Table 1.

True toxicity and efficacy probabilities and utilities (${\pi }_{c,r}^T$, ${\pi }_{c,r}^E$, u_c,r) under eight simulation scenarios, for each dose, schedule, and subgroup. These values for optimal treatment regimes with $u_{c,r}>u_c^{\max }-5$ are underlined, where $u_c^{\max }={\max }_r\{u_{c,r}\}$ is the maximum utility for subgroup c, c = 1, 2. The regimes with a toxicity rate above 15% and, an efficacy rate below 20% are considered inadmissible in scenarios 1–6; The regimes with a toxicity rate above 30% and an efficacy rate below 30% are considered inadmissible in scenarios 7–8.

Scenario		Subgroup 1			Subgroup 2
	s	d=1	d=2	d=3	d=1	d=2	d=3
1	1	(.03,.10,62.2)	(.05,.20,65.0)	(.15,.60,75.0)	(.03,.13,63.4)	(.05,.23,66.2)	(.15,.63,76.2)
	2	(.05,.50,77.0)	(.15,.40,67.0)	(.30,.40,58.0)	(.05,.56,79.4)	(.15,.46,69.4)	(.30,.46,60.4)
	3	(.13,.35,66.2)	(.45,.40,49.0)	(.60,.45,42.0)	(.13,.47,71.0)	(.45,.52,53.8)	(.60,.57,46.8)
2	1	(.10,.30,66.0)	(.27,.40,59.8)	(.55,.50,47.0)	(.10,.40,70.0)	(.27,.50,63.8)	(.55,.60,51.0)
	2	(.25,.25,55.0)	(.30,.30,54.0)	(.40,.40,52.0)	(.25,.35,59.0)	(.30,.40,58.0)	(.40,.50,56.0)
	3	(.08,.15,61.2)	(.12,.35,66.8)	(.25,.35,59.0)	(.08,.25,65.2)	(.12,.45,70.8)	(.25,.45,63.0)
3	1	(.05,.10,61.0)	(.15,.40,67.0)	(.40,.10,40.0)	(.05,.30,69.0)	(.15,.45,69.0)	(.40,.30,48.0)
	2	(.05,.40,73.0)	(.18,.20,57.2)	(.40,.10,40.0)	(.05,.45,75.0)	(.18,.30,61.2)	(.40,.20,44.0)
	3	(.03,.15,64.2)	(.08,.23,64.4)	(.15,.45,69.0)	(.03,.30,70.2)	(.08,.30,67.2)	(.15,.50,71.0)
4	1	(.03,.10,62.2)	(.05,.30,69.0)	(.10,.60,78.0)	(.03,.20,66.2)	(.05,.35,71.0)	(.10,.63,79.2)
	2	(.07,.30,67.8)	(.15,.40,67.0)	(.30,.50,62.0)	(.07,.33,69.0)	(.15,.60,75.0)	(.30,.65,68.0)
	3	(.05,.25,67.0)	(.10,.34,67.6)	(.15,.25,61.0)	(.05,.28,68.2)	(.10,.38,69.2)	(.15,.29,62.6)
5	1	(.05,.10,61.0)	(.12,.25,62.8)	(.20,.33,61.2)	(.05,.15,63.0)	(.12,.30,64.8)	(.20,.38,63.2)
	2	(.07,.05,57.8)	(.13,.45,70.2)	(.25,.30,57.0)	(.07,.20,63.8)	(.13,.50,72.2)	(.25,.40,61.0)
	3	(.02,.23,68.0)	(.05,.15,63.0)	(.08,.10,59.2)	(.02,.28,70.0)	(.05,.45,75.0)	(.08,.28,66.4)
6	1	(.05,.05,59.0)	(.07,.07,58.6)	(.09,.09,58.2)	(.05,.15,63.0)	(.07,.47,74.6)	(.09,.49,74.2)
	2	(.08,.10,59.0)	(.13,.35,66.2)	(.30,.40,58.0)	(.08,.15,61.2)	(.13,.40,68.2)	(.30,.45,60.0)
	3	(.11,.30,65.4)	(.13,.20,60.2)	(.20,.10,52.0)	(.11,.33,66.6)	(.13,.23,61.4)	(.20,.13,53.2)
7	1	(.05,.10,61.0)	(.15,.45,69.0)	(.30,.45,60.0)	(.05,.13,62.2)	(.15,.48,70.2)	(.30,.48,61.2)
	2	(.12,.20,60.8)	(.23,.55,68.2)	(.55,.60,51.0)	(.12,.50,72.8)	(.23,.58,69.4)	(.55,.63,52.2)
	3	(.45,.30,45.0)	(.50,.35,44.0)	(.60,.30,36.0)	(.45,.33,46.2)	(.50,.38,45.2)	(.60,.31,36.4)
8	1	(.05,.10,61.0)	(.10,.20,62.0)	(.15,.50,71.0)	(.05,.15,63.0)	(.10,.25,64.0)	(.15,.53,72.2)
	2	(.10,.15,60.0)	(.25,.15,51.0)	(.40,.15,42.0)	(.10,.20,62.0)	(.25,.20,53.0)	(.40,.20,44.0)
	3	(.07,.25,65.8)	(.08,.25,65.2)	(.18,.25,59.2)	(.07,.25,65.8)	(.08,.30,67.2)	(.18,.60,73.2)