Signature
VE = 1 - AR_v / AR_u
| Inputs | Definition | Unit |
|---|---|---|
AR_v | Attack rate among vaccinated people over the period | proportion |
AR_u | Attack rate among unvaccinated people over the same period, greater than zero | proportion |
VE | Proportionate reduction in risk among vaccinated people, efficacy in a trial or effectiveness in field conditions | proportion, often reported as a percentage |
|---|
Function
Attack rate, secondary attack rate and final epidemic size function
Maps counts of new cases and of people at risk over a stated period to an attack rate, a risk expressed as a proportion rather than a rate per unit of time. The same structure gives the secondary attack rate among contacts of primary cases, and comparing attack rates between groups gives the attack rate ratio and vaccine efficacy or effectiveness. Under the assumptions of the simple susceptible, infectious and recovered model, the final attack rate of a completed epidemic is linked to the basic reproduction number R_0 through the final size relation. In an economic evaluation the attack rate is either a fixed input probability of infection, as in a static model, or an output that changes with the intervention, as in a dynamic transmission model.
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Implementations
Excel
Vaccine effectiveness from two named attack rates
Excel subtracts the ratio of the vaccinated to the unvaccinated attack rate from 1, using named cells.
=1-AttackRateVaccinated/AttackRateUnvaccinated
Assumptions
Comparison groups decide which vaccine effect is measured
Halloran and colleagues show that the choice of comparison groups decides whether 1 minus the risk ratio estimates the effect of vaccination on an individual or the indirect, total or overall effects of a programme. The groups are stated before the estimate is used as the vaccine effect in a cost-effectiveness model.
Same case definition and period for vaccinated and unvaccinated attack rates
Both attack rates are counted over the same period with the same case definition and ascertainment, so the ratio is not distorted by differences in counting.
Worked examples
Varicella vaccine effectiveness in the CDC school outbreak
In the CDC example of a 2002 varicella outbreak in Oregon, 18 of 152 vaccinated and 3 of 7 unvaccinated children developed varicella, attack rates of about 0.1184 and 0.4286. The vaccine effectiveness is about 0.724, which the CDC text reports as 72%.
AR_v = 0.1184; AR_u = 0.4286; VE = 0.724
Common errors
Using the whole-population attack rate as the comparator for vaccine effectiveness
Dividing by the attack rate among all children in the CDC varicella example, about 0.1321, rather than among the unvaccinated gives a vaccine effectiveness of about 0.104 instead of 0.724.
Counting only infections averted among the vaccinated in a programme evaluation
Applying the vaccine effect with a fixed attack rate counts only infections averted among vaccinated people. In the article's illustrative example with R_0 of 2 and 30% coverage, that gives 23,910 of the 43,900 infections averted, about 54%, because reduced transmission also lowers the attack rate among the unvaccinated.
Sources
CDC vaccine efficacy and effectiveness from attack rates
Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice. 3rd ed. Atlanta: CDC; 2006, page last reviewed 2012. Lesson 3: Measures of Risk, section 6: Measures of public health impact. Vaccine efficacy and effectiveness as the proportionate reduction in risk among vaccinated people, the formula as 1 minus the risk ratio or as the risk difference over the risk among the unvaccinated, and the varicella example.
Comparison groups for direct, indirect, total and overall vaccine effects
Halloran ME, Struchiner CJ, Longini IM. Study designs for evaluating different efficacy and effectiveness aspects of vaccines. American Journal of Epidemiology. 1997;146(10):789-803. Vaccine efficacy and effectiveness measured as 1 minus a relative risk, and the framework relating the choice of comparison groups to direct, indirect, total and overall effects.
Canonical Identity
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