Table 2:

True immune response, toxicity, efficacy probabilities, and utility at each dose, and selection percentage and the average number of patients treated at each dose level under the proposed design and the EffTox design. The boldface numbers are the target doses.

	dose level
	1	2	3	4	5
	Scenario 1
E(YI )	2.0	2.9	4.5	5.7	6.3
πT	0.03	0.04	0.1	0.17	0.23
(πE,1, πE,2)†	(0.46, 0.11)	(0.50, 0.13)	(0.35, 0.07)	(0.16, 0.02)	(0.08, 0.01)
Utility	30.9	34.6	26.2	13.1	8
Selection % (proposed)	0.282	0.649	0.069	0	0
# of patients	16.0	16.9	13.9	9.0	4.8
Selection % (EffTox)	0.476	0.521	0.001	0	0.002
# of patients	17.4	16.3	13.1	8.2	4.4
	Scenario 2
E(YI)	2.0	2.9	4.5	5.7	6.3
πT	0.03	0.07	0.19	0.35	0.49
(πE,1, πE,2)	(0.28, 0.14)	(0.31, 0.17)	(0.31, 0.18)	(0.28, 0.14)	(0.25, 0.11)
Utility	24.2	27.8	30.6	23.8	17.7
Selection % (proposed)	0.117	0.094	0.736	0.047	0.006
# of patients	13.0	14.0	14.6	10.9	7.4
Selection % (EffTox)	0.212	0.602	0.183	0.001	0.002
# of patients	14.2	15.2	14.4	10.1	6.2
	Scenario 3
E(YI )	2.0	2.9	4.5	5.7	6.3
πT	0.07	0.09	0.12	0.3	0.49
(πE,1, πE,2)	(0.16, 0.04)	(0.17, 0.05)	(0.22, 0.07)	(0.25, 0.10)	(0.27, 0.12)
Utility	9.8	11.9	19.7	22.1	20.1
Selection % (proposed)	0.028	0.005	0.29	0.572	0.057
# of patients	9.5	9.8	15.0	15.1	9.2
Selection % (EffTox)	0.143	0.103	0.254	0.255	0.203
# of patients	11.1	12.0	13.0	12.9	9.8
	Scenario 4
E(YI )	2.0	2.9	4.5	5.7	6.3
πT	0.16	0.16	0.16	0.16	0.16
(πE,1, πE,2)	(0.21, 0.06)	(0.26, 0.09)	(0.34, 0.17)	(0.36, 0.20)	(0.37, 0.22)
Utility	12.0	17.7	32.8	40.2	42.3
Selection % (proposed)	0.000	0.000	0.006	0.257	0.735
# of patients	7.9	8.7	12.4	15.3	15.6
Selection % (EffTox)	0.008	0.004	0.046	0.207	0.733
# of patients	9.3	10.6	12.4	13.4	14.3
	Scenario 5
E(YI )	2.6	3.4	3.9	4.3	4.6
πT	0.05	0.12	0.2	0.28	0.36
(πE,1, πE,2)	(0.15, 0.09)	(0.22, 0.15)	(0.24, 0.17)	(0.23, 0.16)	(0.21, 0.15)
Utility	13.8	21.9	24.5	23.7	20.6
Selection % (proposed)	0.024	0.036	0.431	0.42	0.077
# of patients	11.6	12.8	13.0	12.3	10.0
Selection % (EffTox)	0.002	0.258	0.711	0.017	0.002
# of patients	11.4	14.7	14.4	11.2	7.8
	Scenario 6
E(YI )	2.6	3.4	3.9	4.3	4.6
πT	0.01	0.04	0.09	0.14	0.2
(πE,1, πE,2)	(0.24, 0.06)	(0.31, 0.10)	(0.34, 0.12)	(0.35, 0.13)	(0.36, 0.13)
Utility	17.3	24.9	28.3	29.6	29.4
Selection % (proposed)	0.016	0.001	0.098	0.401	0.483
# of patients	10.4	11.1	12.1	13.1	13.2
Selection % (EffTox)	0.024	0.094	0.43	0.321	0.129
# of patients	10.3	12.1	12.9	12.7	11.8
	Scenario 7
E(YI )	2.6	3.4	3.9	4.3	4.6
πT	0.16	0.16	0.16	0.16	0.16
(πE,1, πE,2)	(0.16, 0.37)	(0.16, 0.37)	(0.16, 0.37)	(0.16, 0.37)	(0.16, 0.37)
Utility	32.5	34.3	36.9	38.5	39.7
Selection % (proposed)	0.175	0.021	0.038	0.091	0.675
# of patients	11.9	11.8	12.2	11.9	12.2
Selection % (EffTox)	0.351	0.086	0.146	0.07	0.347
# of patients	13.2	12.0	11.4	11.5	11.9
	Scenario 8
E(YI )	2.5	3.1	3.5	3.8	3.9
πT	0.72	0.78	0.84	0.88	0.91
(πE,1, πE,2)	(0.06, 0.04)	(0.08, 0.06)	(0.09, 0.06)	(0.09, 0.07)	(0.10, 0.08)
Utility	2.4	3.5	4.1	4.7	5.2
Selection % (proposed)	0	0	0	0	0
# of patients	4.3	3.2	3.1	1.7	0.7
Selection % (EffTox)	0	0	0	0	0
# of patients	4.1	3.0	2.7	2.0	0.8

^†π_E,₁ = Pr(Y_E = 1), and π_E,2 = Pr(Y_E = 2). ²⁴