  Researchers are often interested in estimating the effect of sustained use of
a treatment on a health outcome. However, adherence to strict treatment
protocols can be challenging for individuals in practice and, when
non-adherence is expected, estimates of the effect of sustained use may not be
useful for decision making. As an alternative, more relaxed treatment protocols
which allow for periods of time off treatment (i.e. grace periods) have been
considered in pragmatic randomized trials and observational studies. In this
article, we consider the interpretation, identification, and estimation of
treatment strategies which include grace periods. We contrast natural grace
period strategies which allow individuals the flexibility to take treatment as
they would naturally do, with stochastic grace period strategies in which the
investigator specifies the distribution of treatment utilization. We estimate
the effect of initiation of a thiazide diuretic or an angiotensin-converting
enzyme inhibitor in hypertensive individuals under various strategies which
include grace periods.
