Nonparametric adjustment techniques for binary covariates

Though a variety of reasons are often articulated for adjusting analyses for covariates, these reasons often fall into one of two general objectives, specifically to increase precision or to decrease bias. In practice, one does not generally choose between these objectives, because the methods that address one tend to address the other, as well. Because of this, no distinction is made in the methods used to correct for a baseline imbalance with respect to a prognostic covariate versus to ensure a fair comparison across treatment groups by making the comparisons within the levels of a prognostic covariate. Yet the literal translation of these two uses of covariate adjustment will lead to two distinct adjustment methods. We illustrate this divergence in the simplest case of a single binary covariate, a binary outcome, and two treatments, and we note that it is possible to combine the two approaches to derive yet a third approach. Each of these approaches is nonparametric and exact, and so it is the precise reason for adjusting that should dictate which would be used in any given situation.