Table 1.

Description of simulation settings 1–6 and simulation results for n = 20,000 based on 100 replicates: mean (SD) of misclassification rates and value functions.

Setting	Functional form of interaction	True optimal treatment	Covariates type	Method	Misclassification	Value
1	Tree${\Delta }_1\left(\mathbf{X}\right)=4\times I\left(X_1>0.5\right)-2$${\Delta }_2\left(\mathbf{X}\right)=2\times I(X_2\ge 0.5)\hspace{0.17em}I\left(X_3<0.25\right)-1$${\Delta }_3(\mathbf{X})=0$	1 or 2 or 3	Continuous$X_1,\dots ,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.101 (0.016)	1.226 (0.010)
				l1-PLS-GL	0.094 (0.015)	1.229 (0.010)
				ACWL	0.028 (0.040)	1.276 (0.023)
				D-learning	0.100 (0.020)	1.226 (0.013)
				BART	0.010 (0.004)	1.286 (0.003)
2	Linear ${\Delta }_1(\mathbf{X})=3X_1-2X_2$${\Delta }_2(\mathbf{X})=5X_3-X_4+X_5-1$${\Delta }_3(\mathbf{X})=0$	1 or 2 or 3	Continuous $X_1,\dots ,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.015 (0.004)	1.736 (0.003)
				l1-PLS-GL	0.013 (0.004)	1.737 (0.003)
				ACWL	0.171 (0.020)	1.662 (0.016)
				D-learning	0.018 (0.005)	1.737 (0.004)
				BART	0.056 (0.004)	1.730 (0.006)
3	Nonlinear${\Delta }_1(\mathbf{X})=3X_1^2-\text{exp}(X_2)$${\Delta }_2(\mathbf{X})=X_3{X}_4$${\Delta }_3(\mathbf{X})=0$	1 or 2 or 3	Continuous $X_1,\dots ,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.566 (0.012)	1.089 (0.008)
				l1-PLS-GL	0.565 (0.014)	1.088 (0.011)
				ACWL	0.561 (0.016)	1.089 (0.009)
				D-learning	0.572 (0.013)	1.087 (0.008)
				BART	0.192 (0.038)	1.209 (0.010)
4	Nonlinear${\Delta }_1(\mathbf{X})=3X_1^2-\text{exp}(X_2)$${\Delta }_2(\mathbf{X})=X_3^3$${\Delta }_3(\mathbf{X})=0$	1 or 2 or 3	Continuous $X_1,\dots ,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.350 (0.011)	1.129 (0.004)
				l1-PLS-GL	0.352 (0.010)	1.128 (0.004)
				ACWL	0.362 (0.011)	1.118 (0.004)
				D-learning	0.359 (0.016)	1.129 (0.004)
				BART	0.163 (0.045)	1.220 (0.012)
5	Nonlinear${\Delta }_1(\mathbf{X})=2\{I(X_1=1)+I(X_1=2)\}{X}_2-1$${\Delta }_2(\mathbf{X})=5I(X_1=5)X_3-2$${\Delta }_3(\mathbf{X})=0$	1 or 2 or 3	Continuous + binary+ categorical$X_1\hspace{0.17em}\sim \hspace{0.17em}$ discrete uniform {1, 5}$X_2\hspace{0.17em}\sim \hspace{0.17em}\text{Bern}(0.5)$$X_3,X_4,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.077 (0.019)	1.101 (0.012)
				l1-PLS-GL	0.078 (0.018)	1.101 (0.011)
				ACWL	0.029 (0.028)	1.129 (0.016)
				D-learning	0.090 (0.032)	1.094 (0.019)
				BART	0.007 (0.005)	1.142 (0.002)
6	Tree${\Delta }_1\left(\mathbf{X}\right)=I\left(X_1>0.5\right)+2$${\Delta }_2\left(\mathbf{X}\right)=2\times I\left(X_2\ge 0.5\right)\hspace{0.17em}I\left(X_3<0.25\right)-3$${\Delta }_3(\mathbf{X})=0$	1	Continuous $X_1,\dots ,X_5\hspace{0.17em}\sim \hspace{0.17em}\mathcal{U}\{-1,1\}$	l1-PLS-HGL	0.000 (0.000)	2.093 (0.000)
				l1-PLS-GL	0.000 (0.000)	2.093 (0.000)
				ACWL	0.000 (0.000)	2.093 (0.000)
				D-learning	0.000 (0.000)	2.093 (0.000)
				BART	0.000 (0.000)	2.093 (0.000)

Note: Methods under comparison include the l₁-penalized least squares with hierarchical group LASSO variable selection (l₁-PLS-HGL), l₁-penalized least squares with group LASSO variable selection (l₁-PLS-GL), adaptive contrast weighted learning (ACWL), direct learning (D-learning), and Bayesian additive regression trees (BART). The smallest misclassification rates and the largest value functions for each setting are in bold.