Biomedical Engineering Reference
In-Depth Information
8
<
if
Y
1
(u)
if I = (1;u]
Note: G(I) =
There are two interpreta-
if
Y
1
;Y
2
(u;v)
if I = (u;v]
:
if
Y
2
(v)
if I = (v;1):
tions of the vector (Y
1
;Y
2
):
(1) Each person has exactly two follow-up times Y
1
and Y
2
;
(2) Y
1
and Y
2
are the two consecutive follow-ups that T happens in
between, unless T is either right- or left-censored.
The first interpretation is unrealistic, as the number of follow-up times
for each patient is not the same in each follow-up study, except for the
animal sacrifice study. The second interpretation violates the assumption
(Y
1
;Y
2
) ? T, as pointed out by Schick and Yu (2000). This drawback
motivates the Case k IC model.
3. Case k IC Model (Wellner, 1995). Assume
8
<
(1;Y
1
]
if T Y
1
(1) I =
(Y
j1
;Y
j
]
if Y
j1
< T Y
j
;j 2f2;::;kg
:
(Y
k
;1) if T > Y
k
;
(2) T ? C, where C = (Y
1
;:::;Y
k
);
(3) F
Y
is noninformative, where Y = (Y
1
;:::;Y
k
).
8
<
if
Y
1
(u)
if I = (1;u]
P
j=1
if
Y
j1
;Y
j
(u;v)
Note: G(I) =
An interpretation
if I = (u;v]
:
if
Y
k
(v)
if I = (v;1):
of the Case k model is that each person has exactly k follow-ups at Y
1
,
..., Y
k
. If there are no right-censored observations, by setting k large
enough, this interpretation is fine. However, if there are right-censored
observations, this interpretation breaks down.
4. The Stochastic IC Model (Gentleman and Geyer, 1994). Assume
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