Quantifying and Explaining Accessibility with Application to the H1N1 Vaccination Campaign

Quantifying and Explaining Accessibility with Application to the H1N1 Vaccination Campaign Jessica L. HeierStamm, PhD Industrial and Manufacturing Systems Engineering Department Kansas State University NicoletaŞerban, PhD, and Julie Swann, PhD Stewart School of Industrial and Systems Engineering Georgia Institute of Technology 2014 Industrial & Systems Engineering Research Conference

Supply Chains for Public Health Response • Equitable access an important concern • Many different organizations involved • Private providers, government, non-governmental organizations, individuals • Rarely a single decision maker X People X X X X Service Locations X

How to Measure Accessibility? • These do not account for • Artificial boundaries on individuals’ willingness to travel • Over/under counting of individuals • Transportation network structure • Individual choice

Outline • Motivation • Equitable access • Decentralized decision making • H1N1 vaccine distribution • Background • Objectives • Measuring accessibility • Decentralized model • Results: General and priority group populations • Accessibility association analysis • Space-varying coefficient model • Results: General and priority group populations • Findings and recommendations

Background for H1N1 Study • Novel H1N1 influenza virus detected in US in April 2009 • Public health emergency declared • National vaccination campaign initiated in Fall 2009 • Federal government working with states, local health departments, providers • Initial demand outpaced H1N1 vaccine supply • Priority groups included children, pregnant women, high-risk adults

Distribution System Vaccine Demand > Supply Federal level allocated to states proportionally Vaccine allocated to service providers within states using variety of methods Individuals have access to vaccine at service locations

Research Goals • Measure accessibility • Distance traveled and scarcity experienced • Scarcity depends on number of people and number of vaccines • Individual choice • Examine equity in accessibility • Absence of systematic disparities • Explain inequities • Relationships with variables such as demographics and provider density • Inform future response plans Optimization, Game Theory Spatial Statistics

Data • Vaccine demand • Census tract population and centroid • Distances to service locations within 50 miles via US highway network • Vaccine supply • Total quantity shipped to each location during shortage period • Shipment addresses • Socioeconomic factors • Demographics: income, minority population, population density (U.S. Census) • National database of health care providers – potential service locations (CMS) • Today’s focus: 9 Southeast states • AL, AR, FL, GA, LA, MS, NC, SC, TN • 11,836 census tracts; 56+ million people • 12,000+ service locations; 13+ million vaccines

Assumptions and Limitations • Data • Measure distances to facilities from census tract centroid using US highway network • Population based on US Census data • Assume people choose one location • Single snapshot: all vaccine up to Dec. 9 • Ignore redistribution of vaccine (more appropriate for some states than others) • Individual choice model • Assume people know where vaccine is • Use particular form of individual utility function that combines travel time and scarcity • Divide census tracts into communities (c = 250 people), all of whom visit same location

Methods – Decentralized Model • Equilibrium condition for community i • No community can change facilities and improve its utility for all j ≠ k • Asymmetric network congestion game with unweighted, atomic, unsplittable flow • Pure equilibrium solution can be found efficiently (HeierStamm 2010)

Summary Statistics • Compared to state level data, model with choice suggests higher average scarcity locally • Model with choice accounts for travel across borders, ignored by simple county ratios • Variability indicates possible inequities *44.5% of AL vaccine sent to one location

Decentralized Scarcity Measure – Entire Population • Darker blue  less accessibility • Some states distributed more vaccine during this period • Some states have greater inequities

Decentralized Scarcity Measure – Children & Young Adults • Darker blue  less accessibility • Similar overall accessibility patterns

Methods – Statistical Analysis • Space-varying coefficient method • Similar to regression • Controls for spatial correlation among data points • Allows regression coefficients, β, to vary across space • Yj= response variable (scarcity) for census tract j • X = set of covariates (socioeconomic factors) indexed by factor r = 1, …, R and census tract j • βr(gj ) = regression coefficient for factor r and census tract j; smooth function of geographic space • Can be constant or nonlinear

Methods – Variables for Statistical Models • Dependent variable • Scarcity = persons/vaccine • Measured at census tract level as average experienced by people in that census tract • Candidate independent variable categories (measured at census tract level) • Income • Minority population • Provider density • Population density

Statistical Models of Accessibility • Population density has significant association with scarcity, and relationship is nonlinear • Provider density also important for entire population • Income and minority population appear more often in models of priority group accessibility

Outline • Motivation • Equitable access • Decentralized decision making • H1N1 vaccine distribution • Background • Objectives • Measuring accessibility • Decentralized models • Results: General and priority group populations • Accessibility association analysis • Space-varying coefficient model • Results: General and priority group populations • Findings and recommendations

Summary of Findings • Significant geographical differences in vaccine accessibility across states • Distinct differences between simple aggregation measures and decentralized measure of accessibility • Inequities associated with population and provider density • Effects vary across state, between states • Integration of optimization, game theory, spatial statistics, and GIS modeling tools can explain past decisions, inform future

Recommendations • Proposed distribution plans can be examined to assess their implications for accessibility and equity • A focus on increasing number and participation rates of providers could improve access in areas with past inequities • Modeling can be used to identify new plans with equitable access • Accounting for decentralized decision making may give new insight about system inequities

Ongoing and Future Research • Expand geographic scope • Regional and national • Incorporate temporal system characteristics • Beyond shortage period • Changes in equity over time • Examine tradeoffs between equity and efficiency

Questions and Discussion Jessica L. Heier Stamm, jlhs@k-state.edu Nicoleta Şerban, nserban@isye.gatech.edu Julie Swann, jswann@isye.gatech.edu Supported in part by: Emory Preparedness and Emergency Response Research Center (PERRC) Pilot Grant (PI: Swann, Co-PIs: Heier Stamm, Şerban) NSF CAREER Award CMMI-0954283 (PI: Şerban) Thanks also to Pascale Wortley, Nathaniel Hupert, and Cindy Weinbaum at the CDC for input

Toward Improving Accessibility Accessibility with County Pro Rata Vaccine Allocation Accessibility with Actual Vaccine Allocation Allocating to small geographic regions (e.g., counties) according to population addresses many, but not all, inequities

Quantifying and Explaining Accessibility with Application to the H1N1 Vaccination Campaign