Abstract
Understanding the population-level effects of vaccines has important public health policy implications. Inferring vaccine effects from an observational study is challenging because participants are not randomized to vaccine (i.e., treatment). Observational studies of infectious diseases present the additional challenge that vaccinating one participant may affect another participant's outcome, i.e., there may be interference. In this paper recent approaches to defining vaccine effects in the presence of interference are considered, and new causal estimands designed specifically for use with observational studies are proposed. Previously defined estimands target counterfactual scenarios in which individuals independently choose to be vaccinated with equal probability. However, in settings where there is interference between individuals within clusters, it may be unlikely that treatment selection is independent between individuals in the same cluster. The proposed causal estimands instead describe counterfactual scenarios which allow for within-cluster dependence in the individual treatment selections. These estimands may be more relevant for policymakers or public health officials who desire to quantify the effect of increasing the proportion of vaccinated individuals in a population. Inverse probability-weighted estimators for these estimands are proposed. The large-sample properties of the estimators are derived, and a simulation study demonstrating the finite-sample performance of the estimators is presented. The proposed methods are illustrated by analyzing data from a study of cholera vaccination in over 100,000 individuals in Bangladesh.