Optimizing Distribution of Influenza Antiviral Drugs
Optimizing Distribution of Influenza Antiviral Drugs
During the 2009 influenza pandemic, the Texas DSHS recruited 1,393 pharmacies from 6 major chains and 71 independent pharmacies to dispense antiviral drugs from the SNS and state cache to underinsured populations. These pharmacies were located in 723 of the 1,023 ZIP code areas in Texas that had ≥1 pharmacy. We estimated that this network provided antiviral drug access for 88% of the state's underinsured population (Figure 2). In comparison, we also estimated that optimization over all possible pharmacy chains produced a network expected to achieve comparable access by using only 526 ZIP code areas, increased access to 92.5% with 723 ZIP code areas, and reached a maximum access of 95.2% with all 1,023 ZIP code areas.
However, optimizing for statewide access can lead to critical gaps in coverage. We categorized all Texas ZIP code areas on the basis of underinsured population sizes into small (<1,000 persons), medium (1,001–7,000 persons), and large (>7,000 persons). These areas contained 7%, 51%, and 42% of the statewide underinsured population, respectively. The actual Texas 2009 distribution network and the corresponding optimized network (with 723 ZIP code areas) were estimated to achieve only 34.5% and 38.3% access in small ZIP code areas, respectively, but reached 88.0% and 92.5% access overall. By definition, the small ZIP code areas do not carry much weight in a statewide optimization model. They also tend to be more remote than larger ZIP code areas, and thus have lower access to selected pharmacies.
To address this gap, we modified the objective function to maximize access specifically in small ZIP code areas. Although these modifications improved coverage in these hard-to-reach populations, the solutions were suboptimal overall. Thus, we developed a hybrid optimization procedure that sequentially ensures high access statewide and in small ZIP code areas. With 723 dispensing points, the hybrid method with P = 75% of dispensing points allocated to small ZIP code areas produced networks that are expected to achieve 60.5% access in small ZIP code areas and 90.5% overall. For comparison, the highest possible access (when all pharmacies in the state dispense antiviral drugs) was estimated to reach 63.8% and 95.2% in the 2 populations, respectively (Table 2). For populations living in ZIP code areas without pharmacies dispensing antiviral drugs, optimization reduced the average travel distance to the nearest dispensing pharmacy from 4.5 miles to 3.8 miles.
A state might opt to limit the number of chains in the distribution network to simplify logistics. The pharmacy chains eligible for participation in Texas include Brookshire, Costco, CVS, HEB, Kmart, Kroger, Randalls, Sam's Club, Target, Tom Thumb, United, Walgreens, Walmart, and independent retail pharmacies (henceforth independents). During the 2009 influenza pandemic, the Texas DSHS distributed antiviral drugs from the SNS and state cache through 6 major chains (Brookshire, HEB, Kroger, United, Walgreens, and Walmart), and independents. When we restricted the optimization to a few major chains, the resulting networks still achieved broad statewide coverage (Figures 2, 3). For example, Walgreens alone was expected to achieve ≈75% coverage if it dispenses in all of its 490 ZIP code areas; CVS and Walmart followed close behind (located in 422 and 372 ZIP code areas, respectively). These 3 chains have the greatest presence in the state (Table 1), but have highly overlapping geographic areas. Broad accessibility can also be achieved through a combination of smaller chains with geographic complementarity, for example, HEB and Kroger (in 189 and 167 ZIP code areas, respectively). Walgreens and Walmart overlap over half of their ZIP code areas (256), whereas HEB and Kroger overlap in only 30 ZIP code areas. However, the number of ZIP code areas alone is not predictive of access. For example, Brookshire has almost as many stores as Target (in 118 and 127 ZIP code areas, respectively), yet provides considerably less statewide access alone and in combination with other stores.
(Enlarge Image)
Figure 3.
Antiviral drug access in underinsured populations for single-chain and 2-chain pharmacy distribution networks during the 2009 influenza pandemic, Texas, USA. Each network contains a maximum of 723 distribution points, and was designed by using a hybrid optimization that maximizes coverage in small ZIP code (US postal code) areas and overall (see text for details). Color indicates the expected percentage of the underinsured population willing to travel to dispensing pharmacies to obtain antiviral drugs A) statewide and B) in small ZIP code areas. Numbers along the baselines and the y-axes indicate single-chain networks. 1, Walgreens; 2, CVS; 3, Walmart; 4, HEB; 5, Kroger; 6, Target; 7, Brookshire; 8, Sam's Club; 9, Tom Thumb; 10, Randalls; 11, United; 12, Costco; 13, Kmart; 14, Independents (independent pharmacies).
However, the major chains did not reach the underinsured populations in the small ZIP code areas, even under the hybrid optimization that explicitly targets these hard-to-reach populations (Figure 2, panel A). Independent pharmacies are essential to bridging this gap in coverage. The maximum access achieved by a 2-chain combination in small ZIP code areas is only 33% (Brookshire and Walmart) (Figure 3). Under the hybrid objective, optimized networks with <500 dispensing points yield solutions for all major pharmacy chains plus independents that provided slightly lower statewide accessibility than the corresponding solutions for major chains (Figure 2, panel B), in exchange for higher coverage in small ZIP code areas (Figure 2, panel A). Of the 1,023 ZIP code areas with ≥1 pharmacy, 271 have only independent pharmacies. Of these pharmacies, 167 are in small ZIP code areas, and were typically selected when optimizing for access in small ZIP code areas, but not when optimizing for access statewide (Figure 4).
(Enlarge Image)
Figure 4.
Number of sites in the antiviral drug distribution network during the 2009 influenza pandemic that contained only independent pharmacies (independents; i.e., no major chains) when optimizing for the underinsured population in small ZIP code (US postal code) areas (i.e., ZIP code areas with <1,000 underinsured persons), statewide, or both (hybrid), Texas, USA.
Results
During the 2009 influenza pandemic, the Texas DSHS recruited 1,393 pharmacies from 6 major chains and 71 independent pharmacies to dispense antiviral drugs from the SNS and state cache to underinsured populations. These pharmacies were located in 723 of the 1,023 ZIP code areas in Texas that had ≥1 pharmacy. We estimated that this network provided antiviral drug access for 88% of the state's underinsured population (Figure 2). In comparison, we also estimated that optimization over all possible pharmacy chains produced a network expected to achieve comparable access by using only 526 ZIP code areas, increased access to 92.5% with 723 ZIP code areas, and reached a maximum access of 95.2% with all 1,023 ZIP code areas.
However, optimizing for statewide access can lead to critical gaps in coverage. We categorized all Texas ZIP code areas on the basis of underinsured population sizes into small (<1,000 persons), medium (1,001–7,000 persons), and large (>7,000 persons). These areas contained 7%, 51%, and 42% of the statewide underinsured population, respectively. The actual Texas 2009 distribution network and the corresponding optimized network (with 723 ZIP code areas) were estimated to achieve only 34.5% and 38.3% access in small ZIP code areas, respectively, but reached 88.0% and 92.5% access overall. By definition, the small ZIP code areas do not carry much weight in a statewide optimization model. They also tend to be more remote than larger ZIP code areas, and thus have lower access to selected pharmacies.
To address this gap, we modified the objective function to maximize access specifically in small ZIP code areas. Although these modifications improved coverage in these hard-to-reach populations, the solutions were suboptimal overall. Thus, we developed a hybrid optimization procedure that sequentially ensures high access statewide and in small ZIP code areas. With 723 dispensing points, the hybrid method with P = 75% of dispensing points allocated to small ZIP code areas produced networks that are expected to achieve 60.5% access in small ZIP code areas and 90.5% overall. For comparison, the highest possible access (when all pharmacies in the state dispense antiviral drugs) was estimated to reach 63.8% and 95.2% in the 2 populations, respectively (Table 2). For populations living in ZIP code areas without pharmacies dispensing antiviral drugs, optimization reduced the average travel distance to the nearest dispensing pharmacy from 4.5 miles to 3.8 miles.
A state might opt to limit the number of chains in the distribution network to simplify logistics. The pharmacy chains eligible for participation in Texas include Brookshire, Costco, CVS, HEB, Kmart, Kroger, Randalls, Sam's Club, Target, Tom Thumb, United, Walgreens, Walmart, and independent retail pharmacies (henceforth independents). During the 2009 influenza pandemic, the Texas DSHS distributed antiviral drugs from the SNS and state cache through 6 major chains (Brookshire, HEB, Kroger, United, Walgreens, and Walmart), and independents. When we restricted the optimization to a few major chains, the resulting networks still achieved broad statewide coverage (Figures 2, 3). For example, Walgreens alone was expected to achieve ≈75% coverage if it dispenses in all of its 490 ZIP code areas; CVS and Walmart followed close behind (located in 422 and 372 ZIP code areas, respectively). These 3 chains have the greatest presence in the state (Table 1), but have highly overlapping geographic areas. Broad accessibility can also be achieved through a combination of smaller chains with geographic complementarity, for example, HEB and Kroger (in 189 and 167 ZIP code areas, respectively). Walgreens and Walmart overlap over half of their ZIP code areas (256), whereas HEB and Kroger overlap in only 30 ZIP code areas. However, the number of ZIP code areas alone is not predictive of access. For example, Brookshire has almost as many stores as Target (in 118 and 127 ZIP code areas, respectively), yet provides considerably less statewide access alone and in combination with other stores.
(Enlarge Image)
Figure 3.
Antiviral drug access in underinsured populations for single-chain and 2-chain pharmacy distribution networks during the 2009 influenza pandemic, Texas, USA. Each network contains a maximum of 723 distribution points, and was designed by using a hybrid optimization that maximizes coverage in small ZIP code (US postal code) areas and overall (see text for details). Color indicates the expected percentage of the underinsured population willing to travel to dispensing pharmacies to obtain antiviral drugs A) statewide and B) in small ZIP code areas. Numbers along the baselines and the y-axes indicate single-chain networks. 1, Walgreens; 2, CVS; 3, Walmart; 4, HEB; 5, Kroger; 6, Target; 7, Brookshire; 8, Sam's Club; 9, Tom Thumb; 10, Randalls; 11, United; 12, Costco; 13, Kmart; 14, Independents (independent pharmacies).
However, the major chains did not reach the underinsured populations in the small ZIP code areas, even under the hybrid optimization that explicitly targets these hard-to-reach populations (Figure 2, panel A). Independent pharmacies are essential to bridging this gap in coverage. The maximum access achieved by a 2-chain combination in small ZIP code areas is only 33% (Brookshire and Walmart) (Figure 3). Under the hybrid objective, optimized networks with <500 dispensing points yield solutions for all major pharmacy chains plus independents that provided slightly lower statewide accessibility than the corresponding solutions for major chains (Figure 2, panel B), in exchange for higher coverage in small ZIP code areas (Figure 2, panel A). Of the 1,023 ZIP code areas with ≥1 pharmacy, 271 have only independent pharmacies. Of these pharmacies, 167 are in small ZIP code areas, and were typically selected when optimizing for access in small ZIP code areas, but not when optimizing for access statewide (Figure 4).
(Enlarge Image)
Figure 4.
Number of sites in the antiviral drug distribution network during the 2009 influenza pandemic that contained only independent pharmacies (independents; i.e., no major chains) when optimizing for the underinsured population in small ZIP code (US postal code) areas (i.e., ZIP code areas with <1,000 underinsured persons), statewide, or both (hybrid), Texas, USA.
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