The Annals of Applied Statistics

Spatial accessibility of pediatric primary healthcare: Measurement and inference

Mallory Nobles, Nicoleta Serban, and Julie Swann

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Although improving financial access is in the spotlight of the current U.S. health policy agenda, this alone does not address universal and comprehensive healthcare. Affordability is one barrier to healthcare, but others such as availability and accessibility, together defined as spatial accessibility, are equally important. In this paper, we develop a measurement and modeling framework that can be used to infer the impact of policy changes on disparities in spatial accessibility within and across different population groups. The underlying model for measuring spatial accessibility is optimization-based and accounts for constraints in the healthcare delivery system. The measurement method is complemented by statistical modeling and inference on the impact of various potential contributing factors to disparities in spatial accessibility. The emphasis of this study is on children’s accessibility to primary care pediatricians, piloted for the state of Georgia. We focus on disparities in accessibility between and within two populations: children insured by Medicaid and other children. We find that disparities in spatial accessibility to pediatric primary care in Georgia are significant, and resistant to many policy interventions, suggesting the need for major changes to the structure of Georgia’s pediatric healthcare provider network.

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Ann. Appl. Stat., Volume 8, Number 4 (2014), 1922-1946.

First available in Project Euclid: 19 December 2014

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Healthcare access optimization model pediatric healthcare spatial accessibility spatial-varying coefficient model


Nobles, Mallory; Serban, Nicoleta; Swann, Julie. Spatial accessibility of pediatric primary healthcare: Measurement and inference. Ann. Appl. Stat. 8 (2014), no. 4, 1922--1946. doi:10.1214/14-AOAS728.

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  • Assuncao, R. M. (2003). Space varying coefficient models for small area data. Environmetrics 14 453–473.
  • Berman, S., Dolins, J. et al. (2002). Factors that influence the willingness of private primary care pediatricians to accept more Medicaid patients. Pediatrics 110 239–248.
  • Braveman, P. and Gruskin, S. (2003). Defining equity in health. Journal of Epidemiology and Community Health 57 254–258.
  • Buja, A., Hastie, T. and Tibshirani, R. (1989). Linear smoothers and additive models. Ann. Statist. 17 453–555.
  • Diggle, P. (1985). A Kernel method for smoothing point process data. J. R. Stat. Soc. Ser. C Appl. Stat. 34 138–147.
  • Drake, B. and Rank, M. R. (2009). The racial divide among American children in poverty: Reassessing the importance of neighborhood. Children and Youth Services Review 31.
  • Fan, J. and Zhang, J.-T. (2000). Two-step estimation of functional linear models with applications to longitudinal data. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 303–322.
  • Fiscella, K. and Williams, D. (2004). Health disparities based on socioeconomic inequities: Implications for urban health care. Academic Medicine 79 1139–1147.
  • Fleurbaey, M. and Schokkaert, E. (2009). Unfair inequalities in health and health care. Journal of Health Economics 28 73–90.
  • Gelfand, A. E., Kim, H.-J., Sirmans, C. F. and Banerjee, S. (2003). Spatial modeling with spatially varying coefficient processes. J. Amer. Statist. Assoc. 98 387–396.
  • Guagliardo, M. F. (2004). Spatial accessibility of primary care: Concepts, methods and challenges. International Journal of Health Geographics 3 1–13.
  • Guagliardo, M. F., Ronzio, C. R., Cheung, I., Chacko, E. and Joseph, J. G., (2004). Physician accessibility: An urban case study of pediatric providers. Health Place 10 273–283.
  • Hambidge, S., Emsermann, C. et al. (2007). Disparities in pediatric preventive care in the United States. Archives of Pediatric and Adolescent Medicine 161 30–36.
  • Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Monographs on Statistics and Applied Probability 43. Chapman & Hall, London.
  • Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. J. R. Stat. Soc. Ser. B Stat. Methodol. 55 757–796.
  • Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85 809–822.
  • Jiang, H. (2010). Statistical computation and inference for functional data analysis. Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
  • Joseph, A. and Phillips, D. (1984). Accessibility and Utilization: Geographical Perspectives on Health Care Delivery. Harper and Row, New York.
  • Khan, A. (1992). An integrated approach to measuring potential spatial access to healthcare services. Socio-Economic Planning Sciences 26 275–287.
  • Kids Count National Indicators (2010). Data Center, Baltimore MD.
  • Krivobokova, T., Kneib, T. and Claeskens, G. (2010). Simultaneous confidence bands for penalized spline estimators. J. Amer. Statist. Assoc. 105 852–863.
  • Li, Y. and Ruppert, D. (2008). On the asymptotics of penalized splines. Biometrika 95 415–436.
  • Luo, W. and Qi, Y. (2009). An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians. Health Place 15 1100–1107.
  • Marcin, J., Ellis, J. et al. (2004). Using telemedicine to provide pediatric subspecialty care to children with special health care needs in an underserved rural community. Pediatrics 13 1–6.
  • Marmot, M., Friel, S. et al. (2008). Closing the gap in a generation: Health equity through action on the social determinants of health. Lancet 372 1661–1669.
  • Marsh, M. T. and Schilling, D. A. (1994). Equity measurement in facility location analysis: A review and framework. European J. Oper. Res. 74 1–17.
  • McGrail, M. R. and Humphreys, J. S. (2009). The index of rural access: An innovative integrated approach for measuring primary care access. BMC Health Services Research 9. DOI:10.1186/1472-6963-9-124.
  • Nobles, M., Serban, N. and Swann, J. (2014). Supplement to “Spatial accessibility of pediatric primary healthcare: Measurement and inference.” DOI:10.1214/14-AOAS728SUPP.
  • Odoki, J., Kerali, H. and Santorini, F. (2001). An integrated model for quantifying accessibility-benefits in developing countries. Transportation Research Part A: Policy and Practice 35 601–623.
  • Parzen, E. (1962). On estimation of a probability density function and mode. Ann. Math. Statist. 33 1065–1076.
  • Pearce, L. D. (2002). Integrating survey and ethnographic models for systematic anomalous case analysis. Sociological Methodology 32 103–132.
  • Penchansky, R. and Thomas, J. W. (1981). The concept of access. Med. Care 19 127–140.
  • Perloff, J., Kletke, P. and Fossett, J. (1995). Which physicians limit their Medicaid participation, and why. Health Services Research 30 7–25.
  • Reardon, S. F., Matthews, S. A., O’Sullivan, D., Lee, B. A., Firebaugh, G., Farrell, C. R. and Bischoff, K. (2008). The geographic scale of metropolitan racial segregation. Demography 45 489–514.
  • Ruppert, D., Wand, M. P. and Carroll, R. J. (2003). Semiparametric Regression. Cambridge Series in Statistical and Probabilistic Mathematics 12. Cambridge Univ. Press, Cambridge.
  • Serban, N. (2011). A space–time varying coefficient model: The equity of service accessibility. Ann. Appl. Stat. 5 2024–2051.
  • Talen, E. and Anselin, L. (1998). Assessing spatial equity: An evaluation of measures of accessibility to public playgrounds. Environment and Planning B: Planning and Design 30 595.
  • Tibshirani, R. and Knight, K. (1999). The covariance inflation criterion for adaptive model selection. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 529–546.
  • Walker, L. O., Sterling, B. S., Hoke, M. M. and Dearden, K. A. (2007). Applying the concept of positive deviance to public health data: A tool for reducing health disparities. Public Health Nurs. 24 571–576.
  • Waller, L. A., Zhu, L., Gotway, C. A., Gorman, D. M. and Gruenewald, P. J. (2007). Quantifying geographic variations in associations between alcohol distribution and violence: A comparison of geographically weighted regression and spatially varying coefficient models. Stoch. Environ. Res. Risk Assess. 21 573–588.
  • Wang, F. and Luo, W. (2005). Assessing spatial and nonspatial factors for healthcare access: Towards an integrated approach to defining health professional shortage areas. Health Place 11 131–146.
  • Williams, D. R. and Mohammed, S. A. (2009). Discrimination and racial disparities in health: Evidence and needed research. Journal of Behavioral Medicine 32 20–47.
  • Wu, H. and Liang, H. (2004). Backfitting random varying-coefficient models with timedependent smoothing covariates. Scand. J. Stat. 31 320–330.

See also

  • Editorial: Spatial accessibility of pediatric primary healthcare: Measurement and inference.
  • Discusion: Discussion of “Spatial accessibility of pediatric primary healthcare: Measurement and inference”.
  • Discusion: Discussion of “Spatial accessibility of pediatric primary healthcare: Measurement and inference”.
  • Discusion: Discussion of “Spatial accessibility of pediatric primary healthcare: Measurement and inference”.
  • Rejoinder: “Spatial accessibility of pediatric primary healthcare: Measurement and inference”.

Supplemental materials

  • Supplementary material: Supplement to “Spatial accessibility of pediatric primary healthcare: Measurement and inference”. Supplementary Materials A, B, C and D contain four sections [Nobles, Serban and Swann (2014)]. In Supplementary Material A we describe methods that we utilized in our study but which are not essential components of our measurement and inference approach. In Supplementary Material B we give further details about the estimation of our space-varying coefficient model. In Supplementary Material C we provide additional details on the data sources we used to implement our models. In Supplementary Material D we present further results on children’s accessibility to primary care pediatricians in Georgia.