Number-needed-to-vaccinate calculations: fallacies associated with exclusion of transmission

Abstract

Background: Number-needed-to-vaccinate (NNV) calculations are used with increasing frequency as metrics of the attractiveness of vaccination programs. However, such calculations as typically applied consider only the direct protective effects of vaccination and ignore indirect effects generated through reduction of force of infection (i.e., risk of infection in susceptible individuals). We postulated that such calculations could produce profoundly biased estimates of vaccine attractiveness.

Methods: We used mathematical models simulating endemic and epidemic diseases with a variety of epidemiological characteristics, and in the face of varying approaches to immunization, to evaluate biases associated with exclusion of transmission. We generated number-needed-to-vaccinate calculations using both traditional methods, and using a more realistic approach that defines this quantity as the ratio of cases prevented through vaccination (directly or indirectly) to individuals vaccinated. We quantified bias as the ratio of estimates produced using these two different methods.

Results: Across a range of simulated infectious diseases with variable epidemiological characteristics, and in the context of both pulsed vaccination and ongoing vaccine programs, traditional NNV calculations based on systems using plausible infectious disease parameters produced estimates biased by up to 3 orders of magnitude (i.e., 1000 fold). Unbiased NNV estimates were seen only in the context of diseases with extremely high reproductive numbers that could be prevented with highly efficacious vaccines.

Conclusions: When evaluated using mathematical models that simulate common vaccine-preventable diseases of public health importance, typical number-needed-to-vaccinate calculation produce marked over-estimates relative to NNV calculations incorporating the fundamental transmissibility of communicable diseases. NNV calculations should be used with caution and interpreted critically when used as metrics for the potential community-level impact of vaccination programs.