Many public health interventions are conducted in settings where individuals are connected and the
\nintervention assigned to some individuals may spill over to other individuals. In these settings, we can
\nassess: i) the individual effect on the treated, ii) the spillover effect on untreated individuals through
\nan indirect exposure to the intervention, and iii) the overall effect on the whole population. Here, we
\nconsider an egocentric network-based randomized design in which a set of index participants is recruited
\nand randomly assigned to treatment, while data are also collected from their untreated network members.
\nSuch design is common in peer education interventions conceived to leverage behavioral influence among
\npeers. Under the potential outcomes framework, we first clarify the assumptions required to rely on an
\nidentification strategy that is commonly used in the well-studied two-stage randomized design. Under
\nthese assumptions, causal effects can be jointly estimated using a regression model with a block-diagonal
\nstructure. We then develop sample size formulas for detecting individual, spillover, and overall effects for
\nsingle and joint hypothesis tests, and investigate the role of different parameters. Finally, we illustrate
\nthe use of our sample size formulas for an ENR experiment to evaluate a HIV peer education intervention.<\/p>\n