliefs, despite potential gains in insurance coverage over the last several years, both rural and urban communities are in need for improvement of accessibility to primary care for publicly insured children.

More generally, the findings in this study suggest that some policies will be more effective than others in addressing disparities in spatial access, while the policy recommendations depend on the state. For some states, incentivizing providers to accept public insurance could improve spatial access for public insurance eligible children, but incentivizing providers in some other states would not generate the same result as access for children likely to be privately insured also needs improvement. For all states, as unserved communities are spread across counties, interventions to provide access to pediatric primary care for these communities need to be more targeted, for example, school telehealth clinics at school‐based health centers.

The study thus shows that generating specific recommendations for small areas within states is needed to shift the needle on access to care for children. This can be performed with additional data specific to local areas with minor modifications to the model. Continuing to refine the model and data will ensure that the approach is reliable and accurate, while promoting the use of interventions that are most appropriate in a given locale.

Supporting information

Appendix SA1: Author Matrix.

Appendix SA2: Additional Information about the Data.

Appendix SA3: Mathematical Model, Parameters and Experiments Setting.

Appendix SA4: Details on Statistical Methods Used.

Appendix SA5 (Part 1): Additional Figures and Tables (Part 1) including Tables 1, 2 ,3a, and 3b and Figure 1.

Appendix SA5 (Part 2): Additional Figures and Tables (Part 2) including Tables 4‐8 and Figure 2‐3.