Improving precision by adjusting for prognostic baseline variables in randomized trials with binary outcomes, without regression model assumptions

In randomized clinical trials with baseline variables that are prognostic for the primary outcome, there is potential to improve precision and reduce sample size by appropriately adjusting for these variables. A major challenge is that there are multiple statistical methods to adjust for baseline variables, but little guidance on which is best to use in a given context. The choice of method can have important consequences. For example, one commonly used method leads to uninterpretable estimates if there is any treatment effect heterogeneity, which would jeopardize the validity of trial conclusions. We give practical guidance on how to avoid this problem, while retaining the advantages of covariate adjustment. This can be achieved by using simple (but less well-known) standardization methods from the recent statistics literature. We discuss these methods and give software in R and Stata implementing them. A data example from a recent stroke trial is used to illustrate these methods.