  Many public health interventions are conducted in settings where individuals
are connected to one another and the intervention assigned to randomly selected
individuals may spill over to other individuals they are connected to. In these
spillover settings, the effects of such interventions can be quantified in
several ways. The average individual effect measures the intervention effect
among those directly treated, while the spillover effect measures the effect
among those connected to those directly treated. In addition, the overall
effect measures the average intervention effect across the study population,
over those directly treated along with those to whom the intervention spills
over but who are not directly treated. Here, we develop methods for study
design with the aim of estimating individual, spillover, and overall effects.
In particular, we consider an egocentric network-based randomized design in
which a set of index participants is recruited from the population and randomly
assigned to treatment, while data are also collected from their untreated
network members. We use the potential outcomes framework to define two
clustered regression modeling approaches and clarify the underlying assumptions
required to identify and estimate causal effects. We then develop sample size
formulas for detecting individual, spillover, and overall effects. We
investigate the roles of the intra-class correlation coefficient and the
probability of treatment allocation on the required number of egocentric
networks with a fixed number of network members for each egocentric network and
vice-versa.
