Biomedical Engineering Reference
In-Depth Information
L
i
= lim
!0
x x, and R
i
= x. We make no assumption of regular
assessment nor make any restrictions on ki
i
unless explicitly stated.
Often we do not use any information about A
i
except the assessments
that bracket the event, fL
i
;R
i
g. For example, consider a 12-month study
with monthly assessments and with the unobserved Xi
i
= 3:4; then often we
will only use Yi
i
= (3; 4]. Although we only keep two assessment times, this
is not a Case II assessment with independent assessment because Li
i
= 3 and
R
i
= 4 are highly dependent on Xi.
i
.
13.2.4
Composite Endpoints and Interval Censoring
X
(1
i
;X
(2)
Consider a composite endpoint where, for example, Xi
i
= min
i
with X
(1
i
and X
(2
i
representing different types of events. Often the two dif-
ferent types of events will have different assessment times. For example, sup-
pose that X
(1)
i
represents death and X
(2)
i
represents cancer progression where
progression is assessed radiographically and is defined as either a specified
increase in tumor size over baseline tumor size or the presence of new tumors.
In this case, Xi
i
is known as the progression-free survival time. The assessment
vector of the two types of events may differ. For example, the assessment vec-
tor for deaths, say A
(1)
i
, may represent daily assessments because usually the
date of death can be known exactly (if the knowledge of date of death comes
retrospectively, this is not a problem as long as it is known by analysis time);
however, the assessment for cancer progression, say A
(2
i
, may have assess-
ments approximately every 3 months. Consider a subject assessed every 12
weeks for cancer progression and daily for death. Then if the i-th subject dies
at week 13 (day 91) after a negative cancer progression assessment at week 12
(day 84), then y
i
= (84; 91]. Notice that the left endpoint of the interval comes
from the assessment for progression while the right endpoint comes from as-
sessment for death. For the general two-event-type composite endpoint, we
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