Combining covariate adjustment with group sequential, information-adaptive designs to improve randomized trial efficiency.

Group sequential designs (GSDs), which involve preplanned interim analyses that allow for early stopping for efficacy or futility, are commonly used for ethical and efficiency reasons. Covariate adjustment, which involves appropriately adjusting for prespecified prognostic baseline variables, can improve precision and is generally recommended by regulators. Combining these, that is, using adjusted estimators at interim and final analyses of a GSD, has potential for dual benefits. We address 2 challenges involved in combining these methods. First, adjusted estimators may lack the independent increments structure (asymptotically) that is required to directly apply standard stopping boundaries for GSDs. We address this by applying a linear transformation to the sequence of adjusted estimators across analysis times, resulting in a new sequence of consistent, asymptotically normal estimators with the independent increments property that either improves or leaves precision unchanged. This approach generalizes foundational results on GSDs with semiparametric efficient estimators to any sequence of regular, asymptotically linear estimators. Second, we address the practical problem of handling uncertainty about how much (if any) precision gain will result from covariate adjustment. This is important for trial planning, since an incorrect projection of a covariate's prognostic value risks an over- or underpowered trial. We propose using information-adaptive designs, that is, continuing the trial until the required information level is achieved. This design enables faster, more efficient trials, without sacrificing validity or power.