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Epidemiologists have used secondary attack rates (SARs) to estimate the protective effects of vaccination since the 1930s. SARs can also be used to estimate the effect of vaccination on reducing infectiousness in breakthrough cases. The conventional SAR approach has been to pool the denominators and numerators across transmission units, then to use a confidence interval for a simple relative risk. We demonstrate appropriate model-based methods to estimate vaccine efficacy (VE) from SARs using generalized estimating equations taking correlation within transmission units into account. The model-based procedures require transformation of the parameter estimates to the SAR scale to obtain vaccine efficacy estimates. Appropriate confidence intervals are then based on the bootstrap, with resampling done by transmission unit. We show that the usual confidence intervals are too narrow. We estimated the effect of pertussis vaccination on person-to-person transmission. The results show that pertussis vaccination reduces the ability of a breakthrough clinical case to produce other clinical cases. The methods can be used in evaluating VE for susceptibility and infectiousness from SARs in other infectious diseases.
Halloran et al. (Sat,) studied this question.