# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## 3 Empirical Studies
### Study 2: Right Heart Catheterisation
The remaining rows show the results of policy trees aiming to optimise the treatment allocation and increase the survival rate. Given the relatively small sample size, this study focuses on optimal trees with depths of two and three, alongside policy trees with depths of 3 and 4, including a final sequentially optimal sub-tree (+1). Figure 3: Distribution of IATE. Mean (average standard error) of the IATEs: \(-0.04\) (\(0.06\)). Table 2 first reveals that the observed treatment allocation outperforms a random treatment assignment in terms of the survival rate (68.23% vs. 67.88%). Considering the performance of the policy trees, the findings suggest treatment allocations that could further increase the average survival rate within six months after the intervention up to 69.99%, while significantly diminishing the number of individuals receiving surgery by more than 50%. The maximum welfare gain, among the policy trees estimated, is already achieved with a policy tree of depth two. Deeper trees do not lead to a relevant increase in the survival rate. However, they reduce the share of individuals undergoing an operation. For example, compared to the depth-2 tree, the depth-3+1 tree indicates a reduction in survival rate by only 0.02 percentage points (69.99% vs. 69.97%) but decreases the share of patients having surgery by nearly three percentage points (19.21% vs. 16.22%). Since the maximum welfare gain is already attained with a depth-2 tree, Figure 4 displays the decision rules established by this tree, which is also the most straightforward to interpret. The policy tree performs the first split on age, while the second splitting variable is the estimated probability of surviving within two months, measured before the surgery. The decision tree allocates individuals with an age below 65 years and a survival probability below 48%, as well as those with an age above 65 years and a survival probability below 40%, to surgery. Note that tables representing all policy tree rules used are available in Appendix A. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Policy** & **Welfare (\%)** & **Treatment Shares (\%)** & \\  & **Survival Rate** & **No RHC** & **Yes RHC** \\ \hline Observed & 68.23 & 60.51 & 39.49 \\ Random & 67.88 & 59.00 & 40.99 \\ \hline Unconstrained optimal policy tree & & & \\ Depth-2 & 69.99 & 80.78 & 19.21 \\ Depth-3 & 69.95 & 82.73 & 17.27 \\ \hline Unconstrained sequentially optimal policy trees & & & \\ Depth-2+1 & 69.98 & 82.88 & 17.11 \\ Depth-3+1 & 69.97 & 83.78 & 16.22 \\ \hline \hline \end{tabular} Note: The table displays empirically observed, randomly assigned, and optimised treatment allocations as policies, where the final two policy trees add a second optimal sub-tree (+1).  
\end{table} 
Table 2: Treatment allocations: right heart catheterisation. Figure 4: Allocation rule for an optimal policy tree of depth-2. Note: The policy tree shows the shares of individuals allocated to treatment. The split variables are age and the probability of surviving within two months. The variable is measured before the decision of surgery. The final leaves of the trees indicate the treatments and corresponding shares of individuals allocated.