1.
Optimizing Geographic Access to Health Care
Eric Delmelle
University of North Carolina, Charlotte, U.S.A.
October 8 2019
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2.
Introduction Disparities
Disparities in Health Care
• Maldistribution of the health care workforce leads to the shortages amid
surplus paradox
• Disparities between races and between the haves and have-nots lead to
excessive deaths in the US (100K+ in the US)
• Enactment of the Patient Protection and Affordable Care Act;
implications for supply, distribution of health care providers.
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3.
Introduction Disparities
Disparities in Health Care...
• US: DHSS implemented programs including the designation of Medically
Underserved Areas/Populations (MUA/P) and Health Professional
Shortage Areas (HSPAs) for improving access for the underserved
• How effective are such programs? Can be estimated through
accessibility metrics
• Resources can be allocated to the needliest areas.
• Research has greatly benefited from GIS and spatial analysis
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4.
Introduction Optimization
Optimization approaches to measure access
• Maximize service coverage
• Minimize travel needs of patients
• Limit the number of facilities
• Maximize health (how to measure that?!)
• Combine some of these goals (multi-objective)
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5.
Introduction Inequalities
Equity
• Equity (equal access to health care, for those in equal need) is
appropriate to use. Minimizing inequality in health care accessibility
helps identifying the adjustment needed to chose these gaps
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6.
Introduction Inequalities
Inequality
• Inequality comes at a personal and societal cost, evidenced by
disparities in various health outcomes (can you afford this?)
• Different rates of infant mortality and birth weight
• Vaccination rates
• Complications from preventive and common diseases
• Late-stage cancer diagnosis (access?)
• Quality patient care and survival
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7.
Accessibility measures
Accessibility is an important metric
• ..refers to the relative ease by which services, here health care, can be
reached from a given location
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8.
Accessibility measures Spatial Access
Spatial Accessibility ...
• Emphasizes the importance of spatial separation between supply (health
care providers) and demand (population) and how they are connection in
space.
• Solid, reliable metrics are particularly important for the optimization of
health care
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9.
Accessibility measures Spatial Access
Spatial Accessibility...
• Spatial access is determined by where you are. One simple approach is
the supply-demand ratio, e.g. population-to-physician ratio.
• Population-to-physician ration does not reveal the detailed spatial
variation within an areal unit not account for the interaction between
population and physicians
• Gravity-based model? (Pk: population at k and Sj: capacity of health care
provider at j, n number of physicians, m: population locations)
Ai =
n
j=1
Sjd−β
ij
m
k=1 Pkd−β
kj
(1)
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10.
Accessibility measures Spatial Access
Spatial Accessibility...
• Distance friction β can be location-specific, like defined in Huff.
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11.
Accessibility measures 2SFCA
Two-steps floating catchment
1 Define the catchment of physical location j as an area composed
of all population locations (k) within a threshold travel time (d0)
from j and compute the physician-to-population ration (Rj) within
the catchment areas Rj =
Sj
k∈{dkj≤d0} Pk
2 For each population location i search all physician locations j
within the threshold travel time (d0) from i and sum up the ratios Rj
at these locations.
Ai =
j∈{dij≤d0}
Rj =
j∈{dij≤d0}
Sj
k∈{dkj≤d0} Pk
(2)
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12.
Accessibility measures 2SFCA
Two-steps floating catchment...
• The model is essentially a ratio between supply (S) and demand
(P), which interacts with each other only within a catchment area
• 30-min driving time
• easy to implement in GIS
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13.
Accessibility measures 2SFCA
generalizing...
• Generalize distance decay effect as a term f(d), then we have:
Ai =
n
j=1
Sj f(dij)
m
k=1 Pk f(dij)
(3)
• f(d) can be discrete or continuous.
• What is an acceptable size for catchment area Rj? (different in
urban and rural areas)
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14.
Accessibility measures 2SFCA
Modeling equity
• Equity = equal access to health care, equal utilization of health care
services, or equal (equitable) health outcomes
• Maximize health? - what does it mean in practice?
• Given an accessibility measure, minimize the variance of accessibility
index Ai across all population locations by redistributing the total amount
of supply S among health care facilities
min =
m
i=1
Pi(Ai − a)2
(4)
S1 + S2 + ... + Sn = S (5)
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15.
Modeling
So what popular models exist out there in health care to optimize
geographic access (and minimize costs)?
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16.
Optimization p-median
Location-allocation
• Seeks to locate a given number of health care center among a set of
candidate sites so that the total travel distance (or time) is between
demands and supply facilities is minimized.
MINIMIZE F =
i j
aidijZij (6)
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17.
Optimization coverage
Location Set Covering Problem
• Minimizes the number of facilities needed to cover all demand within a
critical distance or time
MINIMIZE F =
j
Xj (7)
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18.
Optimization coverage
Maximum Covering Location Problem
• Maximizes the demand covered within a desired distance or time
threshold by locating p facilities.
MAXIMIZE F =
i
aiYi (8)
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19.
Optimization center
p-center
• p-center identifies a location arrangement for p facilities that minimizes
the maximum distance to cover all clients
• minimax
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20.
Optimization Modeling issues
Some commonalities and issues
• Emphasizes various objectives such as travel time (distance)
minimization, resources minimization, maximal coverage and a
combination of them
• Cost? Capacity? Maximum distance? Closest hospital?, match ratio?
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21.
Optimization Modeling issues
Modeling equity....
• Ensure that an area is no further than some maximum travel or distance
threshold γ
• health service area must be served by a facility no further away from γ
dij ≤ γ (9)
φi = {j|dij ≤ γ} (10)
j∈φi
Zij = 1 (11)
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22.
Optimization Modeling issues
Modeling equity....
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23.
Utilization
Under or over-utilized
• We want to make sure that a set of health facilities is not under or
over-utilized
• Performance remains feasible and justified under these conditions
• lj ≤ aiZij ≤ uj
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24.
Hierarchy
all services are on the same level
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25.
Hierarchy
What if you are have different levels of service K
• Wellness -diagnostic - surgery. k can be assigned to higher level, not
vice-versa.
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26.
Discussion Models
Modification of the models
• Model can be modified for a particular or unique set of
circumstances for a given region (by boat?)
• Not all objectives and constraints are relevant
• Multiple objectives not straightforward to solve
• Single weighted approach (how to assign the weights?)
• Move objective to a constraint
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27.
Discussion Utilization
Capacity constrains
• Minimum and maximum service requirements can lead to strange
assignments
• Fractional demand - could lead to spatial inequity
• Allocate demand to more than one health care provider
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28.
Discussion Distance
Effect of distance
• Is closer better? Not always, but generally it is agreed that better
proximity increases access
• Not all services will follow the same distance decay function
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29.
Discussion Dynamic
Demand changes
• Increasing demand suggests more (new) facilities
• Good time to rethink the network
• Not all facilities may remain open j∈φ Xj = T
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30.
Discussion Conclusions
Take-home message
• Location planning and analysis of health care facilities is a
dynamic and complex process
• It is important to balance the costs (objectives) and the constrains
• Rigorous exercise
• Clear objectives are easily defendable
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31.
Discussion Conclusions
Take-home message...
• Taken individually, equity and utilization, cost, access are easy to
solve, but not together (much more complex)
• Some criteria could be in conflict with one another
• Hierarchical model is important: A system must be able to offer
the right mix of services across a complex network
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