Page 139 - Contributed Paper Session (CPS) - Volume 1

CPS1201 M. Iftakhar Alam et al.

parameter space Θ is chosen for each scenario so that the true values of the
̃
parameters lie in the middle of the corresponding intervals. For instance, since
T
Scenario 1 has the true parameters = (1.44,0.26,−1.70,0.25) , we consider
Θ = { Θ: 0 < < 2.88,0 < < 0.52, −3.40 < < 0, 0 < < 0.50} . The
̃
4
1
3
2
same approach is followed for the other scenarios. A trial can stop early for
futility and/or toxicity. Apart from that, it stops when the same dose is
repeated for r cohorts or when the trial reaches the maximum number of m
cohorts, whichever comes first. It is assumed that r = 6 and m = 20. The
number of patients in each cohort is 3, that is, c = 3.
3. Results
With the control parameter values set to 1, we run the penalised combined
criterion for each of the scenarios. One thousand simulated trials are
generated in each case for various values of the weight . Note that, when
= 0, the dose selection is based on the probability of success only. On the
other hand, the criterion reduces to the penalised D-criterion for = 1: see (1).
Table 1 illustrates the simulation results for the penalised combined
criterion for the considered scenarios. The higher the values of %OD and %AD
are, the better the design is. Similarly, %TD is expected to be as small as
possible. The sampling and decision efficiency measures can be obtained once
the distributions of dose allocation and optimum dose selection are available.
The information obtained per observation, information obtained per cost and
various risk measures are also obtained. We expect the information per
observation and information per cost to be as much as possible. Similarly, the
risks are expected to be as small as possible.
Table 1: Performance of the penalised combined criterion for the six
scenarios. Percentage of optimum doses chosen as the true optimum one,
recommended for further studies (%OD), percentage of no dose
recommended (%ND), percentage of doses recommended as optimum, but
carrying the probability of toxicity above the acceptable level (%TD),
percentage of cohorts treated at the true optimum doses throughout the trials
(%AD), decision efficiency (DE), sampling efficiency (SE), average cohorts (AC),
information per observation (IPO), information per cost (IPC) and some risk
measures. The value of in bold is regarded as the best in terms of the
performance measure DE.

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