Estimating vaccine efficacy under the heterogeneity of vaccine action in a nonrandomly mixing population

Vaccines often have heterogeneous actions because of possible variation in the immune systems of hosts. One must consider such heterogeneity of vaccine action when developing a vaccine efficacy parameter. Addressing this issue the summary model of vaccine action has been proposed in the literature to estimate vaccine efficacy in a randomly mixing population. However, nonrandom mixing is common, particularly in a small-group-mixing population. This article extends the summary model of vaccine action to such a nonrandomly mixing population. The interpretation and estimation of the summary vaccine efficacy were discussed in light of other two models of vaccine action: the leaky and all-or-nothing model. Vaccine efficacy under all models is defined as the relative reduction in transmission probability due to vaccine. Estimation of the transmission probabilities is described based on a deterministic epidemic model of an acute transmitted disease. This article further discusses, based on the above vaccine models, the estimation of vaccination coverage required to control epidemic. Methods are illustrated using data simulated by considering different patterns of mixing and vaccine action. Results confirm that the summary model performs better than other two models when vaccine action is heterogeneous.