Biomedical Engineering Reference
In-Depth Information
(1) I = (Y
i1
;Y
i
] if Yi
i1
< T Y
i
for some i;
(2) Y
i
's are random variables and 0 Y
i
Y
i+1
;
(3) T ? Y, where Y = fY
i
: i 1g;
(4) if
Y
is noninformative.
This model avoids the drawback of the Case 2 or Case k model, that
each patient in the study has the same number of follow-ups. But if Yi
i
<
Y
i+1
for infinitely many i, then according to this model, right-censored
observations occur only after infinitely many follow-ups are made by a
patient; thus the model is not realistic. Hence, the model makes sense
if it is further assumed that Y
j
= Y
K
8 j K, where K is a random
integer. Moreover, the model does not assume that limi→∞
i!1
Y
i
! 1 in
probability. Consequently, it is possible that P(sup
i
Y
i
< ) = 1 for some
nite . Under this model, they claim a strong consistency result on the
NPMLE, but the claim is false (see Schick and Yu (2000)).
5. The Discrete IC Model (Petroni and Wolfe, 1994). Assume
(1) 0 < y
1
< < y
k
are predetermined appointment times;
(2)
i
is the indicator function that the patient keeps the i-th appoint-
ment;
(3) There are K (=
P
i=1
i
) follow-ups, say Y
j
, where Y
j
= y
i
j
i
j
and
i
1
, ..., i
K
are the ordered indices of i's that
i
= 1;
(4) I = (Y
j1
;Y
j
] if T 2 (Y
j1
;Y
j
] for some j, where Y
0
= 1 and
Y
K+1
= 1;
(5) T ? C, where C = (
1
;:::;
k
);
(6) f
1
;:::;
k
is noninformative.
This model also avoids the drawback of the Case 2 or Case k model, that
each patient in the study has the same number of follow-ups. However,
it cannot be extended to the continuous case and it is actually a special
case of the next model.
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