A test for direct and indirect effect interaction under treatment interference

Abstract

Treatment interference occurs when the treatment effect of one unit affects the response of another unit. Under interference, treatment effects can be classified as direct—those attributable to treatment given to the unit itself—or indirect—those that are due to the treatment status of “neighboring” units. However, definitions for many important quantities of interest can be ambiguous and hard to interpret unless no interaction between direct and indirect effects holds. Intuitively, this assumption a the direct effect of treatment for a unit will be the same regardless of what treatment allocation is given to that unit’s neighbors. Such an assumption may also help improve precision of direct and indirect effect estimates by allowing additional units to be used in the estimation of these effects. In this report, we develop a test for interaction between direct and indirect effects. Using sampling theory, we argue for approximate normality of our test statistic under a null hypothesis of no treatment interaction between direct and indirect effects. We then perform a simulation study to verify nominal Type I errors for our test and to assess how differences in sample size, interference model, and magnitudes of the treatment effect interactions impact the power of the test.