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: i) the individual effect on the treated, ii) the spillover effect on untreated individuals through
an indirect exposure to the intervention, and iii) 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 from their untreated network members.
Such design is common in peer education interventions conceived to leverage behavioral influence among
peers. Under 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 ENR experiment to evaluate a HIV peer education intervention.

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