# Evaluating the Accessibility of Healthcare Facilities Using an Integrated Catchment Area Approach

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Conceptual Framework

#### 2.2. The Access Probability Indexes

_{1}, f

_{2}, …, f

_{n}} be the set of healthcare facilities in SA, and k be any location within SA. The MAP of the resident at location k visiting a healthcare facility f

_{i}can be expressed as Formula (1):

_{i}denotes the distance from k to f

_{i}and n denotes the total number of facilities in the study area. For instance, as Figure 2 shows, the travel distance from location k to facilities f

_{1}, f

_{2}, f

_{3}are represented by the inverted power function weight (in parentheses on the line). The MAP of location k to the three healthcare facilities are: $MAP({\alpha}_{k}^{{f}_{1}})=\frac{0.3}{0.3+0.5+0.5}=0.231$, $MAP({\alpha}_{k}^{{f}_{2}})=\frac{0.5}{0.3+0.5+0.5}=0.385$, and $MAP({\alpha}_{k}^{{f}_{3}})=\frac{0.5}{0.3+0.5+0.5}=0.385$.

_{i}denotes the number of residents who visit f

_{i}from k and n denotes the total facilities number in the study area. As shown in Figure 2, the number of residents from k to f

_{1}, f

_{2}, f

_{3}are shown in parentheses below the line. Therefore, $DAP({\alpha}_{k}^{{f}_{1}})=\frac{80}{80+100+100}=0.286$, $DAP({\alpha}_{k}^{{f}_{2}})=\frac{100}{80+100+100}=0.357$, and $DAP({\alpha}_{k}^{{f}_{3}})=\frac{100}{80+100+100}=0.357$.

_{i}is expressed as Formula (5):

_{1}, λ

_{2}denotes the weight of MAP and DAP respectively. If there are no residents visiting f

_{i}, p

_{i}is equal to zero and thus $DAP({\alpha}_{k}^{{f}_{i}})$ is equal to zero. In this case, $IAP({\alpha}_{k}^{{f}_{i}})$ is determined only by $MAP({\alpha}_{k}^{{f}_{i}})$, which is the same as the traditional methods.

#### 2.3. The Integrated Catchment Area

_{i}under δ is the collection of location k whose access probability is greater than or equal to δ. Therefore, three catchment areas, MCA, DCA and ICA are formed as Formulas (6)–(8):

#### 2.4. Accessibility Measurement Based on ICA

_{i}with IAP of δ. Then, each catchment area is divided into multiple subzones of subzone

_{1}, subzone

_{2}, …, subzone

_{r}when the thresholds of IAP are δ

_{1}, δ

_{2}, …, δ

_{r}, respectively. Search all population units (here, a grid cell) that are within subzone

_{j}from facility f

_{i}and compute the weighted physician-to-population ratio R

_{i}, which is represented by Formula (9):

_{j}is the IAP threshold of subzone

_{j}, $ICA\left({f}_{i},{\delta}_{j}\right)$ is the integrated catchment area (ICA) of f

_{i}under δ

_{j}, pop

_{k}denotes the population unit of location k falling within $ICA\left({f}_{i},{\delta}_{j}\right)$ and S

_{i}is the number of physicians in a healthcare facility f

_{i}, and w

_{r}is the distance weight for r

_{th}subzone.

_{k}represents the accessibility of location k, and R

_{i}denotes the physician-to-population ratio of facility f

_{i}that falls within the catchment area centered at population k. The same IAP threshold of subzone and distance weights in Step 1 are applied in Step 2.

_{k}, the higher the accessibility of location k is to healthcare facilities. The smaller the differences in accessibility between different locations, the more equitable the distribution of healthcare facilities is, and vice versa. The advantage of this method is that the catchment areas and subzones are determined by the characteristics of the specific study area instead of an arbitrary value.

## 3. Case Study

#### 3.1. Study Area

^{2}and a permanent population of about 10.35 million in 2010 according to the Sixth National Census of China. The population of each sub-district is obtained from the Shenzhen statistical yearbook (http://www.sztj.gov.cn/). The year of the road network used in this study is 2010.

#### 3.2. Data Processing

_{1}= λ

_{2}= 0.5 in the following experiments to derive the ICAs of each hospital. These catchment areas thus reflect the link impedance of the transport network in the study area in many ways. The results and discussion of the ICA and accessibility are presented in Section 4 below.

## 4. Results and Discussion

#### 4.1. Analysis of the Access Probability Threshold

#### 4.2. Analysis of the Differences among MCA, DCA, and ICA

^{2}and the area of the DCA (H1, 0.9) is 38.15 km

^{2}, which means the DCA is about two times the size of the MCA. At a medium access probability level, the area of the MCA (H1, 0.2) is 83.32 km

^{2}and the area of the DCA (H1, 0.5) is 60.86 km

^{2}, which means that the MCA is only slightly larger than the DCA. At a low access probability level, the area of the MCA (H1, 0.1) is 310.27 km

^{2}and the area of DCA (H1, 0.1) is 90.61 km

^{2}, which indicates that the MCA is more than 3 times the size of the DCA. In addition to the large differences in size, the differences in shape between the MCA and DCA are also significant. Figure 6a shows that with the decrease in δ, the MCA mainly expands to the north of H1, which means that the users of this hospital are mainly distributed in areas in the north of H1 based on a largely conceptual understanding of accessibility (i.e., influenced mainly by distance). However, the DCA (Figure 6b) shows that distribution of the actual users of this hospital is extended in the east-west direction of H1, which is consistent with the distribution of the population in this region.

_{1}= λ

_{2}) is allocated to the MCA and DCA. In other words, the effects of the MCA and DCA on the ICA are given the same weight and considered equally in the experiment, but the ICA is still more similar to the DCA in shape, especially at a middle probability threshold level. This further illustrates the capability of the DCA in capturing more realistic catchment areas when compared to catchment areas based on conventional models of accessibility.

#### 4.3. Analysis of the Characteristics of the ICA

#### 4.4. The Accessibility of the Top-Tier Hospitals

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Hansen, W.G. How Accessibility Shapes Land Use. J. Am. Inst. Plan.
**1959**, 25, 73–76. [Google Scholar] [CrossRef] - Kwan, M.-P. Space-time and integral measures of individual accessibility: A comparative analysis using a point-based framework. Geogr. Anal.
**1998**, 30, 191–216. [Google Scholar] [CrossRef] - Kwan, M.-P. Gender and individual access to urban opportunities: A study using space-time measures. Prof. Geogr.
**1999**, 51, 210–227. [Google Scholar] [CrossRef] - Luo, W.; Wang, F. Measures of spatial accessibility to health care in a GIS environment: Synthesis and a case study in the Chicago region. Environ. Plan. B Plan. Des.
**2003**, 30, 865–884. [Google Scholar] [CrossRef] - Kwan, M.-P.; Weber, J. Scale and accessibility: Implications for the analysis of land use-travel interaction. Appl. Geogr.
**2008**, 28, 110–123. [Google Scholar] [CrossRef] - Wang, H.D.; Yue, Y.; Li, Y.G.; Huang, L. Spatial Correlation Analysis of Attractiveness of Commercial Facilities. Geomat. Inf. Sci. Wuhan Univ.
**2011**, 36, 1102–1106. [Google Scholar] - Dussault, G.; Franceschini, M.C. Not enough there, too many here: Understanding geographical imbalances in the distribution of the health workforce. Hum. Resour. Health
**2006**, 4, 12. [Google Scholar] [CrossRef] [PubMed] - McGrail, M.R.; Humphreys, J.S. Measuring spatial accessibility to primary health care services: Utilising dynamic catchment sizes. Appl. Geogr.
**2014**, 54, 182–188. [Google Scholar] [CrossRef] - McGrail, M.R.; Humphreys, J.S. Measuring spatial accessibility to primary care in rural areas: Improving the effectiveness of the two-step floating catchment area method. Appl. Geogr.
**2009**, 29, 533–541. [Google Scholar] [CrossRef] - Luo, W.; Qi, Y. An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians. Health Place
**2009**, 15, 1100–1107. [Google Scholar] [CrossRef] [PubMed] - Hu, R.; Dong, S.; Zhao, Y.; Hu, H.; Li, Z. Assessing potential spatial accessibility of health services in rural China: A case study of Donghai county. Int. J. Equity Health
**2013**, 12, 35. [Google Scholar] [CrossRef] [PubMed] - Wan, N.; Zhan, F.B.; Zou, B.; Chow, E. A relative spatial access assessment approach for analyzing potential spatial access to colorectal cancer services in Texas. Appl. Geogr.
**2012**, 32, 291–299. [Google Scholar] [CrossRef] - Delamater, P.L. Spatial accessibility in suboptimally configured health care systems: A modified two-step floating catchment area (M2SFCA) metric. Health Place
**2013**, 24, 30–43. [Google Scholar] [CrossRef] [PubMed] - McGrail, M.R. Spatial accessibility of primary health care utilising the two step floating catchment area method: An assessment of recent improvements. Int. J. Health Geogr.
**2012**, 11, 50. [Google Scholar] [CrossRef] [PubMed] - Guagliardo, M.F. Spatial accessibility of primary care: Concepts, methods and challenges. Int. J. Health Geogr.
**2004**, 3, 3. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dai, D. Racial/ethnic and socioeconomic disparities in urban green space accessibility: Where to intervene? Landsc. Urban Plan.
**2011**, 102, 234–244. [Google Scholar] [CrossRef] - Delmelle, E.M.; Cassell, C.H.; Dony, C.; Radcliff, E.; Tanner, J.P.; Siffel, C.; Kirby, R.S. Modeling travel impedance to medical care for children with birth defects using geographic information systems. Birth Defects Res. Part A Clin. Mol. Teratol.
**2013**, 97, 673–684. [Google Scholar] [CrossRef] [PubMed] - Wang, F.; Luo, W. Assessing spatial and nonspatial factors for healthcare access: Towards an integrated approach to defining health professional shortage areas. Health Place
**2005**, 11, 131–146. [Google Scholar] [CrossRef] [PubMed] - Hyndman, J.C.; D’Arcy, C.; Holman, J.; Pritchard, D.A. The influence of attractiveness factors and distance to general practice surgeries by level of social disadvantage and global access in Perth, Western Australia. Soc. Sci. Med.
**2003**, 56, 387–403. [Google Scholar] [CrossRef] - Dony, C.C.; Delmelle, E.M.; Delmelle, E.C. Re-conceptualizing accessibility to parks in multi-modal cities: A variable-width floating catchment area (vfca) method. Landsc. Urban Plan.
**2015**, 143, 90–99. [Google Scholar] [CrossRef] - Casas, I.; Delmelle, E.; Delmelle, E.C. Potential versus revealed access to care during a dengue fever outbreak. J. Transp. Health
**2016**, 4, 18–29. [Google Scholar] [CrossRef] - Yang, G.; Song, C.; Shu, H.; Zhang, J.; Pei, T.; Zhou, C. Assessing patient bypass behavior using taxi trip origin-destination (OD) data. ISPRS Int. J. Geo-Inf.
**2016**, 5, 157. [Google Scholar] [CrossRef] - Wang, F.H. Measurement, optimization, and impact of health care accessibility: A methodological review. Ann. Assoc. Am. Geogr.
**2012**, 102, 1104–1112. [Google Scholar] [CrossRef] [PubMed] - Zinszer, K.; Charland, K.; Kigozi, R.; Dorsey, G.; Kamya, M.R.; Buckeridge, D.L. Determining health-care facility catchment areas in Uganda using data on malaria-related visits. Bull. World Health Organ.
**2014**, 92, 178–186. [Google Scholar] [CrossRef] [PubMed] - Shortt, N.K.; Moore, A.; Coombes, M.; Wymer, C. Defining regions for locality health care planning: A multidimensional approach. Soc. Sci. Med.
**2005**, 60, 2715–2727. [Google Scholar] [CrossRef] [PubMed] - Lovett, A.; Haynes, R.; Sünnenberg, G.; Gale, S. Car travel time and accessibility by bus to general practitioner services: A study using patient registers and GIS. Soc. Sci. Med.
**2002**, 55, 97–111. [Google Scholar] [CrossRef] - Parker, E.B.; Campbell, J.L. Measuring access to primary medical care: Some examples of the use of geographical information systems. Health Place
**1998**, 4, 183–193. [Google Scholar] [CrossRef] - Kwan, M.-P. The uncertain geographic context problem. Ann. Assoc. Am. Geogr.
**2012**, 102, 958–968. [Google Scholar] [CrossRef] - Shen, Y.; Kwan, M.P.; Chai, Y. Investigating commuting flexibility with GPS data and 3D geovisualization: A case study of Beijing, China. J. Transp. Geogr.
**2013**, 32, 1–11. [Google Scholar] [CrossRef] - Song, C.; Qu, Z.; Blumm, N.; Barabási, A.L. Limits of predictability in human mobility. Science
**2010**, 327, 1018–1021. [Google Scholar] [CrossRef] [PubMed] - González, M.C.; Hidalgo, C.A.; Barabási, A.L. Understanding individual human mobility patterns. Nature
**2008**, 453, 779–782. [Google Scholar] [CrossRef] [PubMed] - Lazer, D.; Pentland, A.; Adamic, L.; Aral, S.; Barabasi, A.L.; Brewer, D.; Christakis, N.; Contractor, N.; Fowler, J.; Gutmann, M. Life in the network: The coming age of computational social science. Science
**2009**, 323, 721–723. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Beijing Statistical Yearbook. Available online: http://www.bjstats.gov.cn/tjsj/ (accessed on 23 July 2018).
- Shanghai Urban Transportation Administrative Dept. Available online: http://www.shygc.net/pageHome.do?page=init (accessed on 23 July 2018).
- Guangzhou Statistical Yearbook. Available online: www.gzstats.gov.cn (accessed on 23 July 2018).
- Shenzhen Transportation Commission. Available online: http://www.sztb.gov.cn/ (accessed on 23 July 2018).
- Li, L.; Wang, S.; Li, M.; Tan, J. Comparison of travel mode choice between taxi and subway regarding traveling convenience. Tsinghua Sci. Technol.
**2018**, 2, 135–144. [Google Scholar] [CrossRef] - Didi Media Research Institute & CBNData. 2016 Intelligent Travel Big Data Report. 2017. Available online: http://www.imxdata.com/archives/20017 (accessed on 12 April 2017).
- Ingram, D.R. The concept of accessibility: A search for an operational form. Reg. Stud. J. Reg. Stud. Assoc.
**1971**, 5, 101–107. [Google Scholar] [CrossRef] - Zhou, Y.; Fang, Z.; Thill, J.C.; Li, Q.; Li, Y. Functionally critical locations in an urban transportation network: Identification and space-time analysis using taxi trajectories. Comput. Environ. Urban Syst.
**2015**, 52, 34–47. [Google Scholar] [CrossRef] - Joseph, A.E.; Bantock, P.R. Measuring potential physical accessibility to general practitioners in rural areas: A method and case study. Soc. Sci. Med.
**1982**, 16, 85–90. [Google Scholar] [CrossRef] - Kwan, M.-P. Beyond space (as we knew it): Toward temporally integrated geographies of segregation, health, and accessibility. Ann. Assoc. Am. Geogr.
**2013**, 103, 1078–1086. [Google Scholar] [CrossRef] - Alford-Teaster, J.; Lange, J.M.; Hubbard, R.A.; Lee, C.I.; Haas, J.S.; Shi, X.; Carlos, H.A.; Henderson, L.; Hill, D.; Tosteson, A.N.A.; et al. Is the closest facility the one actually used? An assessment of travel time estimation based on mammography facilities. Int. J. Health Geogr.
**2016**, 15, 8. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Qi, L.L.; Zhou, S.H.; Yan, X.P. Endpoint Attractive Factors of Medical Facilities’ Accessibility: Based on GPS Floating Car Data in Guangzhou. Sci. Geogr. Sin.
**2014**, 34, 580–586. [Google Scholar] - Chen, B.Y.; Yuan, H.; Li, Q.; Wang, D.; Shaw, S.L.; Chen, H.P.; Lam, W.H. Measuring place-based accessibility under travel time uncertainty. Int. J. Geogr. Inf. Sci.
**2016**, 31, 783–804. [Google Scholar] [CrossRef] - Didi Media Research Institute & CBNData. 2016 Smart Travel Data and Medical Reports. Available online: http://www.sohu.com/a/79676781_355066 (accessed on 12 June 2017).
- Yang, L.; Kwan, M.-P.; Pan, X.; Wan, B.; Zhou, S. Scalable space-time trajectory cube for path-finding: A study using big taxi trajectory data. Transp. Res. Part B
**2017**, 101, 1–27. [Google Scholar] [CrossRef] - Wang, X.; Pan, J. Assessing the disparity in spatial access to hospital care in ethnic minority region in sichuan province, china. BMC Health Serv. Res.
**2016**, 16, 399. [Google Scholar] [CrossRef] [PubMed] - Vadrevu, L.; Kanjilal, B. Measuring spatial equity and access to maternal health services using enhanced two step floating catchment area method (e2sfca)—A case study of the Indian sundarbans. Int. J. Equity Health
**2016**, 15, 87. [Google Scholar] [CrossRef] [PubMed] - Dewulf, B.; Neutens, T.; Weerdt, Y.D.; Weghe, N.V.D. Accessibility to primary health care in Belgium: An evaluation of policies awarding financial assistance in shortage areas. BMC Fam. Pract.
**2013**, 14, 122. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wan, N.; Zou, B.; Sternberg, T. A three-step floating catchment area method for analyzing spatial access to health services. Int. J. Geogr. Inf. Sci.
**2012**, 6, 1073–1089. [Google Scholar] [CrossRef] - Ursulica, T.E. The relationship between health care needs and accessibility to health care services in Botosani County-Romania. Procedia Environ. Sci.
**2016**, 32, 300–310. [Google Scholar] [CrossRef] - Luo, W.; Whippo, T. Variable catchment sizes for the two-step floating catchment area (2SFCA) method. Health Place
**2012**, 18, 789–795. [Google Scholar] [CrossRef] [PubMed] - Ren, F.; Tong, D.; Kwan, M.-P. Space-time measures of demand for service: Bridging location modeling and accessibility studies through a time-geographic framework. Geografiska Annaler B
**2014**, 96, 329–344. [Google Scholar] [CrossRef]

**Figure 1.**The relationship among model-based catchment area (MCA), data-based catchment area (DCA), integrated catchment area (ICA) and actual catchment area.

**Figure 7.**(

**a**) Area differences of MCA and DCA at low level; (

**b**) Area differences of MCA and DCA at middle level; (

**c**) Area differences of MCA and DCA at high level; (

**d**) The area of ICA at low, middle and high level.

**Figure 8.**The boundary of the MCA, DCA and ICA at a high, middle and low level of probability threshold. (black line represents MCA boundary, blue line represents DCA boundary, red line represents ICA boundary).

Hospital Name | Abbreviation |
---|---|

Peking University Shenzhen Hospital | H1 |

Shenzhen People’s Hospital | H2 |

The Second People’s Hospital of Shenzhen | H3 |

The SIXTH people’s Hospital of Shenzhen | H4 |

The Eighth People’s Hospital of Shenzhen | H5 |

The Ninth People’s Hospital of Shenzhen | H6 |

Shenzhen Traditional Chinese Medicine Hospital | H7 |

The Second Traditional Chinese Medicine Hospital of Shenzhen | H8 |

Shenzhen Maternity & Child Healthcare Hospital | H9 |

Shenzhen Pingle Orthopedic Hospital | H10 |

**Table 2.**The statistical results and levels of model-based access probability (MAP), data-based access probability (DAP) and integrated access probability (IAP).

MinValue | MaxValue | Std. | High Level | Middle Level | Low Level | |
---|---|---|---|---|---|---|

MAP | 0.000085 | 0.314345 | 0.038918 | 0.3 | 0.2 | 0.1 |

DAP | 0 | 1 | 0.053472 | 0.9 | 0.5 | 0.1 |

IAP | 0.000042 | 0.656681 | 0.036113 | 0.5 | 0.3 | 0.1 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pan, X.; Kwan, M.-P.; Yang, L.; Zhou, S.; Zuo, Z.; Wan, B.
Evaluating the Accessibility of Healthcare Facilities Using an Integrated Catchment Area Approach. *Int. J. Environ. Res. Public Health* **2018**, *15*, 2051.
https://doi.org/10.3390/ijerph15092051

**AMA Style**

Pan X, Kwan M-P, Yang L, Zhou S, Zuo Z, Wan B.
Evaluating the Accessibility of Healthcare Facilities Using an Integrated Catchment Area Approach. *International Journal of Environmental Research and Public Health*. 2018; 15(9):2051.
https://doi.org/10.3390/ijerph15092051

**Chicago/Turabian Style**

Pan, Xiaofang, Mei-Po Kwan, Lin Yang, Shunping Zhou, Zejun Zuo, and Bo Wan.
2018. "Evaluating the Accessibility of Healthcare Facilities Using an Integrated Catchment Area Approach" *International Journal of Environmental Research and Public Health* 15, no. 9: 2051.
https://doi.org/10.3390/ijerph15092051