  Adaptive treatment assignment algorithms, such as bandit and reinforcement
learning algorithms, are increasingly used in digital health intervention
clinical trials. Causal inference and related data analyses are critical for
evaluating digital health interventions, deciding how to refine the
intervention, and deciding whether to roll-out the intervention more broadly.
However the replicability of these analyses has received relatively little
attention. This work investigates the replicability of statistical analyses
from trials deploying adaptive treatment assignment algorithms. We demonstrate
that many standard statistical estimators can be inconsistent and fail to be
replicable across repetitions of the clinical trial, even as the sample size
grows large. We show that this non-replicability is intimately related to
properties of the adaptive algorithm itself. We introduce a formal definition
of a "replicable bandit algorithm" and prove that under such algorithms, a wide
variety of common statistical analyses are guaranteed to be consistent. We
present both theoretical results and simulation studies based on a mobile
health oral health self-care intervention. Our findings underscore the
importance of designing adaptive algorithms with replicability in mind,
especially for settings like digital health where deployment decisions rely
heavily on replicated evidence. We conclude by discussing open questions on the
connections between algorithm design, statistical inference, and experimental
replicability.
