GIS-automated delineation of hospital service areas in Florida: from Dartmouth method to network community detection methods

Figures & data

Figure 1. Spatial network of major hospitalization flows (volume ≥15) between ZIP code centroids.

Figure 2. Schematic illustration of the original Dartmouth method for delineating HSAs.

Figure 3. Schematic illustration of the refined Dartmouth method for delineating HSAs.

Figure 4. Schematic illustration of ScLouvain method.

Figure 5. Schematic illustration of ScLeiden method.

Table 1. Indices for HSAs delineated by various methods in Florida

		117 Original HSAs (1993)	136 Comparable HSAs			Global optimal modularity
HSAs Indices			Refined Dartmouth^a	ScLouvain	ScLeiden	22 HSAs by ScLouvain	18 HSAs by ScLeiden
Resolution		–	–	30.23	29.64	1.38	0.88
Modularity		–	–	0.510	0.519	0.846	0.844
No. of Destination ZIP Code Areas	Total	208	208	208	208	208	208
	Mean	2	2	2	2	9	12
	Min	0^b	1	1	1	1	2
	Max	14	7	5	5	28	29
	SD	2	1	1	1	7	6
Localization Index (LI)	Mean	0.515	0.513	0.472	0.472	0.869	0.909
	Min	0	0.188	0.001	0.001	0.286	0.727
	Max	0.946	1	1	1	1	0.985
	SD	0.219	0.153	0.228	0.227	0.154	0.065
Geographic compactness (PAC)	Mean	2.402	2.200	2.179	2.181	2.927	3.191
	Min	1.143	1.267	1.267	1.267	1.496	1.731
	Max	11.154	7.258	6.071	7.251	6.363	6.363
	SD	1.600	0.771	0.689	0.743	1.204	1.189
Population (in 1,000)	Mean	161	138	138	138	855	1,045
	Min	1	6	7	12	8	53
	Max	1,908	602	400	394	3,209	3,234
	SD	250	121	80	77	765	743

Note: SD for standard deviation; ^athe same HSAs are derived with and without the constraint of population threshold of 1,000. ^bfive HSAs do not have any hospitals.

Figure 6. Localization index in (a) 117 original HSAs and (b) 136 HSAs by the refined Dartmouth.

Figure 7. (a) LI of 136 HSAs by the refined Dartmouth method with overlaid major service flows (volume ≥150); (b) LI of 136 ScLeiden-derived HSAs with overlaid major service flows (volume ≥150); and (c) 136 HSAs with the refined Dartmouth method versus ScLeiden.

Figure 8. (a) LI of 22 ScLouvain-derived HSAs with overlaid major service flows (volume ≥150); (b) LI of 18 ScLeiden-derived HSAs with overlaid major service flows (volume ≥150); and (c) 22 HSAs with ScLouvain versus 18 HSAs with ScLeiden.

Table 2. Comparing Refined Dartmouth Method versus ScLouvain and ScLeiden Methods

	Refined Dartmouth method	Network community detection methods
		ScLouvain	ScLeiden
Core conceptual model	Plurality rule: a ZIP code area is assigned to a hospital if its patients visit the hospital with the largest volume.	Maximum modularity: a network with ZIP code areas as nodes linked by patient flows is segmented into communities of densely connected nodes where the interaction between communities is minimal and the interaction in each community is maximal.
Critical technical concern(s)	The key refinement addresses the ‘non-independent HSA problem’ in the original Dartmouth method, i.e. a ZIP code area receiving the highest patient volume from one ZIP has its highest patient flow going to another ZIP.	Accommodate spatial constraints; but may yield poorly connected or even disconnected communities.	Accommodate spatial constraints; its added refinement step addresses poorly connected or disconnected communities.
Number(s) of HSAs to derive	Only one set of HSAs is derived, and the number (n = 136) is close to the number of ZIP code areas with at least one hospital.	Almost any number of HSAs from 1 to the number of ZIP code areas with at least one hospital can be derived, include the set with the global optimal modularity value (n = 22 for ScLouvain, n = 18 for ScLeiden).
Key quality measure: average localization index (LI)	0.51 (n = 136), relatively low	0.47 (n = 136), low; 0.87 (n = 22), high	0.47 (n = 136), low; 0.91 (n = 18), high
Recommendation	Use it to define HSAs as a baseline; the number of derived HSAs may be too numerous for today’s highly interconnected health care market.	Consider using it if other network community detection methods are not available.	Recommended; simulate various sets of HSAs to strike a balance between the resolution (number) of HSAs and desirable LI value.