Combining data from Randomized Controlled Trials (RCTs) is a widely used method to estimate causal treatment effects. In order to combine data, the property of transportability, under which different covariate vectors exhibit similar treatment benefit, must hold between the RCTs. However, differences in study design, execution, and the underlying effect modifier distributions can violate transportability which could in turn lead to estimating incorrect causal treatment effect estimates. This thesis addresses the challenge of validating transportability between multiple RCTs and identifying subsets of RCTs between which transportability holds. Our contributions include studying a linear regression-based framework for testing transportability between multiple RCTs and a clustering-based approach for identifying transportable RCT subgroups. Through simulations and analysis of real-world RCTs concerning corticosteroid treatment for Community-acquired pneumonia (CAP), we evaluate the power, robustness, and limitations of our proposed framework.

This study tackles an important issue in evaluating the reliability of confidence intervals in causal forests by examining how data characteristics and hyperparameters influence actual coverage rates compared to theoretical benchmarks. Using synthetic data sets with polynomial treatment effects, Sobol sampling, High-Dimensional Model Representation (HDMR), and comprehensive grid searches, the study assesses causal forest performance in different data contexts.

A primary discovery is the identification of a practical limit for reliable confidence interval coverage: When the sum of confounders and effect modifiers exceeds 4, coverage rates drop considerably below 80%, even for simple treatment effect functions. This limitation remains steady despite substantial increases in computational resources.

The examination of hyperparameters revealed that the most influential parameters are the maximum tree depth and the balance tolerance in splits, which demonstrate substantial changes in performance, both of which performed best at their maximums (unlimited and 0.5, respectively). Other key suggestions involve increasing the training data fraction per tree from 0.45 to 0.5, keeping the minimum impurity decrease threshold at 0.0, and utilizing at least ≈ 2400 trees to meet theoretical expectations.

In addition, this paper did not identify any noteworthy interaction between tree count and sample size. As a result, both of these characteristics can be optimized independently of each other.

These findings provide systematic guidelines for practitioners to assess when causal forest confidence intervals are reliable and how to optimize them, bridging the gap between theoretical guarantees and practical performance.

Causal inference, particularly the estimation of the Conditional Average Treatment Effects (CATE), is necessary for understanding the impact of interventions beyond simple predictions. This study analyzes the influence of key hyperparameter choices, specifically maximum tree depth and minimum leaf size, on the accuracy and generalization of CATE estimates derived from honest and adaptive causal trees. The research explores how these hyperparameters affect the bias-variance trade-off and the model's tendency to overfit or underfit across various simulated data scenarios and a real-world dataset.

The results reveal that optimal hyperparameter configurations are dependent on the data characteristics, such as dimensionality, noise levels, and the complexity of the true causal effects. Honest causal trees demonstrate a better performance in high-dimensional and noisy environments due to their effective variance control. Conversely, in simpler, low-noise settings or complex CATE structures, adaptive causal trees or baseline models frequently achieve better results by reducing bias. The study also highlights the challenges of using moderately sized datasets, where the sample splitting limitations can lead to higher estimation errors. This work provides thorough suggestions for hyperparameter selection, emphasizing the fact that tuning based on the underlying characteristics of the data is needed for achieving the best CATE estimates possible.

Estimating the Conditional Average Treatment Effect (CATE) with neural networks adapted for causal inference, like TARNet, is a promising approach, yet the impact of model architecture on performance remains underexplored.
This paper systematically investigates how the depth and width of TARNet affect the CATE estimation in diverse simulated data environments. The research investigates two central questions: how TARNet's performance varies across data regimes (e.g., confounding strength, sample size), and how its optimal architecture changes in response to these conditions.
A comprehensive set of simulation-based experiments is conducted using the CATENets framework, isolating and varying factors such as sample size, feature dimensionality, confounding strength, and the presence of noise. The results demonstrate that deeper architectures generally yield better performance in complex or high-dimensional scenarios, whereas narrower networks are preferable in small-sample or high-noise settings due to their regularizing effect. Furthermore, the findings suggest that there is no universally optimal architecture. The best configuration depends on the specific characteristics of the data. The study concludes with practical recommendations for architecture selection based on the experiments conducted.

Causal Multi-task Gaussian Processes (CMGPs) provide a Bayesian approach for estimating in-
dividualized treatment effects by modeling potential outcomes as correlated functions. However,
they struggle under high-dimensionality and treatment imbalance, leading to overfitting and unre-
liable uncertainty estimates. This study examines two failure modes: poor generalization in high-
dimensional spaces and overconfident predictions in low-overlap regions. To address these, two
data-aware enhancements are proposed: an overlap-adaptive kernel that scales similarity based on
local treatment density, and a regularized prior that down-weights unstable features using marginal
treatment effect variance. Evaluations on synthetic data and the IHDP benchmark show improved
effect estimation, credible interval calibration, and robustness in challenging settings. These find-
ings highlight practical strategies for enhancing CMGPs in real-world causal inference tasks.

Interventional Normalizing Flows (INFs) are a recently proposed method for estimating interventional outcome distributions from observational data. A central component of this approach is the nuisance flow, whose function is to estimate the propensity score and the conditional outcome distribution. INFs are claimed to be doubly robust, meaning they can yield valid estimates even if only one of these components is correctly specified. This study investigates the practical limits of this robustness by asking two questions: (1) How do interventional estimates behave when nuisance flow components are entirely misspecified? and (2) How sensitive are these estimates to more realistic imperfections such as suboptimal hyperparameters or injected noise? Through experiments on four benchmark datasets with varying levels of confounding and distributional complexity, we find that INFs remain robust under low-confounding conditions even when both nuisance components are broken. However, in highconfounding settings, even partial misspecification can cause estimates to degrade substantially, undermining the doubly robust property. These results highlight the importance of carefully validating nuisance components and suggest that the theoretical guarantees of INFs may not always hold in practice.

Causal inference methods are often used for estimating the effects of an action on an outcome using observational data, which is a key task across various fields, such as medicine or economics. A number of methods make use of representation learning to try to obtain more
informative feature representations, which are then used for effect estimation. However, such feature representations can introduce confounding bias in the results if they lose confounding information contained within the original features. In this work, we evaluate an existing metric for measuring confounding bias in representations and use this metric to study two representation learning methods in terms of their biases in settings with low overlap between treated and control populations. We show that the metric is a suitable measure for the amount of confounding bias in a representation and representation learning methods that minimise this bias lead to better average treatment effect estimation in our experiments.

This research investigates the use of Causal Multi-task Gaussian Process (CMGP) for estimating the individualized treatment effect (ITE) of low versus high Positive End-Expiratory Pressure (PEEP) regimes on ICU patients requiring mechanical ventilation. The study addresses the complexities of determining ITE due to the inability to observe counterfactual outcomes and the confounding bias in observational studies. By employing Conditional Average Treatment Effect (CATE) estimators, such as S-Learner, T-Learner, and CMGP, the research evaluates the impact of different PEEP settings on patient survival across varied patient characteristics. The precision of these estimators is assessed using simulated data, real-world observational data from the MIMIC-IV dataset, and an external RCT dataset. The findings of this study are inconclusive, highlighting the need for further research to refine these methods and explore larger, more balanced datasets.

Positive end-expiratory pressure (PEEP) is one of the components of mechanical ventilation treatment for patients with acute respiratory distress syndrome (ARDS). Correct PEEP level can reduce additional lung injuries sustained during the hospitalisation, significantly increasing patients' chances for survival. In this paper, we focus on estimating the difference in patient mortality when assigned high or low PEEP level. We look at three machine learning models specifically designed for such tasks: S-learner, T-learner and causal forest. Through a series of experiments, we determine their best use cases based on simulated data and measure their performance on a real-life dataset - MIMIC-IV. In our analysis, we find that after tuning the hyperparameters, the models can, to some degree, make valuable predictions and reveal heterogeneity in the treatment effect. However, when evaluated on a separate dataset, the models' performance drops significantly.

In the intensive care unit (ICU), optimizing mechanical ventilation settings, particularly the positive end-expiratory pressure (PEEP), is crucial for patient survival. This paper investigates the application of neural network-based machine learning methods to personalize PEEP settings in the ICU, aiming to improve patient survival outcomes. The research focuses on two specific algorithms, TARNet and CFR, evaluating their ability to estimate individualized treatment effects of lower versus higher PEEP regimes. The study is structured into three phases: controlled simulations, application to the MIMIC-IV dataset, and validation using a randomized control trial dataset. TARNet and CFR showed potential for estimating the individualized treatment effects but required large datasets for optimal performance. In the case where limited data is available, these models are upstaged by simpler learners, such as the S- and T-learners. The study concludes that while neural network-based methods hold promise for personalizing ICU treatment, their efficacy is heavily influenced by data availability and quality.

Mechanical ventilation with positive end-expiratory pressure (PEEP) is a critical intervention for patients in intensive care units (ICUs) with acute respiratory failure. Identifying the optimal PEEP level is challenging due to conflicting evidence from studies comparing low and high PEEP regimes. This research explores machine learning methods for estimating individualized treatment effects (ITE) in ICU patients on different PEEP levels using the observational MIMIC-IV dataset. Various conditional average treatment effect (CATE) estimators, including S-, T-, and DR-learners, are applied to control for confounders and identify PEEP effects on patient subgroups. This research aims to compare the performance of the aforementioned CATE estimators, with a focus on the doubly-robust (DR) learner, and determine which one is best suited for causal inference in this context. The DR-learner offers increased resilience to model errors since it integrates two models. Simulations using mean squared error (MSE) show the DR-learner performs well with confounded data and differing linear response functions between control and treatment groups. However, when looking at the performance on the MIMIC-IV dataset, the predictions are unstable, failing to reliably identify the optimal PEEP for increasing patient survival. This trend is also observed in a randomized controlled trial (RCT) dataset, with the area under the Qini curve (AUQC) close to zero, indicating difficulties in identifying the effects of PEEP settings. Despite promising simulation results, real-world application shows limitations in these machine learning methods for optimal PEEP identification.

Mechanical ventilation is a vital supportive measure for patients with acute respiratory distress syndrome (ARDS) in the intensive care unit. An important setting in the ventilator is the positive end-expiratory pressure (PEEP), which can reduce lung stress but may also cause harmful side effects. This research investigates the personalization of PEEP settings based on patient characteristics using three meta-learning algorithms (S-, T-, and X-learner) to estimate the conditional average treatment effect. Additionally, the hypothesis that the X-learner performs particularly well under a significant imbalance in patient numbers between treatment groups is tested. Results show that the X-learner slightly outperforms the S- and T-learners in terms of mean squared error under various unbalanced conditions in simulated data. However, the overall ability of these meta-learners to identify patients benefiting from high PEEP remains inconclusive. When using gradient boosted trees or random forest as base models, cumulative gain curves on MIMIC-IV data indicate potential overfitting. While the X-learner performs somewhat better on this data, the low area under the curve scores suggests a minimal distinction between high and low PEEP groups. External validation with data from a randomized control confirms that the models do not effectively distinguish between treatment groups. These findings suggest that further investigation with more complex models and real-world data is needed to validate the potential of meta-learning algorithms in personalizing PEEP settings for ARDS patients.

Causal inference is a widely recognized concept in various domains, including medicine, for estimating the effect of a medication on a certain disease. During this estimation, overlap is commonly used to eliminate the error caused by other features. However, finding the real overlap region in practice is challenging due to the limited sample size and unknown data distribution. Therefore, some machine-learning methods have been proposed to estimate the overlap region. One such method is Overrule, a Python package proposed by Oberst et al. Overrule is based on rule-based lassification and estimates the overlap region by interpreting it as several rules across the features. However, it is still unclear how Overrule performs under different circumstances. Thus, the primary bjective of this project is to test the performance of Overrule with different datasets. To accomplish this, a series of tests are built and executed to evaluate the performance of Overrule in diverse scenarios.

For causal inference, sufficient overlap is needed. It is possible to use propensity scores with the positivity assumption to ensure overlap is present. However, positivity is not enough to properly identify the region of overlap. For this, propensity scores need to be used in combination with density estimation. This project aims to evaluate this method, discovering in which scenarios it performs well or fails in identifying the region of overlap. More specifically, how it scales with more features or outliers, and how using different classifiers affects the performance. The method was tested with samples from a simulated dataset. The predicted overlap was compared with the true overlap of the known distributions.
Following the experiments, the method seems to perform best when the treatment and control groups share one region of overlap. In this case, logistic regression works best out of the classifiers that were tested. The overall performance drops when the two groups have multiple regions of overlap. For this, the random forest classifier performs best instead. Throughout all scenarios, the performance of the model drops with increasing dimensionality. Furthermore, having a small percentage of outliers only slightly affects the model. With more outliers, logistic regression is the only classifier further affected.

Generalizing models for new unknown datasets is a common problem in machine learning. Algorithms that perform well for test instances with the same distribution as their training dataset often perform severely on new datasets with a different distribution. This problem is caused by distributional shifts between the training of the model and applying that model to a test domain. This paper addresses whether and in what situations Risk Extrapolation (REx) can tackle this problem of Out-Of-Distribution generalization by exploiting invariant relationships. These relationships are based on features that are invariant across all domains. By learning these relationships, REx aims to learn the concept of the problem we are trying to solve. We show in what situations REx can learn these invariant relationships and when it does not. We translate the definition of an invariant relationship into a homoscedastic synthetic dataset with either covariate, confounded, anti-causal, or hybrid shift. We expose REx to experiments in sample complexity, the number of training domains, and the training domain distance. We show that REx performs better for invariant prediction in situations with larger sample sizes and training domain distance and that if these criteria are met, REx performs equivalently in all four distributional shifts. We also compare REx to Invariant- and Empirical Risk Minimization and show that; REx is less sensitive and thus robust to the shifting of the average distributional variance in the training domains; REx asymptotically out-performs the methods in the more complex distributional shifts.

The front-door adjustment is a causal inference method with which it is possible to determine the causal effect of applying a treatment given a setting which satisfies the front-door criterion. This involves having a mediator through which all the causal effect flows from treatment to outcome. The front-door adjustment adjusts for confounders and tries to only measure the causal effect from treatment to outcome. The goal is to test the applicability of the front-door adjustment using the game of Dota 2 as a testing ground. The front-door adjustment has been applied to find the effect of picking ‘Slark’ on the outcome of the game. The mediator in this case is the enemy team buying an item called ‘Hurricane Pike’. Two different approaches have been used, both giving varying results. These varying results lead to different possible interpretations. This variety of interpretations therefore suggest that the front-door adjustment is not a valid method for this specific scenario, likely due to the complexity of the game and perhaps the simplified representation of the game in the data-set.

Strategy games could be considered as an amazing playground for using Causal inference methods. The complex nature of the data and the built-in randomization help with testing causal inference in a scenario where in reality it would be hard and expensive. Randomized data in coherence with causal inference is well documented and tested, but not regarding the strategy game of interest DotA 2. To evaluate the quality of causal inference using randomized data for predictions in the game, the average causal effect estimand is used. The calculation of the average causal effect of certain events between different intervals and their comparison in addition to the calculation of the statistical Independence between variables of concern comprise the bulk of the research. The calculations allow for logical deductions and statistical correlations between values to reach a conclusion. The final verdict being that causal inference with randomized data is helpful for predicting events in DotA 2 but the amount of data and existing complex biases can be deceiving and can heavily influence the results.

Commonly, when researchers are figuring out the effect of a putative cause, additional variables influence the cause and the effect. These are called confounders, and they obfuscate causal relationships. Inverse Probability Weighting is a method that can be applied to remove confounding and show a causal effect. This study aims to determine if Dota 2 game outcomes can be predicted based on team composition diversity and if 'Inverse Probability Weighing is a helpful tool for this. First, metrics to assess team diversity were determined, and the two confounders, "Player skill" and "Hero skill", to the 'is-diverse' treatment and game outcome were identified. Next, a dataset with Dota 2 games was gathered containing all the relevant variables to measure the confounders. Finally, inverse probability weighting was applied to measure the Average Treatment Effect of the putative cause.
The results suggest that team diversity significantly impacts the game outcome. However, the results were close in most cases when comparing the results with data that was not corrected for by confounders. A possible explanation may be that the confounders didn't have enough influence on some diversity metrics since they were too vague. For example, the most complex diversity metric, which covered the most team-composition characteristics, showed a clear difference between the average treatment effect with inverse probability weighting being applied and not applied.

Out-of-domain (OOD) generalization refers to learning a model from one or more different but related domain(s) that can be used in an unknown test domain. It is challenging for existing machine learning models. Several methods have been proposed to solve this problem, and multi-domain calibration is one of these methods. Model selection with the average expected calibration error (ECE) across training domains and naive calibration are two approaches to implementing multi-domain calibration. However, it might happen that neither approach can learn a genuinely well-calibrated model in the multi-domain setting. Hence, this paper intends to evaluate how naive calibration and model selection with average ECE perform in the OOD generalization problem for binary classifiers. We generated many synthetic datasets and set up three experiments to answer this question. Finally, the conclusions based on empirical results are obtained: 1) Although naive calibration can improve the average accuracy across unseen domains (OOD accuracy) and the average area under the ROC Curve across unseen domains (OOD AUROC) for some binary classifiers, it does not work for all binary classifiers. However, at least it does not make the model worse for OOD generalization. 2) On the synthetic datasets we generated, if the number of training domains increases, most binary classifiers' OOD accuracy will also increase. 3) Average ECE is a reasonable metric for selecting a model in the OOD generalization problem and is better than validation accuracy. This is because a strong linear relationship exists between OOD accuracy and the average ECE across the training domains. This linear relationship is stronger than the linear relationship between OOD accuracy and validation accuracy.

Out-of-Domain (OOD) generalization is a challenging problem in machine learning about learning a model from one or more domains and making the model perform well on an unseen domain. Empirical Risk Minimization (ERM), the standard machine learning method, suffers from learning spurious correlation in the training domain, therefore may perform badly when the unseen domain has different distribution from the training domain. Group Distributionally Robust Optimization (group DRO) is a method proposed to handle the OOD generalization problem. In this paper, the goals are to 1) measure if group DRO has a better OOD generalization performance than ERM. 2) evaluate if group DRO finds causally invariant relationships between the input and output. Semi-synthetic bird images with different backgrounds are used to form our data sets to construct a binary image classification problem for experiments. Results show that group DRO improves OOD generalization performance over ERM, and group DRO can find invariant relationships. However, the ability of group DRO to find invariant relationships is limited when the spurious correlation in the training domain is strong.