• Simple supply-demand ratio within a geopolitical unit (Cervero, 1989) • FCA with a radius (Peng, 1997) • FCA with a travel time range (Wang & Minor, 2002) • Two-step FCA method (Radke & Mu, 2000; Luo & Wang, 2003)
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Comparisons
Accessibility Score of 2-step FCA Method (d 0=50 min)
• Larger d0 ~ smaller β è stronger smoothing • Which one to use?
Day 4. GIS-Based Measures of Spatial Accessibility and Application in Examining Healthcare Access
Fahui Wang CNU
Dec 9, 2010 (Thursday)
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– Scale availability at S – Sum up accessible S around D – IT IS NOT DOUBLE COUNT!
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wang, 2002-12-10
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Gravity-based Model
• Joseph & Bantock (1982); Shen (1998) • Physician accessibility at resident location i:
– Distance matters – Road network matters – Transportation means matters as well
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Evolvement of FCA Methods
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From S/D Ratio to FCA
• Simply S/D Ratio • FCA with a Radius
– Improvements
• Within-unit variation • Cross-border
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Recap: 2-Step FCA (2SFCA)
1.1 For each physician location j, select all resident locations k within a reasonable travel time from j (catchment Cj). 1.2 Compute the physician to population ratio within Cj: R =S / P
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Access Matters!
• Convenience of access to activities (job, school, park, playground, public service, healthcare, etc.) • Spatial vs. nonspatial factors • Spatial: Unequal access because of uneven distributions of supply and demand • A social justice issue • Roles of governments and planners
– “Being (in)accessible” is continuous, not dichotomous.
• A physician surrounded by more population is less accessible • Weighted average of Ai (wi =Pi) is equal to the physician to population ratio in the whole study area.
j j k∈C j
∑
k
2.1 For each resident location i, search all physician locations j within the travel time range from i (catchment Zi). 2.2 Sum up the physician to population ratios at these physician locations: Ai = ∑ R j = ∑ ( S j / ∑ Pk )
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Synthesis of the Two Methods
• 2SFCA Method is a special case of the Gravity-based Model • If dij≤d0, code dij = 1, then dij-β=1; • If dij>d0, code dij = ∞, then dij-β=0. • Connection to the kernel estimation
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Measuring Accessibility
• If the supply capacity is no issue, only distance (time) matters. • If the services are scarce, supply vs. demand need to account for • The spatial separation between supply and demand
Contents
• • • • • • • The issue of access Floating Catchment Area (FCA) Methods Gravity-based Model Synthesis Case Study 4: Healthcare access in Chicago Extra 1: nonspatial factors in healthcare access Extra 2: commuting studies
j∈Z i j∈Z i k∈C j
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幻灯片 8 w1 Step 1 computes availability (S/D ratio) at each physician location; Step 2 overlays physican service areas---in overlapped areas, sum up the S/D ratios because residents have access to multiple physican locations.
– Limitations
• Straight-line
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From 1-Step to 2-Step FCA
• FCA with a Time Range
– S-D time > threshold – Unequal availability (S)
− V j = ∑ Pk d kj β
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幻灯片 9 w2 Access to a physician is first discounted by the travel time; secondly, it is discounted by its potential w.r.t. surounding population. It uses a continuous measure. For instance, given a yardstick of 30', 5' is more accessible than 25'.
Ai = ∑
j =1 n − S j d ij β
Vj
,
where
m
d ij
k =1
travel time between population location i and physician location j competition intensity for health services at physician location j
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Comparison of Accessibility Measures
Method 2SFCA (threshold time) Parameter 20 min 25 min 30 min 35 min 40 min 45 min 50 min Gravity-based method Min 0 0 0.017 0.110 0.175 0.174 0.130 1.447 1.236 1.055 0.899 0.767 0.656 0.562 Max 14.088 7.304 5.901 5.212 4.435 4.145 3.907 2.902 3.127 3.362 3.606 3.858 4.116 4.380 Std Dev 2.567 1.548 1.241 1.113 1.036 0.952 0.873 0.328 0.430 0.527 0.618 0.705 0.787 0.863 Mean 2.721 2.592 2.522 2.498 2.474 2.446 2.416 2.353 2.373 2.393 2.413 2.433 2.452 2.470 Weighted Mean 2.647