  Inferring causal effects from an observational study is challenging because
participants are not randomized to treatment. Observational studies in
infectious disease research present the additional challenge that one
participant's treatment may affect another participant's outcome, i.e., there
may be interference. In this paper recent approaches to defining causal 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 select treatment 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 in which the treatment selection correlation structure is the same as
in the observed data distribution, allowing for within-cluster dependence in
the individual treatment selections. These estimands may be more relevant for
policy-makers or public health officials who desire to quantify the effect of
increasing the proportion of treated 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.
