Interference between units in randomized experiments

In a randomized experiment comparing two treatments, there is interference between units if applying the treatment to one unit may affect other units. Interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit, one under treatment and the other under control, but instead are inherently more complex. Interference is common in social settings where people communicate, compete, or spread disease; in studies that treat one part of an organism using a symmetrical part as control; in studies that apply different treatments to the same organism at different times; and in many other situations. Available statistical tools are limited. For instance, Fisher's sharp null hypothesis of no treatment effect implicitly entails no interference, and so his randomization test may be used to test no effect, but conventional ways of inverting the test to obtain confidence intervals, say for an additive effect, are not applicable with interference. Another commonly used approach assumes that interference is of a simple parametric form confined to units that are near one another in time or space; this is useful when applicable but is of little use when interference may be widespread and of uncertain form. Exact, nonparametric methods are developed for inverting randomization tests to obtain confidence intervals for magnitudes of effect assuming nothing at all about the structure of the interference between units. The limitations of these methods are discussed. To illustrate the general approach, two simple methods and two simple empirical examples are discussed. Extension to randomization based covariance adjustment is briefly described.