Distinguishing vaccine efficacy and effectiveness

Abstract

Background: Mathematical models of disease transmission and vaccination typically assume that protective vaccine efficacy (i.e. the relative reduction in the transmission rate among vaccinated individuals) is equivalent to direct effectiveness of vaccine. This assumption has not been evaluated.

Methods: We used dynamic epidemiological models of influenza and measles vaccines to evaluate the common measures of vaccine effectiveness in terms of both the protection of individuals and disease control within populations. We determined how vaccine-mediated reductions in attack rates translate into vaccine efficacy as well as into the common population measures of 'direct', 'indirect', 'total', and 'overall' effects of vaccination with examples of compartmental models of influenza and measles vaccination.

Results: We found that the typical parameterization of vaccine efficacy using direct effectiveness of vaccine can lead to the underestimation of the impact of vaccine. Such underestimation occurs when the vaccine is assumed to offer partial protection to every vaccinated person, and becomes worse when the level of vaccine coverage is low. Nevertheless, estimates of 'total', 'indirect' and 'overall' effectiveness increase with vaccination coverage in the population. Furthermore, we show how the measures of vaccine efficacy and vaccine effectiveness can be correctly calculated.

Conclusions: Typical parameterization of vaccine efficacy in mathematical models may underestimate the actual protective effect of the vaccine, resulting in discordance between the actual effects of vaccination at the population level and predictions made by models. This work shows how models can be correctly parameterized from clinical trial data.

Figure 1

Measures of vaccination effectiveness and study designs for the evaluation of each measure based on comparison populations. Population A and B are separated in every way relevant to transmission dynamics. In population A, some but not necessarily all individuals are vaccinated. In population B, all individuals are unvaccinated (Adapted from [29])

Figure 2

Four types of vaccine effectiveness (VE_I, VE_IIA, VE_IIB, and VE_III) produced by a mathematical model for influenza. Parameters specific to influenza were used: α=0.7, τ₁ = τ₂ = 4 (days), β=0.6, and R₀=2.4 [25]. The vaccine coverage (f) and the reduction in infectivity among the vaccine breakthrough cases (σ) compared to unvaccinated infections were varied. Vaccine effectiveness produced by the model were often much lower than the protective vaccine efficacy, α. The discrepancy between the value of α and resulting direct effectiveness (VE_I) indicates the potential underestimation in the predicted impact of vaccination produced by mathematical models arising from common approaches in parameterization of vaccine efficacy.

Figure 3

Four types of vaccine effectiveness (VE_I, VE_IIA, VE_IIB, and VE_III) predicted for measles by using a mathematical model (Eqs. 1–8). We parameterized our model based on measles epidemiology and its vaccine: α =0.95, τ₁ = τ₂ = 7 (days), β=2.143, and R₀=15 [–28]. The vaccine coverage (f) and the reduction in infectivity among the vaccine breakthrough cases (σ) compared to unvaccinated infections were varied. In general, the resulting vaccine effectiveness are lower than the reduction in individual infection risk by vaccination, α. Such discrepancy was highlighted with lower vaccine coverage or with lower vaccine efficacy in reducing infectivity among vaccinated individuals when vaccine breakthrough occurs.

Figure 4

Four types of vaccine effectiveness (VE_I, VE_IIA, VE_IIB, and VE_III) predicted for influenza and ‘all-or-nothing’ vaccine (Eqs. 13–20). We used parameters that are influenza-specific: α=1, τ₁ = τ₂ = 4 (days), β=0.6, and R₀=2.4 [25].