Global Optimization of Complex Healthcare Systems
Zelda B. Zabinsky
Industrial and Systems Engineering
University of Washington
Seattle, WA
April 18, 2017
Institute for Disease Modeling (IDM) Symposium
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Global Optimization of Complex
Healthcare Systems
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Often need numerical simulations to describe a
complex healthcare system:
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Natural progression, spread and management of disease
New technologies becoming available
Allocation of scarce resources
Global optimization (or simulation-optimization):
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Problem may be non-convex, black-box, discontinuous,
involve integer and real-valued decision variables
Uncertainties may be present
Multiple objectives
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Several Random Search
Algorithms for Global Optimization
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Sequential random search algorithms:
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Simulated annealing
Cross-entropy
Population-based:
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Genetic algorithms (cross-over, mutation)
Particle swarm (position, velocity)
Interacting particle algorithm with hit-and-run
[Zabinsky, Stochastic Adaptive Search in Global Optimization, 2003]
[Zabinsky, Stochastic Search Methods for Global Optimization, a book chapter in the
Wiley Encyclopedia of Operations Research and Management Science, 2011]
[Zabinsky, Random Search Algorithms for Simulation Optimization, a
book chapter in the Handbook on Simulation Optimization, 2015]
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Improving Hit and Run (IHR)
IHR: choose a random direction and a random point
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160
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x2
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80
60
40
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x2
x1
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40
60
80
100
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180
x1
[Zabinsky and Smith, Hit-and-Run Methods, a book chapter in Springer’s
Encyclopedia of Operations Research & Management Science, 2013]
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Optimization: What Do We
Really Want?
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Do we really just want the optimum?
What about sensitivity?
Do we want to approximate the entire
surface? Or just a region of interest?
Multiple objectives? Role of objective
function and constraints?
How to account for uncertainty?
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Probabilistic Branch and Bound
(PBnB)
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Approximate a set of “good” solutions
(quantile, level set approximation)
Handles black-box, noisy functions, including
both integer and real-valued variables
Single or multiple objective functions
Provide probability bounds assuring the
quality of solution set
[Huang and Zabinsky, “Adaptive Probabilistic Branch and Bound with Confidence Intervals for
Level Set Approximation,” Proceedings of the 2013 Winter Simulation Conference, 2013. ]
[Huang and Zabinsky, “Multiple Objective Probabilistic Branch and Bound for Pareto Optimal
Approximation,” Proceedings of the 2014 Winter Simulation Conference, 2014. ]
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Approximated Level Set
(Best 10%)
Three test functions with contours:
(A) Rosenbrock
(B) Sinusoidal function (centered)
(C) Sinusoidal function (shifted)
Bold contour is target level set
pruned
maintained
undecided
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Parameter Estimation
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Given m=10,000 data points that have been
randomly generated from the density
with undisclosed parameters
Determine the parameters by solving a maximum
likelihood problem
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Parameter Estimation
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PBnB finds the optimal solution (2,5) in
seven iterations with 285 sample points
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Allocation of Portable Ultrasound
Machine to Orthopedic Clinics
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Simulate costs: (MRI expensive, ultrasound
relatively low cost) and benefits (less travel
time, less wait time)
Diagnosis quality: Experience and training
on using portable ultrasound machines may
influence the diagnosis quality
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MRI accurate
Ultrasound as accurate if well-trained
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Allocation of Portable Ultrasound
Machine to Orthopedic Clinics
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Simulate costs (MRI
expensive, ultrasound
relatively low cost) and
benefits (less travel
time, less wait time)
Diagnosis quality:
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MRI accurate
Uncertain accuracy of
portable ultrasound
Current Specialty Centers/Radiology
Current Major Primary Care Clinics
(Potential locations for orthopedic care)
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Simulation-Optimization for
Medical Imaging Resources
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Multiple
objectives
Tradeoff health
utility and cost
Efficient
frontier
[Huang, et al., 2015]
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Results with 0.9 Accuracy
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Four Pareto optimal
designs
Solutions ranged from
11 to 5 portable
ultrasound machines
Varying amounts of
reserved MRI capacity
Burien and Northshore
in all four designs
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Hepatitis C Screening and
Treatment Policies
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Chronic hepatitis C virus (HCV) infection is the
most common blood-borne infection in the
United States (~ 2.7 million are HCV infected)
Policy decisions for HCV care:
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Determine the optimal HCV birth-cohort screening
and treatment allocation strategies under spending
budget constraints
Analyze the impact of screening and treatment
allocation strategies for each cohort group by
decision time periods
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Markov Chain of Health Status
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Three population groups:
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Group A: HCV unknown
A: HCV Unknown
B: HCV Positive
C: HCV Negative
Group B: HCV+
Severity of disease
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Healthy: H
Fibrosis: F0, F1, F2, F3, F4
Untreatable: UT
Recovered: R1, R2, R3
Dead: M
Group C: HCV-
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Optimization Model
Maximize the discounted quality-adjusted life years (QALYs)
Dynamic constraints based on the Markov model
Budget constraint for each year:
Cost for screening
Cost for treatment
Percentage of
the budget for
screening
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Analysis and Policy Decisions
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Analysis Approach
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Use grid search to identify time periods with obvious
dominant strategy
[Li, Huang, Zabinsky, and Liu, accepted in Medical Decision Making
(MDM) Policy & Practice, Dec. 2016]
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PBnB Analysis
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First look at low budget (LB) scenarios
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Maximize discounted QALYs
Subject to yearly budget constraint
Decision variables – first two time periods
Identify a set of solutions in the top 10
percent of QALYs
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Approximated 0.1 Level Set for
50-59, Low Budget pruned
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maintained
undecided
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Approximated 0.1 Level Set for
50-59, High Budget pruned
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maintained
undecided
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Conclusions
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Many applications are non-linear, include uncertainty,
and have multiple objectives
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Probabilistic Branch and Bound provides a set of
solutions and enables trade-offs to be made
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Many possible simulation models
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On-going research into extensions of PBnB
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