  In conventional randomized controlled trials, adjustment for baseline values
of covariates known to be at least moderately associated with the outcome
increases the power of the trial. Recent work has shown particular benefit for
more flexible frequentist designs, such as information adaptive and adaptive
multi-arm designs. However, covariate adjustment has not been characterized
within the more flexible Bayesian adaptive designs, despite their growing
popularity. We focus on a subclass of these which allow for early stopping at
an interim analysis given evidence of treatment superiority. We consider both
collapsible and non-collapsible estimands, and show how to obtain posterior
samples of marginal estimands from adjusted analyses. We describe several
estimands for three common outcome types. We perform a simulation study to
assess the impact of covariate adjustment using a variety of adjustment models
in several different scenarios. This is followed by a real world application of
the compared approaches to a COVID-19 trial with a binary endpoint. For all
scenarios, it is shown that covariate adjustment increases power and the
probability of stopping the trials early, and decreases the expected sample
sizes as compared to unadjusted analyses.
