Biomedical Engineering Reference
In-Depth Information
mative censoring and would bias the estimate of the survival distribution. In
a similar way, we could have informative assessments (also called informative
censoring) if subjects who felt very ill avoided getting assessed or got assessed
earlier than scheduled.
For testing we would like to distinguish between two types of independent
assessment:
•
Total independent assessment (TIA), where the assessments are inde-
pendent of the event time and of the treatment, and
•
Conditional independent assessment (CIA), where within each treatment
group the assessments are independent of event time, but we may have
different assessment processes for each treatment group.
When we have CIA but not TIA, then we have assessment-treatment depen-
dence.
In the following subsections we give precise mathematical definitions of
TIA and CIA. Further, we talk about composite endpoints such as progression-
free survival, the earlier of cancer progression or death. Although these end-
points may appear to be much more complicated because they are defined as
the minimum of two events that may be assessed according to different sched-
ules, the definitions of TIA, CIA, and ATD can be used in a similar way with
progression-free survival as with simple endpoints. Finally, we discuss how the
informative assessment may affect validity of tests.
13.2.2
Basic Notation
For the i-th subject, let xi
i
be the unobserved time to event (e.g., HIV de-
tectable), yi
i
be the observed interval so that xi
i
2 y
i
, we write yi
i
= (`
i
;r
i
]
where for example, `
i
is the time of the last HIV-negative blood draw and ri
i
is
the time of the first positive HIV blood draw. With a slight abuse of notation,
we allow ri
i
= 1 to represent right-censored observations. Let z
i
be the treat-
ment group indicator (e.g., zi
i
= 0 for placebo and zi
i
= 1 for vaccine). Let Xi
i
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