# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## 3 Empirical Studies
### Study 2: Right Heart Catheterisation  
In a seminal study, ref. [23] investigated the impact of right heart catheterisation (RHC) on various outcomes, including subsequent survival, healthcare costs, intensity of care, and length of hospital stay. Their findings revealed a positive association between RHC and mortality, as well as increased costs and prolonged length of stay. This conclusion was corroborated by subsequent research utilising different estimation methods, such as those employed by [24; 25; 26; 27]. In accordance with previous research, we also use the dataset originally collected from the SUPPORT prospective cohort study (Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments), as in [23]. This dataset includes 5735 observations on ill and hospitalised individuals between 1989 and 1994 in five medical centres in the US. Of these individuals, 38% received the surgery. Ref. [13]  
Figure 2: Allocation rule for a constrained optimal policy tree of depth-2. Note: The policy tree shows the shares of individuals allocated to each treatment. The splitting variables of the tree are age and an indicator variable for living in a metropolitan area (MSA). The final leaves of the trees indicate the treatments and corresponding shares of allocated individuals. The treatment used in the analysis is the indicator for being assigned to the lottery, which consequently gives access to Medicaid. For representation reasons, the tree reports the following: No-MA, no access to Medicaid (not extracted for the lottery); MA, access to Medicaid (extracted for the lottery). utilises the same information to provide new results on effect heterogeneity by exploring the functionalities of the _mcf_ package. In this empirical application, we focus on finding an optimal allocation of RHC to patients to increase their probability of survival six months after the medical surgery. Previous work has exploited expert opinion to identify eight features as relevant confounding factors [25]. These features include an index of activities of daily living two weeks before admission, age, the acute physiology and chronic health evaluation score (APACHE III), the Glasgow coma score, mean blood pressure, the probability of surviving two months (based on model estimations), an indicator for do not resuscitate status on the first day, and information on nine primary disease categories. Recognising the significance of these factors, we employ them as features in the policy tree to obtain assignment rules for decision making. Age and mean blood pressure are continuous variables, and we allow the tree algorithm to automatically determine the optimal split points based on the default number of evaluation points in the _mcf_ package. Our analysis starts by estimating the policy scores and IATEs. Additionally to the high-priority factors, we include potential confounding features (e.g., information on having cancer, possessing health insurance, etc.) to achieve identification through a selection-on-observable approach. Tables 15 and 16 of Appendix 16 comprehensively describe all 55 confounders. Figure 3 displays the density function of the IATEs, the most granular treatment effects. While slightly right-skewed, the distribution shows positive and negative treatment effects, ranging from \(-0.12\) to \(0.08\), and an average standard error of \(0.06\). This result underscores the (rather moderate) heterogeneous response to the surgery, indicating that while some individuals benefit from the intervention, others do not. Such heterogeneity emphasisises the importance of conducting a treatment allocation analysis to investigate potential improvements in the allocations of individuals. Table 2 shows that simple allocation schemes may improve the overall survival rate while decreasing the number of surgeries at the same time. Again, the first two rows of Table 2 present results using the empirically observed and random assignment of individuals to treatments, which are used as baseline comparison policies.