Table 1.

The second column gives the number of treatment options m. The third column gives the set of ϕ functions used in the outcome models. The fourth column specifies the form of the optimal regime π^opt (x) = arg max_a ϕ(x, a) where: “linear” indicates that π^opt(x) = arg max_a{(1, x^T)β_a} for some coefficient vectors β_a ∈ ℝ^p+1, a ∈ A, “decision list” indicates that π^opt is representable as a decision list; and “nonlinear” indicates that π^opt(x) is neither linear nor representable as a decision list.

Setting	m	Expression of ϕ	Form of πopt
I	2	ϕ1(x, a) = I(a = 2){3I(x1 ≤ 1, x2 > −0.6) −1}	decision list
II	2	ϕ2(x, a) = I(a = 2)(x1 + x2 − 1)	linear
III	2	ϕ3(x, a) = I(a = 2) arctan(exp(1+x1) −3x2 −5)	nonlinear
IV	2	ϕ4(x, a) = I(a = 2)(x1 − x2 + x3 − x4)	linear
V	3	ϕ5(x, a) = I(a = 2){4I(x1 > 1) −2} + I(a = 3)I(x1 ≤ 1){2I(x2 ≤ −0.3) −1}	decision list
VI	3	ϕ6(x, a) = I(a = 2)(2x1) + I(a = 3)(−x1x2)	nonlinear
VII	3	ϕ7(x, a) = I(a = 2)(x1 − x2)+ I(a = 3)(x3 − x4)	linear