Table 1.

Simulation Settings. The last column refers to the percentage of the population for whom Treatment 1 would be more beneficial than Treatment −1

Setting	T i	Treatment 1 benefit
1 (linear)	$1-X_{i,1}^{(1)}+2X_{i,2}^{(1)}-X_{i,1}^{(2)}+X_{i,2}^{(2)}+2X_{i,5}^{(2)}$	60%
2 (quadratic)	$1+X_{i,1}^{(1)}+2X_{i,2}^{(1)}+X_{i,1}^{(2)}-{\left(X_{i,2}^{(2)}\right)}^2+{\left(X_{i,5}^{(2)}\right)}^2$	60%
3 (quadratic, more predictors)	$1+X_{i,1}^{(1)}+2X_{i,2}^{(1)}-{\left(X_{i,3}^{(1)}\right)}^2+X_{i,1}^{(2)}-X_{i,2}^{(2)}+2{\left(X_{i,5}^{(2)}\right)}^2+2{\left(X_{i,6}^{(2)}\right)}^2$	80%
4 (quadratic, weak signal)	$1+X_{i,1}^{(1)}+0.5X_{i,2}^{(1)}-{\left(X_{i,3}^{(2)}\right)}^2+X_{i,1}^{(2)}-0.5X_{i,2}^{(2)}+0.5{\left(X_{i,5}^{(2)}\right)}^2$	60%
5 (two-way interaction)	$1-{\left(X_{i,1}^{(1)}+2X_{i,2}^{(1)}\right)}^2+{\left(X_{i,1}^{(2)}-X_{i,2}^{(2)}\right)}^2+X_{i,5}^{(2)}$	50%
6 (exponential)	$1-\text{exp}\left(X_{i,1}^{(1)}\right)-X_{i,2}^{(1)}+\text{exp}\left(X_{i,1}^{(2)}\right)+X_{i,2}^{(2)}$	70%