The document discusses the optimization of geographic access to healthcare, highlighting disparities in healthcare access and the effectiveness of various programs aimed at improving it. It explores different accessibility measures and optimization models, such as p-median and center p-center, to minimize travel distance and maximize coverage. The document emphasizes the complexity of balancing equity, cost, and utilization in healthcare planning and the importance of adapting models to meet specific regional needs.

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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