Biomedical Engineering Reference
In-Depth Information
be the random variable associated with xi
i
and denote its survival distribution
as S(xjj) = Pr[X
i
> xjz
i
= j] when z
i
= j; j = 0; 1. Similarly let Y
i
, L
i
, and
R
i
denote random variables for yi,
i
, `
i
, and r
i
. The two-sample null hypothesis
is that S(xj0) = S(xj1) for all x.
13.2.3
Assessment of Simple Endpoints
We first consider simple endpoints where the event Xi
i
is just one event (e.g.,
HIV detectable in blood). Suppose after baseline each subject is assessed at k
times (a = [a
1
;:::;a
k
]) throughout the course of the study, so there are k + 1
possible intervals,
f(0;a
1
]; (a
1
;a
2
];:::; (a
k1
;a
k
]; (a
k
;1)g:
For regular assessments with no missing assessments or assessments at un-
scheduled times, the vector of assessments a is the same for all subjects and
is therefore independent of the events.
Now consider the case where there are regularly scheduled assessment
times, but each subject may miss some assessments or have an assessment
that is not at the scheduled time. Let A
i
= [A
i1
;:::;A
ik
i
] be the vector of
random variables representing assessments for the i-th subject. For example,
consider the 12-month study with scheduled assessments every 2 months and
suppose the i-th subject missed one assessment, the assessment at month =
4, then
A
i
= [2; 6; 8; 10; 12] :
If the j subject made all the scheduled assessments but was also assessed at
month = 3, then
A
j
= [2; 3; 4; 6; 8; 10; 12] :
When A
i
is independent of Xi
i
and z
i
, we say we have totally independent
assessment (TIA). When A
i
is independent of Xi
i
given zi,
i
, we say we have
conditionally independent assessment (CIA); and when the distribution of A
i
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