Biomedical Engineering Reference
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tem of structural equations; in other words, Z
q
should not be affected by the
monitoring process associated to time t
q
. If certain portions of Z
q
do involve
q1
, these should be removed altogether from consideration; any component
of Z
q
not involving
q1
will generally provide additional information and
render the resulting estimation procedure more ecient. In extreme cases, it
may warranted to remove all components of Z
q
from consideration.
In practice, it is possible that only few participants have been monitored
at the last study visit time t
m+1
. This would result in only a very small num-
ber of observations satisfying the restriction
m
= 1 imposed as part of the
interventions defining the counterfactuals considered and would necessarily
lead to increased estimation variability. To circumvent this problem, a de-
gree of artificial coarsening of the data may be useful. Specifically, the last
several study visit times can be merged into a single monitoring time, with
data summarized across such visits in an appropriate fashion. For example,
any participant monitored at least once during these merged times would be
considered to have been monitored at this single merged visit, and this par-
ticipant would have a positive event indicator if and only if at least one of the
event indicators collected during these merged visits was positive as well. This
approach would inflate the number of participants satisfying the intervention
requirement and thus decrease estimation variability. Nonetheless, this rem-
edy should be used sensibly because it would necessarily entail a change in
the definition of the target parameter and consequently a deviation from the
intended interpretation of such a parameter. In practice, the level of coars-
ening should be chosen to achieve an appropriate balance between estimator
variability and parameter interpretability.
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