Biomedical Engineering Reference
In-Depth Information
8
<
R
s
k
s
k1
uq(u;c
i
)ds=
R
c
i
0
q(u;c
i
)du; if c
i
> s
k
;
R
c
i
s
k1
q(u;c
i
)ds=
R
c
i
E
ik
=
0
q(u;c
i
)du;
if c
i
2 I
k
:
0;
otherwise:
With quantities calculated the in E-step, = ( ~
1
; ~
2
;
1
;
2
;
3
;(
2
)) are
updated in the M-step.
P
i=1
i
p
ik
P
i=1
e
z
0
i
1
E
(R
i
)T
NT
@l
1
@ ~
1k
=
;
ik
P
i=1
i
d
i
P
i=1
e
z
0
i
2
E
(R
i
)T
NT
@l
1
@ ~
2k
=
;
+ e
z
0
i
3
E
(R
i
)T
WT
ik
ik
X
X
X
@l
@
1
i
e
z
0
i
1
i
T
NT
1k
T
NT
ik
E
[R
i
]
=
z
i
=
z
i
;
0i
i=1
i=1
k=1
X
X
X
@l
@
2
d
i
(1
i
)e
z
0
i
2
d
i
(1
i
) T
NT
2k
T
NT
ik
E
[R
i
]
=
z
i
=
z
i
;
1i
i=1
i=1
k=1
X
X
X
@l
@
3
d
i
i
e
z
0
i
3
d
i
i
T
WT
1k
T
ik
E
[R
i
]
=
z
i
=
z
i
;
1i
i=1
i=1
k=1
X
@l
@
= n[ () + log + 1] +
[E
(log) E
(R
i
)]; = 1=
i=1
Then standard errors of the estimated parameters are calculated with the
information matrix.
5.4
Software: R PackageCSD
TheRpackageCSDhas been developed to fit frailty models for current status
data with dependent censoring. The use ofCSDis as follows:
CSD(data,int,failty=c(
`
gamma
'
,
`
normal
'
),init=c(0,0.1,1),
tol=0.001,plots=F).
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