  Background: A common intercurrent event affecting many trials is when some
participants do not begin their assigned treatment. Many trials use a modified
intention-to-treat (mITT) approach, whereby participants who do not initiate
treatment are excluded from the analysis. However, it is not clear the estimand
being targeted by such an approach or the assumptions necessary for it to be
unbiased.
  Methods: We demonstrate that a mITT analysis which excludes participants who
do not begin treatment is estimating a principal stratum estimand (i.e. the
treatment effect in the subpopulation of participants who would begin
treatment, regardless of which arm they were assigned to). The mITT estimator
is unbiased for the principal stratum estimand under the assumption that the
intercurrent event is not affected by the assigned treatment arm, that is,
participants who initiate treatment in one arm would also do so in the other
arm.
  Results: We identify two key criteria in determining whether the mITT
estimator is likely to be unbiased: first, we must be able to measure the
participants in each treatment arm who experience the intercurrent event, and
second, the assumption that treatment allocation will not affect whether the
participant begins treatment must be reasonable. Most double-blind trials will
satisfy these criteria, and we provide an example of an open-label trial where
these criteria are likely to be satisfied as well.
  Conclusions: A modified intention-to-treat analysis which excludes
participants who do not begin treatment can be an unbiased estimator for the
principal stratum estimand. Our framework can help identify when the
assumptions for unbiasedness are likely to hold, and thus whether modified
intention-to-treat is appropriate or not.
