  This manuscript explores the intersection of surrogate outcomes and adaptive
designs in statistical research. While surrogate outcomes have long been
studied for their potential to substitute long-term primary outcomes, current
surrogate evaluation methods do not directly account for the potential benefits
of using surrogate outcomes to adapt randomization probabilities in adaptive
randomized trials that aim to learn and respond to treatment effect
heterogeneity. In this context, surrogate outcomes can benefit participants in
the trial directly (i.e. improve expected outcome of newly-enrolled
participants) by allowing for more rapid adaptation of randomization
probabilities, particularly when surrogates enable earlier detection of
heterogeneous treatment effects and/or indicate the optimal (individualized)
treatment with stronger signals. Our study introduces a novel approach for
surrogate evaluation that quantifies both of these benefits in the context of
sequential adaptive experiment designs. We also propose a new
Covariate-Adjusted Response-Adaptive (CARA) design that incorporates an Online
Superlearner to assess and adaptively choose surrogate outcomes for updating
treatment randomization probabilities. We introduce a Targeted Maximum
Likelihood Estimator that addresses data dependency challenges in adaptively
collected data and achieves asymptotic normality under reasonable assumptions
without relying on parametric model assumptions. The robust performance of our
adaptive design with Online Superlearner is presented via simulations. Our
framework not only contributes a method to more comprehensively quantifying the
benefits of candidate surrogate outcomes and choosing between them, but also
offers an easily generalizable tool for evaluating various adaptive designs and
making inferences, providing insights into alternative choices of designs.
