  The STEP 1 randomized trial evaluated the effect of taking semaglutide vs
placebo on body weight over a 68 week duration. As with any study evaluating an
intervention delivered over a sustained period, non-adherence was observed.
This was addressed in the original trial analysis within the Estimand Framework
by viewing non-adherence as an intercurrent event. The primary analysis applied
a treatment policy strategy which viewed it as an aspect of the treatment
regimen, and thus made no adjustment for its presence. A supplementary analysis
used a hypothetical strategy, targeting an estimand that would have been
realised had all participants adhered, under the assumption that no
post-baseline variables confounded adherence and change in body weight. In this
paper we propose an alternative Instrumental Variable method to adjust for
non-adherence which does not rely on the same `unconfoundedness' assumption and
is less vulnerable to positivity violations (e.g., it can give valid results
even under conditions where non-adherence is guaranteed). Unlike many previous
Instrumental Variable approaches, it makes full use of the repeatedly measured
outcome data, and allows for a time-varying effect of treatment adherence on a
participant's weight. We show that it provides a natural vehicle for defining
two distinct hypothetical estimands: the treatment effect if all participants
would have adhered to semaglutide, and the treatment effect if all participants
would have adhered to both semaglutide and placebo. When applied to the STEP 1
study, they both suggest a sustained, slowly decaying weight loss effect of
semaglutide treatment.
