  Adaptive interventions (AIs) are increasingly becoming popular in medical and
behavioral sciences. An AI is a sequence of individualized intervention options
that specify for whom and under what conditions different intervention options
should be offered, in order to address the changing needs of individuals as
they progress over time. The sequential, multiple assignment, randomized trial
(SMART) is a novel trial design that was developed to aid in empirically
constructing effective AIs. The sequential randomizations in a SMART often
yield multiple AIs that are embedded in the trial by design. Many SMARTs are
motivated by scientific questions pertaining to the comparison of such embedded
AIs. Existing data analytic methods and sample size planning resources for
SMARTs are suitable for superiority testing, namely for testing whether one
embedded AI yields better primary outcomes on average than another. This
represents a major scientific gap since AIs are often motivated by the need to
deliver support/care in a less costly or less burdensome manner, while still
yielding benefits that are equivalent or non-inferior to those produced by a
more costly/burdensome standard of care. Here, we develop data analytic methods
and sample size formulas for SMART studies aiming to test the non-inferiority
or equivalence of one AI over another. Sample size and power considerations are
discussed with supporting simulations, and online sample size planning
resources are provided. For illustration, we use an example from a SMART study
aiming to develop an AI for promoting weight loss among overweight/obese
adults.
