Biomedical Engineering Reference
In-Depth Information
8.6
Concluding Remarks
In this chapter, the main interest resided in estimating the causal effect of a
baseline treatment on an end-of-study endpoint using longitudinal data sub-
ject to a combination of interval- and right-censoring. In certain circumstances,
however, it may be of interest to study the impact of this treatment on a mid-
study outcome. A simple way of addressing this question consists of applying
the methodology developed in this chapter using only data points collected up
to and including the time of the outcome of interest. While easy to implement,
this approach may fail to make an optimal use of the available data. Indeed,
information about a mid-study outcome may be contained in data recorded
after this outcome.
Under alternative causal assumptions, the information from data collected
after the endpoint considered may be utilized in drawing inference about the
outcome of interest. Essentially, if Y
q
is the outcome of interest, with 1 q
m, one may wish to consider the modified observation unit
O = (M
0
;A;Y
0
;:::;Y
q1
;
q
;:::;
m
;M
m+1
;Y
m+1
;
q1
;M
q
;Y
q
)
where all observations collected after time t
q
have been inserted between Y
q1
and
q1
. If a nonparametric system of structural equations can be con-
structed respecting the modified time-ordering and the sequential randomiza-
tion assumption can be reasonably imposed on the intervention nodes of this
system, then full use of the data, collected both before and after the time-
point of interest, can be utilized. The adequateness of the sequential random-
ization assumption for this modified structure will not always be scientifically
sensible without modification and should be adjudicated in the context of
each application. To facilitate this adjudication, it is useful to note that, for
this revised assumption to be plausible, it will generally be necessary that
Z
q
= (
q
;M
q+1
;Y
q+1
;:::;Y
m+1
) not involve
q1
in the nonparametric sys-
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