Biomedical Engineering Reference
In-Depth Information
in standardized time I
1
= (0; 1=8]; ;I
8
= (7=8; 1]: The rst line of expression
(12.11) is the probability that the clot is dissolved instantaneously by the bolus, the
second line is the probability that the clot is dissolved during the ci, and third line
is the probability that the clot is not dissolved by standardized time s = 1, each
computed either with or without toxicity, that is, YT
T
= 1 or 0.
12.3
Utilities and Trial Design
The usual concern in phase I trials where only toxicity is considered is overdosing
patients. In the IA tPA trial, this is counterbalanced by the concern that patients
may be given too little tPA to dissolve their clots, formalized by the numerical utility
U(Y ): Given , the mean of U(Y ) for a patient treated using (c;q) is
Z
1
1
X
u(c;q;) = E
Y
fU(Y ) j c;q;g =
U(y) f
E;T
(y j c;q;)dy
E
: (12.12)
y
E
=0
y
T
=0
During the trial, a Bayesian model is exploited by adaptively selecting each new
cohort's optimal (c;q) to maximize the posterior mean of u(c;q;) based on the
most recent data D
n
from the previous n patients (Berger, 1985),
u(c;q)
opt
(D
n
) = argmax
c;q
E
fu(c;q;) jD
n
g:
(12.13)
Interval-censoring motivates the practical approach of eliciting numerical
utilities for each set of observed outcomes obtained from the cross-product
fI
0
;I
1
; ;I
M
;I
M+1
gf0; 1g; where I
M+1
= (1;1) and Y
E
2 I
M+1
is the out-
come that the clot was not dissolved by the end of the infusion. The elicited utilities
of the observation intervals [0, 15], ..., (105, 120], (120;1] for the IA tPA trial are
given in Table 12.1.
Denoting the utility of fY
E
2 I
m
; Y
T
g by U(I
m
;Y
T
); the optimal utility (12:13)
takes the form
1
X
M+
X
U(I
m
;y
T
) E
E;T
(I
m
;y
T
j c;q;) jD
n
:
u(c;q)
opt
(D
n
) = argmax
c;q
y
T
=0
m=0
(12.14)
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