Biomedical Engineering Reference
In-Depth Information
FIGURE 12.2: Illustration of possible shapes of (s;c;q) as a function of s
for xed (c;q) = (0:5; 0:1):
a and b by a^b and = (
0
; ;
4
); the model for this probability is given by
logf1
T
(Y
E
;c;q;)g =
0
+
2
c
1
q+
3
c
1
(1q)(Y
E
^1)+
4
1(Y
E
> 1): (12.6)
The bolus effect is
2
c
1
q, the ci effect is
3
c
1
(1 q)(Y
E
^ 1); the eect of failing
to dissolve the clot is
4
; and 1e
0
is the probability of SICH if no tPA is given.
Because
3
> 0; the faster the clot is dissolved, the smaller the probability of SICH.
Figure 12.3 illustrates possible forms of
T
(Y
E
;c;q;):
The model parameter vector is = (;); with dim() = 11.
If no bolus were given (q = 0), the effective delivered dose at s would be
d(s;c
1
; 0) = c
1
s, so
2
would be dropped, the hazard function (12:4) would become
(s;c; 0;) =
3
+
4
5
(c
1
s)
5
1
1 +
4
(c
1
s)
5
for s > 0;
(12.7)
and the cumulative hazard function (12:5) would become
(s;c; 0;) =
3
s + c
1
logf1 +
4
(c
1
s)
5
g for s > 0:
(12.8)
The model for
T
would drop
2
and the linear component (12:6) would be reduced
to
0
+
3
c
1
(Y
E
^ 1) +
4
1(Y
E
> 1); so dim() = 9.
The joint distribution of Y = (Y
E
;Y
T
) is
for yT
T
= 0; 1 and y
E
f
E;T
(y
E
;y
T
jc;q;) = f
E
(y
E
jc;q;) Pr(Y
T
= y
T
jy
E
;c;q;)
0:
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