Page 142 - Contributed Paper Session (CPS) - Volume 1

CPS1201 M. Iftakhar Alam et al.
0.0 - - 81.3 12.4 - - 0.813 - - 17.3 1.733 - - 13.300 618.8 35.7
38.2
0.2
0.788
16.5
78.8
642.5
2.038
16.691
16.8
5 0.4 - 76.7 20.7 - 0.767 - 16.7 2.392 - 20.820 659.2 39.5
0.6 - - 62.9 32.3 - - 0.629 - - 16.1 3.170 - - 32.371 671.5 41.7
0.533
0.8
660.1
39.342
4.175
39.3
53.3
42.0
15.7
1.0 - 100.0 0.0 - 1.000 - 17.5 3.008 - 0.0 591.1 33.8
- 99.9 0.0 - 0.999 - 20.0 - - 0.015 - -
b(πˆ ) - 99.5 0.5 - 0.995 - 1.8 0.087 - 0.251 14.8 8.2
0.0
0.2 - 99.8 0.2 - 0.998 - 1.8 0.090 - 0.142 13.9 7.7
6 0.4 - 99.7 0.3 - 0.997 - 1.8 0.100 - 0.137 19.1 10.5
0.6 - 99.4 0.6 - 0.994 - 1.8 0.105 - 0.317 17.3 9.4
0.8 - 99.7 0.3 - 0.997 - 1.8 0.093 - 0.212 18.9 10.3
1.0 - 99.7 0.3 - 0.997 - 1.8 0.103 - 0.115 13.0 7.3
b(πˆ ) - 93.5 6.5 - 0.935 - 20.0 - - 2.054 - -

dose allocation and SE for the sampling efficiency, with a sharp drop at = 1.
All of the performance values indicate that the penalised D-criterion on its own
is performing poorly compared to the other cases. However, it might be worth
combining the criteria in this case, with ∈ [0.2, 0.8]. Also, the proposed design
outperforms the benchmark design in this scenario. Similar conclusions can
be drawn in the case of the simple combined criterion, as seen in Table 2.
For the penalised combined criterion in Scenario 4, it can be argued that the
design is performing similarly for weights between 0.4 and 0.8. But the
penalised D-optimum design on its own is not performing well in this scenario
either. The proposed design is more efficient than the benchmark design in
identifying the true OD. However, DE at the benchmark design is the maximum
value in this scenario. It happens as the distrbution of OD in the benchmark
design is more around the true OD than that by the other design. A good
percentage of trials do not recommend any dose for further developtment in
this scenario. As the most extreme dose is the true OD here, a trial has more
chance to stop early for futility. The results obtained for the simple combined
criterion are found to be quite competitive with those for the penalised
combined criterion.
The design is most efficient when = 1 in Scenario 5. The DE decreases
until = 1. The design is equally as efficient as the benchmark design when
= 1. The similar results are found when the simple combined criterion is used.
In Scenario 6, the performance of the penalised combined is very similar across
the values of . Also, the DE of our design at these values is well above that
at the benchmark design. The average number of cohorts utilised in each trial
is very small. Also, the results are very consistent with those produced by the
simple combined criterion in Table 2. Since very small number of cohorts are
engaged in each trial, the penalised/simple combined has little role in the
identification of the OD. It is the stopping rule for futility and/or toxicity that
plays the significant role and thereby lead to the very similar results.
Interesting observations can also be made by comparing the results for
penalised and non-penalised D-optimality, that is, when = 1. Tables 1 and 2
clearly show the superiority of the penalised criterion. Most of the measures
have better values for the scenarios. It is worth mentioning that the penalised
D-optimum design ( = 1) always requires on average more cohorts than the
designs for = 0 and for the best . The penalised combined criterion with

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