## 5 Experimental Analysis  
In this section, we present a series of experiments for evaluating the ability of the proposed approach for supporting the QoL of patients with osteogenicia undergoing treatment with Als. Our scope is to compare the performance of state-of-the-art ML models, ranging from traditional linear models to tree-based and neural network-based models, in estimating treatment effects. For conducting the experiments, we use synthetic datasets, which were produced in a completely controlled setting by the SDG, based on the causal DAG developed in the \"Model Development\" stage (see Section 4.2), for the case of osteopenia and osteoporosis studied as a comorbidity of breast cancer treatment with aromatase inhibitors. At this point, it is worth recalling that the primary reason for utilizing synthetic datasets in our research is that it is impossible to observe the causal effect of a single unit, since only the factual outcome can be measured, which constitutes the fundamental problem of causal inference [16]. In detail, a BCP can either receive or not receive a specific treatment or an intervention and, thus, we cannot calculate the real causal effect of the particular treatment on the patient. Therefore, when using RWD for causal inference, we cannot observe but only estimate the missing counterfactual outcomes and then estimate the causal effects [58; 59]. Next, we present the models, which are included and evaluated in the REBECCA workflow and are characterized as some of the most effective and widely used models for the estimation of causal effects:  
* \"LR1\", which stands for the \"S-learner\" methodology proposed by [PERSON] et al. [30], using Linear Regression as a base learner [60]. * \"LR2\", which stands for the \"T-learner\" methodology proposed by [PERSON] et al. [30], using Linear Regression as a base learner [60]. * \"R-Forest\", which stands for the \"S-learner\" methodology proposed by [PERSON] et al. [30], using Random Forest as a base learner [43]. * \"BART\", which stands for the model proposed by [PERSON] et al. [28]. * \"TARTNet\", which stands for the model proposed by [PERSON] et al. [32]. * \"Dragonnet\", which stands for the Dragonnet model proposed by [PERSON] et al. [35]. * \"NN-Dragonnet (C)\", which stands for the model proposed by [PERSON] et al. [36; 37], using Chebyshev distance for calculating the average of the nearest instances' outcomes. * \"NN-Dragonnet (E)\", which stands for the model proposed by [PERSON] et al. [36; 37], using Euclidean distance for calculating the average of the nearest instances' outcomes. * \"NN-Dragonnet (M)\", which stands for the model proposed by [PERSON] et al. [36; 37], using Manhattan distance for calculating the average of the nearest instances' outcomes. The implementation code was written in Python 3.10 and executed on a PC (3.2 GHz Quad-Core processor, 32 GB RAM) using the Windows operating system. We experimented with several configurations of each causal inference model through a grid hyperparameter search. For example, all neural network-based models (i.e., TARNet, Dragonnet and NN-Dragonnet) were evaluated using a varying number of neurons in the hidden layers as well as different learning rates. In addition, all versions of NN-Dragonnet were evaluated with several values of parameter \(k\) (number of neighboring instances) ranging from 5 to 15, while R-Forest was evaluated with different values of the \"number of trees\" and \"max depth\" hyperparameters, which are reported in Appendix C.  
The performance of all causal inference models was measured using the absolute error of the ATE \(|\epsilon_{\text{ATE}}|\) and the Precision in Estimation of Heterogeneous Effect (PEHE) metrics, which are, respectively, defined by (2) and (8). It is worth noticing that the PEHE assesses the precision of the causal inference models for estimating the ITE by measuring the accuracy of individualized predictions.