Biomedical Engineering Reference
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min(C
1
;C
2
). We assume that C
2
is independent of both T and C
1
, and dene
a death indicator as D = I(C
1
< C
2
) showing the occurrence of death. For
subject i, (Ci,∆i,
i
;
i
;D
i
;Z
i
) is available data and the corresponding lowercase
letters are used for realized data, (ci,
i
;
i
;d
i
;z
i
). In this study, we suggest the
use of a frailty effect, Ri,
i
, for the possible correlation between tumor onset and
death. The illness-death model is shown in Figure 5.1.
FIGURE 5.1: Three-state model for current status data with death.
States 0, 1, and 2 represent the state \Health," \Tumor," and \Death",
respectively. Their intensity functions
01
;
02
, and
12
, are dened as
01
(t) = lim
!0
P[T 2 [t;t + ]jT t;C
1
t]=;
02
(c
1
) = lim
!0
P[C
1
2 [c;c + ]jT c;C
1
c]=;
12
(c
1
jt) = lim
!0
P[C
1
2 [c;c + ]jT = t;C
1
c]=; t < c
1
;
and corresponding cumulative intensity functions are defined as A
01
;A
02
, and
A
12
, respectively. Then a likelihood function is composed of four cases de-
pending on tumor onset and death: (i) SNT (Sacrifice and with Non-Tumor),
(ii) DNT (Death with Non-Tumor), (iii) SWT (Sacrifice With Tumor) and
(iv) DWT (Death With Tumor). Each subject contributes one of four factors
to the likelihood corresponding to the four possible values of (;d),
(1) SNT :(;d) = (0; 0)
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