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. Author manuscript; available in PMC: 2023 Mar 30.
Published in final edited form as: Stat Med. 2021 Nov 25;41(7):1205–1224. doi: 10.1002/sim.9265

Table 3:

Selection percentage and the average number of patients treated at each dose for the two subgroups under the BIPSE design and the two conventional designs which ignore the immune response Y or the subgroup Z. The numbers in boldface are target doses.

Z=0
Z=1
Scenario 1
Sel % (BIPSE) 0.075 0.615 0.254 0.038 0.019 0.092 0.752 0.156 0.000 0.000
# of patients 7.9 8.3 7.4 4.4 2.1 10.2 10.8 6.3 2.0 0.6
Sel % (conventional I) 0.036 0.338 0.462 0.150 0.014 0.100 0.536 0.338 0.024 0.002
# of patients 8.3 8.7 7.8 3.9 1.1 9.6 9.9 7.6 2.6 0.6
Sel % (conventional II) 0.042 0.664 0.286 0.002 0.006 0.042 0.664 0.286 0.002 0.006
# of patients 9.2 10.0 7.1 2.5 1.0 9.2 10.2 7.1 2.5 1.0
Scenario 2
Sel % (BIPSE) 0.000 0.046 0.738 0.181 0.035 0.000 0.110 0.765 0.098 0.027
# of patients 6.0 7.2 7.3 6.0 3.9 6.2 7.6 7.1 5.5 3.2
Sel % (conventional I) 0.000 0.018 0.104 0.308 0.570 0.000 0.032 0.212 0.472 0.284
# of patients 6.1 6.6 7.0 6.2 3.9 6.8 7.4 7.1 5.9 3.0
Sel % (conventional II) 0.000 0.060 0.792 0.110 0.038 0.000 0.060 0.792 0.110 0.038
# of patients 5.9 7.6 7.5 5.6 3.6 6.0 7.7 7.1 5.8 3.3
Scenario 3
Sel % (BIPSE) 0.000 0.002 0.004 0.021 0.967 0.000 0.000 0.000 0.019 0.979
# of patients 3.5 6.7 6.9 6.7 6.0 5.0 6.0 6.6 6.5 5.8
Sel % (conventional I) 0.000 0.004 0.002 0.004 0.990 0.000 0.000 0.000 0.008 0.992
# of patients 4.8 5.6 6.4 6.6 6.2 5.2 5.7 6.4 6.6 6.2
Sel % (conventional II) 0.000 0.000 0.002 0.006 0.988 0.000 0.000 0.002 0.006 0.988
# of patients 4.3 6.2 6.6 6.6 6.2 4.4 6.0 6.7 6.7 6.1
Scenario 4
Sel % (BIPSE) 0.004 0.129 0.633 0.185 0.046 0.062 0.785 0.142 0.002 0.006
# of patients 6.2 6.9 6.7 5.9 4.2 6.7 7.0 6.7 5.6 4.0
Sel % (conventional I) 0.004 0.092 0.472 0.380 0.052 0.118 0.454 0.384 0.040 0.004
# of patients 6.3 6.6 6.8 5.9 4.1 6.8 6.8 6.9 5.9 3.9
Sel % (conventional II) 0.004 0.338 0.590 0.048 0.018 0.004 0.338 0.590 0.048 0.018
# of patients 6.4 6.9 6.7 5.5 4.2 6.5 6.8 6.6 5.9 4.4
Scenario 5
Sel % (BIPSE) 0.000 0.002 0.033 0.210 0.750 0.000 0.042 0.656 0.169 0.129
# of patients 5.1 6.5 7.0 6.2 4.9 5.8 7.5 7.2 5.5 4.0
Sel % (conventional I) 0.000 0.000 0.048 0.344 0.608 0.000 0.006 0.444 0.528 0.022
# of patients 5.3 6.4 7.1 6.6 4.6 6.2 7.4 7.2 5.7 3.6
Sel % (conventional II) 0.000 0.002 0.124 0.454 0.420 0.000 0.002 0.124 0.454 0.420
# of patients 5.2 6.9 7.1 6.0 4.7 5.4 6.8 7.1 6.0 4.8
Scenario 6
Sel % (BIPSE) 0.040 0.415 0.369 0.117 0.058 0.112 0.727 0.156 0.000 0.002
# of patients 7.5 7.9 7.2 4.8 2.7 10.6 10.8 5.8 2.0 0.5
Sel % (conventional I) 0.012 0.210 0.454 0.272 0.052 0.112 0.518 0.350 0.020 0.000
# of patients 7.9 8.4 7.6 4.5 1.5 9.9 10.2 6.9 2.6 0.5
Sel % (conventional II) 0.032 0.602 0.330 0.018 0.014 0.032 0.602 0.330 0.018 0.014
# of patients 9.5 10.0 6.4 2.7 1.3 9.6 10.1 6.6 2.7 1.1
Scenario 7
Sel % (BIPSE) 0.000 0.010 0.450 0.406 0.131 0.000 0.031 0.631 0.273 0.062
# of patients 5.4 6.9 6.9 6.1 4.5 5.7 7.0 6.9 6.1 4.4
Sel % (conventional I) 0.000 0.000 0.010 0.078 0.912 0.000 0.010 0.120 0.456 0.414
# of patients 5.2 6.1 6.6 6.4 5.7 6.0 6.7 6.7 6.0 4.6
Sel % (conventional II) 0.000 0.000 0.384 0.494 0.122 0.000 0.000 0.384 0.494 0.122
# of patients 5.2 6.9 6.7 6.3 4.6 5.5 6.6 7.0 6.4 4.9
Scenario 8
Sel % (BIPSE) 0.000 0.000 0.006 0.188 0.806 0.000 0.000 0.029 0.350 0.621
# of patients 4.7 6.4 6.8 6.7 5.5 5.0 6.5 6.9 6.2 5.3
Sel % (conventional I) 0.000 0.000 0.000 0.008 0.992 0.000 0.000 0.000 0.020 0.980
# of patients 4.6 5.7 6.4 6.7 6.4 5.3 6.1 6.7 6.5 5.6
Sel % (conventional II) 0.000 0.000 0.006 0.256 0.732 0.000 0.000 0.006 0.256 0.732
# of patients 4.8 6.2 6.6 6.4 5.6 4.9 6.2 6.9 6.3 5.7
Scenario 9
Sel % (BIPSE) 0.000 0.002 0.144 0.333 0.521 0.008 0.498 0.383 0.013 0.098
# of patients 5.6 6.8 7.0 6.1 4.8 6.4 7.3 6.6 5.4 3.9
Sel % (conventional I) 0.000 0.006 0.084 0.598 0.312 0.008 0.176 0.668 0.144 0.004
# of patients 6.2 6.7 6.6 6.0 4.6 6.9 7.4 6.7 5.5 3.5
Sel % (conventional II) 0.000 0.036 0.426 0.208 0.330 0.000 0.036 0.426 0.208 0.330
# of patients 5.9 6.8 6.8 5.9 4.7 6.0 7.3 6.5 5.7 4.3
Scenario 10
Sel % (BIPSE) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
# of patients 1.8 1.0 0.3 0.0 0.0 1.9 1.5 0.3 0.0 0.0
Sel % (conventional I) 0.020 0.006 0.000 0.000 0.000 0.010 0.000 0.000 0.000 0.000
# of patients 5.8 3.2 0.9 0.1 0.0 10.7 2.8 0.5 0.1 0.0
Sel % (conventional II) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
# of patients 1.9 1.1 0.3 0.0 0.0 1.7 1.1 0.3 0.0 0.0