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In randomized trials, appropriately adjusting for baseline variables andshort-term outcomes can lead to increased precision and reduced sample size. Weexamine the impact of such adjustment in group sequential designs, i.e.,designs with preplanned interim analyses where enrollment may be stopped earlyfor efficacy or futility. We address the following questions: how muchprecision gain can be obtained by appropriately adjusting for baselinevariables and a short-term outcome? How is this precision gain impacted byfactors such as the proportion of pipeline participants (those who enrolled buthaven't yet had their primary outcomes measured) and treatment effectheterogeneity? What is the resulting impact on power and average sample size ina group sequential design? We derive an asymptotic formula that decomposes theoverall precision gain from adjusting for baseline variables and a short-termoutcome into contributions from factors mentioned above, for efficientestimators in the model that only assumes randomization and independentcensoring. We use our formula to approximate the precision gain from a targetedminimum loss-based estimator applied to data from a completed trial of a newsurgical intervention for stroke. Our formula implies that (for an efficientestimator) adjusting for a prognostic baseline variable leads to at least asmuch asymptotic precision gain as adjusting for an equally prognosticshort-term outcome. In many cases, such as our stroke trial application, theformer leads to substantially greater precision gains than the latter. In oursimulation study, we show how precision gains from adjustment can be convertedinto sample size reductions (even when there is no treatment effect).

Improving Precision through Adjustment for Prognostic Variables in Group  Sequential Trial Designs: Impact of Baseline Variables, Short-Term Outcomes,  and Treatment Effect Heterogeneity