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

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## 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

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**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 |

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**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