Effect Aliasing in Observational Studies

In experimental design, aliasing of effects occurs in fractional factorial experiments, where certain low order factorial effects are indistinguishable from certain high order interactions: low order contrast weights may be orthogonal to one another, while their higher order interactions are aliased and not identified. In observational studies, aliasing occurs when certain combinations of covariates—for example, time period and various eligibility criteria for treatment—perfectly predict the treatment that an individual will receive, so a covariate combination is aliased with a particular treatment. In this situation, when a contrast among several groups is used to estimate a treatment effect, collections of individuals defined by contrast weights may be balanced with respect to summaries of low-order interactions between covariates and treatments, but necessarily not balanced with respect high-order interactions. We develop a theory of aliasing in observational studies, illustrate that theory in an observational study whose aliasing is more robust than conventional difference-in-differences, and develop a new form of matching to construct balanced confounded factorial designs from observational data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.