POLICY MODEL INPUT PARAMETERS

This chapter incorporates the Matlab-specific data from the previous chapter into an integrated economic model that summarizes the costs and benefits of cholera vaccination. In addition to these data, I need to make a number of assumptions. Model input parameters are summarized in Table 7.1. This table includes my best estimate for each parameter in addition to a range of possible low and high values. I split the Matlab area into four different subgroups: children in high incidence villages, children in average incidence villages, adults in high

incidence villages, and adults in average incidence villages. The population is split such that 10% of the population resides in high incidence villages and the remaining 90% live outside these villages. Based on Table 4.1, it appears that villages with the top 10% of incidence experience about four times greater incidence than the rest of the villages. This represents the maximum potential difference between the highest incidence villages compared to the rest of the Matlab area. It is possible that incidence is underestimated in many villages because patients seek treatment at other facilities besides the ICDDR,B hospital, especially patients that live in villages located farther from the hospital in the northern part of the surveillance area. In personal

conversations with hospital doctors, they stated that they believed that certain areas are more prone to cholera than others. However, it is possible that these doctors are somewhat biased by their experience of working at the hospital. Alternatively, differences may occur at geographical areas smaller than villages, such that differences are small after averaging across entire village populations. Among the villages in my CV survey sample, which included the majority of those located within two hours of the hospital, the top 10% of villages experienced twice the incidence

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of the remaining 90% of villages over 10 years. If I restrict the observation period to 3 years instead of 10 years, the top 10% experience more than 4 times the incidence of the remaining 90%. I explore this maximum difference (i.e. 4 times greater incidence in the top 10%) to understand whether it is useful to attempt to target high incidence geographical areas in Matlab. Thus, the baseline scenario represents an upper bound difference in incidence rates between high and average incidence villages. Smaller differences are explored in the sensitivity analysis. If it is not useful to target prices assuming a larger discrepancy in incidence, it definitely would also not be useful for smaller discrepancies.

Thus, I adjusted my estimates of population average incidence rates for the high

incidence villages to be four times greater than the remaining 90%. This adjustment is made such that the expected number of cases remains constant. Relative to the population average incidence, the risk of infection is almost four times greater in the high incidence villages and slightly less than average in the remaining 90% of villages where most of the population resides. The ranges of low-to-high incidence values used in the sensitivity analysis are one half and double the best estimates. Incidence may be less than the best estimate if the recent trend of declining incidence rates continues into the future. In contrast, incidence may be higher than expected if a large fraction of the population seeks treatment at alternative locations or if the recent downward trend in incidence were to be reversed.

I use the same demand equations for both low and high incidence groups because incidence rates were not significant in any of the demand models that I evaluated. Vaccination demand function parameters are taken from the previous chapter. The range in child demand intercepts is based on an assumption that between 50% and 80% of children would be willing to pursue free vaccinations if these were available. The adult intercept bounds are assumed to be smaller than the child bounds, 25% to 60% of the adult population.

This basic herd protection relationship is shown in Figure 3.2 and is the basis of the estimates in Table 7.1. As discussed in Section 3.5, Emch et al. (2009) found a strong correlation

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between herd protection effects and environmental connectivity, specifically baris collocated with water bodies. These findings suggest that herd protection effects are highly localized. Thus, I assume that herd protection occurs primarily within village groups rather than between village groups. Specifically, I assume that coverage rates in high incidence villages have no impact on herd protection for average incidence villages. Similarly, I assume that coverage rates in average incidence villages have no impact on high incidence villages.

In the absence of age-group-specific herd protection effects, I assume that adult and child coverage rates have the same impact on herd protection effects within a village grouping.

Because I express coverage rates in terms of the number of people vaccinated rather than as percentages, the coefficients for the average incidence villages must be smaller to account for the larger population. Specifically, the coefficients for high incidence villages are nine times greater to account for the fact that total population of the high incidence villages is nine times smaller than for the average incidence villages. The coefficients are determined by fitting an exponential expression to the data reported in Longini et al.’s (2007) model of herd protection observed during the 1985 vaccination trial. In the sensitivity analysis, I allow herd protection coefficients to vary separately for adults and children. The range of herd protection coefficients is 50% to 150% of the baseline values. For the lower bound, this is analogous to assuming that functional form remains the same, but twice as many people must be vaccinated to achieve the same herd protection effect. The herd protection results are based on the first year after vaccination and effects may diminish in years two and three (Longini et al., 2007).

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Table 7.1. Population, herd protection and other model input parameters

Variable Children high

incidence (ch subscript) Adults high incidence (ah subscript) Children average incidence (cl subscript) Adults average incidence (al subscript) Values from literature

Population, POPxx 9,800 12,300 89,000 109,000 Demand intercept, αxx 5,300 [4,600 – 7,100] 3,900 [3,000 – 7,400] 47,000 [34,000 – 68,000] 35,000 [26,000 – 62,000] Price coefficient, βxx -0.36 [-0.20 – -0.50] -0.33 [-0.20 – -0.75] -0.36 [-0.20 – -0.50] -0.33 [-0.20 – -0.75] Baseline annual incidence,

INCU0xx, cases per 1,000

persons 8.9 [2.9 – 18] 3.2 [1.0 – 6.3] 2.2 [1.1 – 4.4]

0.80 [0.4 – 2.0] Herd protection coefficient

for coverage γxx -1.8E-04 [-8.9E-05 – -2.7E-04] -1.8E-04 [-8.9E-05 – -2.7E-04] -2.0E-05 [-1.0E-05 – -3.0E-05] -2.0E-05 [-1.0E-05 – -3.0E-05]

Fixed cost, F, US$ 22,000 [10,000 -50,000]

Variable cost, C, US$ 2.0 [1.5 – 4.0]

Public COI per case- PUBCOI, US$

20 [10 - 30] 20 [10 – 30] 20 [10 - 30] 20 [10 - 30]

Vaccine efficacy, Eff, 65% [50 - 75]

Duration of vaccine protection, t (years)

3 [2 - 4]

Present worth factor, PWF 2.58

DALY weight, DALYweight 0.105 [0.08 - 0.4]

Case fatality rate, CFRxx

(%)

1 [0.5 – 3]

Expected remaining life years, LE xx

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Variable Children high

incidence (ch subscript) Adults high incidence (ah subscript) Children average incidence (cl subscript) Adults average incidence (al subscript) Length of illness, DUR

(days)

3 [1 – 7]

Financial discount rate (%) 8

DALY discount rate (%) 3

Indirect protection valuation correction coefficient for vaccinated, πv

0.75 [0.5 – 1.0]

Herd protection valuation coefficient- indirect

protection for unvaccinated,

πu

0.75 [0.5 – 1.0]

The fixed cost is assumed to be US$22,000, which is equivalent to US$0.10 per person. This is similar to the amount used in a recent optimization study for typhoid vaccination

programs in Asia (Lauria et al., 2009). The uncertainty range for fixed cost is US$10,000 to US$50,000, which corresponds to per person costs of US$0.05 to about US$0.25. The variable cost of vaccination is assumed to be US$2.2 for two doses of the cholera vaccination. Following Jeuland et al. (2009), this assumes a procurement cost per dose, inclusive of wastage, would be US$0.60 and that the delivery cost per dose would also be about US$0.50. The delivery costs are based on a study of delivery costs in low income countries (Lauria and Stewart, 2007). Overall, the uncertainty range is US$1.5 to US$4. The upper bound delivery cost may be greater than the average for low income countries if estimates are based on rural (rather than urban) areas.

The public treatment cost savings per case avoided is estimated to be US$20 as reported in Section 5.2. The uncertainty range (US$10 to US$30) is small because ICDDR,B keeps precise records of operations. Vaccination direct efficacy is assumed to be 65% based on Longini’s reanalysis of vaccination efficacy (Longini et al., 2007). This is greater than the 50% direct

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efficacy reported in the original analysis (Clemens et al., 1990b) because that study did not account for herd protection effects. Thus, at any coverage rate, vaccinated persons’ risk of contracting cholera is 65% less than unvaccinated persons. I estimated that the duration of vaccine protection is 3 years based on a recent oral cholera vaccination effort in Vietnam (Thiem et al., 2006) with an uncertainty range of 2 to 4 years.

I estimate that the average duration of cholera illness is seven days and that the DALY disutility weight is 0.105 for those that survive the illness. This weight is based on the World Health Organization’s standard for diarrheal disease ((WHO), 2003). For the sensitivity analysis, I assume DALY disutility weights range from 0.08 to 0.40 because cholera is an especially virulent form of diarrheal disease and patients are often unable to perform any other tasks during the short duration of symptoms. The case fatality rate is estimated at 1% based on personal communications with epidemiologists from the International Vaccine Institute. The range for case fatality rate is 0.5% to 3%. I would expect that the Matlab rate is at the low end of the range because of the high quality treatment facilities available at the ICDDR,B hospital. These

estimates and ranges are consistent with those reported in a recent multicountry cost utility study of cholera vaccination (Jeuland et al., 2009).

The remaining life years per cholera death are 65 for children and 36 for adults based on life tables developed from ICDDR,B’s surveillance efforts. I used the average adult age to calculate adult life expectancy. However, Table 2.1 suggests that elderly adults are considerably more likely to die from diarrheal disease than younger adults. Thus, I include a range of 10 to 36 years for adult life expectancy in the sensitivity analysis. There is little uncertainty for children because life expectancies are similar across all child ages. Overall, I estimate that 0.22 DALYs are saved per adult case prevented and 0.29 are saved per child case prevented. Most of the DALYs saved result from avoided mortality rather than avoided morbidity. Thus, case fatality rate would be especially important to estimate for an accurate DALY measure.

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In the absence of data, I assume that πu and πv are equal to 0.75. This would indicate that indirect protection is less valuable than direct protection. It also indicates that WTP decreases per additional unit of protection. Indirect protection may be less valuable than direct protection for at least two reasons: 1) people are not protected when they spend time outside of the Matlab area or 2) estimates of indirect protection are much more uncertain than estimates of direct efficacy. I assume that the uncertainty ranges for πu and πv are 0.5 to 1.0.