Design of egocentric network-based studies to estimate causal effects under interference

Many public health interventions are conducted in settings where individuals are connected and the intervention assigned to some individuals may spill over to other individuals. In these settings, we can assess: (a) the individual effect on the treated, (b) the spillover effect on untreated individuals through an indirect exposure to the intervention, and (c) the overall effect on the whole population. Here, we consider an egocentric network-based randomized design in which a set of index participants is recruited and randomly assigned to treatment, while data are also collected on their untreated network members. Such a design is common in peer education interventions conceived to leverage behavioral influence among peers. Using the potential outcomes framework, we first clarify the assumptions required to rely on an identification strategy that is commonly used in the well-studied two-stage randomized design. Under these assumptions, causal effects can be jointly estimated using a regression model with a block-diagonal structure. We then develop sample size formulas for detecting individual, spillover, and overall effects for single and joint hypothesis tests, and investigate the role of different parameters. Finally, we illustrate the use of our sample size formulas for an egocentric network-based randomized experiment to evaluate a peer education intervention for HIV prevention.