# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## Appendix A
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **No RHC** & \multicolumn{2}{c}{**RHC**} \\  & **Mean** & **Mean** & **Std. Diff.** \\ \hline add3 pc & 1.63 & 1.47 & (11.36) \\ age & 61.76 & 60.75 & (6.14) \\ alb1 & 3.16 & 2.96 & (27.85) \\ amihx & 0.03 & 0.04 & (7.43) \\ aps1 & 50.93 & 60.74 & (50.14) \\ bili1 & 1.93 & 2.64 & (16.25) \\ card & 0.28 & 0.42 & (29.49) \\ cardiohx & 0.16 & 0.20 & (11.56) \\ cat2\_miss & 0.81 & 0.77 & (9.93) \\ chfhx & 0.17 & 0.19 & (6.95) \\ chrpulhx & 0.22 & 0.14 & (19.23) \\ crea1 & 1.92 & 2.47 & (27.78) \\ das2d3 pc & 20.37 & 20.70 & (6.26) \\ demethx & 0.12 & 0.07 & (16.31) \\ edu & 11.57 & 11.86 & (9.14) \\ gastr & 0.15 & 0.19 & (12.09) \\ gibledhx & 0.04 & 0.02 & (7.04) \\hema & 0.07 & 0.05 & (6.17) \\ hema1 & 32.70 & 30.51 & (26.93) \\ hrt1 & 112.87 & 118.93 & (14.69) \\ immunhx & 0.26 & 0.29 & (8.04) \\ income & 0.70 & 0.83 & (13.52) \\ liverhx & 0.07 & 0.06 & (4.89) \\ malighx & 0.25 & 0.20 & (10.14) \\ meanbp1 & 84.87 & 68.20 & (45.51) \\ meta & 0.05 & 0.04 & (2.81) \\ neuro & 0.16 & 0.05 & (35.30) \\ ortho & 0.00 & 0.00 & (2.70) \\ paco21 & 39.78 & 36.71 & (25.57) \\ pafi1 & 240.18 & 192.39 & (43.40) \\ ph1 & 7.39 & 7.38 & (11.98) \\ pot1 & 4.08 & 4.05 & (2.71) \\ psychhx & 0.08 & 0.05 & (14.32) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Descriptive statistics for the right hearth catheterisation study. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **No Medicaid** & \multicolumn{2}{c}{**Medicaid**} \\  & **Mean** & **Mean** & **Std. Diff.** \\ \hline age & 42.31 & 42.20 & (0.90) \\ numhh\_list & 1.25 & 1.35 & (20.22) \\ draw & 3.91 & 4.33 & (16.75) \\ birthyear\_list & 1966 & 1966 & (0.90) \\ have\_phone\_list & 0.89 & 0.90 & (2.52) \\ popox\_list & 0.13 & 0.13 & (0.04) \\ english\_list & 0.92 & 0.91 & (3.53) \\ female\_list & 0.60 & 0.58 & (2.94) \\ zip\_msa & 0.75 & 0.75 & (1.01) \\ doc\_any\_12m & 0.49 & 0.51 & (3.85) \\ \hline N. observations & 11,844 & \multicolumn{2}{c}{11,683} \\ \hline \hline \end{tabular} Note: The table shows the means and standardised differences (in parentheses) of the conditioning variables for each treatment state.  
\end{table} 
Table 4: Descriptive statistics for the Oregon health experiment. Appendix A.3.1. Policy Trees Running Time: Oregon Health Insurance Experiment \begin{tabular}{l r r r} \hline \hline
**Task and Sample** & \multicolumn{3}{c}{**Running Time**} \\ \hline Unconstrained tree depth & 2 & 3 & \\ \hline Policy tree training data: & 0:02.116 & 0:08.093 & \\ Evaluation of training data: & 0:00.172 & 0:00.125 & \\ Policy tree allocation data: & 0:00.534 & 0:00.424 & \\ Evaluation of test data & 0:00.109 & 0:00.093 & \\ \hline Constrained tree depth & 2 & 3 & 4 \\ \hline Policy tree training data: & 0:02.686 & 0:10.297 & 3:03.169 \\ Evaluation of training data: & 0:00.156 & 0:00.140 & 0:00.141 \\ Policy tree allocation data: & 0:00.486 & 0:00.486 & 0:00.534 \\ Evaluation of test data: & 0:00.158 & 0:00.079 & 0:00.110 \\ \hline Constrained sequential trees depth & 2+1 & 3+1 & \\ \hline Policy tree training data: & 0:03.093 & 0:29.504 & \\ Evaluation of training data: & 0:00.141 & 0:00.267 & \\ Policy tree allocation data: & 0:00.580 & 0:01.098 & \\ Evaluation of test data: & 0:00.141 & 0:00.320 & \\ \hline \hline \end{tabular}   
Appendix A.3.2. Policy Trees Running Time: Right Heart Catheterisation Study \begin{tabular}{l r r r r} \hline \hline
**Task and Sample** & \multicolumn{3}{c}{**Running Time**} \\ \hline Tree depth & 2 & 3 & 2+1 & 3+1 \\ \hline Policy tree training: & 0:08.327 & 13:23.021 & 0:28.872 & 11:18.153 \\ Evaluation of training: & 0:00.126 & 0:00.137 & 0:00.152 & 0:00.177 \\ Policy tree allocation: & 0:00.258 & 0:00.287 & 0:00.508 & 0:00.388 \\ Evaluation of allocation: & 0:00.079 & 0:00.125 & 0:00.139 & 0:00.168 \\ \hline \hline \end{tabular}   
Appendix A.3.3. Policy Trees Running Time: Interest Rates and Loan Returns Study