Biomedical Engineering Reference
In-Depth Information
write Yi
i
mathematically as
i
A
(1)
ih
;A
(2)
A
(1)
i;h+1
;A
(2)
Y
i
=
min
; min
;
ij
i;j+1
where h : X
i
2 (A
(1)
ih
;A
(1)
i;h+1
] and j : X
i
2 (A
(2)
ij
;A
(2)
i;j+1
] :
In this two-event-type composite endpoint, we define total independent assess-
ment as the case when (X
(1
i
;X
(2
i
) are jointly independent of both A
(1
i
and
A
(2)
i
, and conditional independent assessment as the case when (X
(1)
i
;X
(2)
i
)
are independent of both A
(1)
i
and A
(2
i
given zi.
i
. Let assessment treatment
dependence be whenever the distribution of either A
(1)
i
or A
(2)
i
depends on
z
i
.
13.2.5
Informative Assessment
A simple kind of informative assessment that we study in the simulation sec-
tion is when the probability of assessment changes after the event has oc-
curred. Note that if all treatment groups have the same type of informative
assessment, then there is no assessment treatment dependence under the null
hypothesis of equal event time distributions. With no ATD, then permutation-
based hypothesis tests are known to be theoretically valid, because the null
distribution does not depend on treatment group. The problem for test valid-
ity with informative assessment is when it differs between treatment groups.
We explore this situation in the simulation section.
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