Enterprise AI Analysis

Alzheimer's Disease Ground Truth Graph Overview

For the Alzheimer's disease dataset, a ground truth causal graph (Figure 2 in the original paper) was derived from a known structural causal model. This graph illustrates causal relationships between variables such as sex (protected attribute), education, age, APOE4, MOCA, AV45, tau, brain volume, and ventricular volume (outcome), including mediators and confounders. This expert-defined benchmark serves as the basis for evaluating causal discovery algorithms.

PC (Fisher-Z) achieved the best structural recovery on the Alzheimer's dataset with an F1 score of 0.50 and the lowest Structural Hamming Distance (SHD) of 13. Continuous-optimization methods like DAG-GNN performed poorly.

Discovered graphs from PC and GES collapsed the fairness decomposition to direct effect only, showing Ctf-IE and Ctf-SE as zero. This indicates structural misspecification by these algorithms regarding indirect and spurious pathways.

For the ground truth graph, 'apoe4' was the largest positive contributor to spurious effect, while 'av45' and 'tau' showed significant negative contributions.

Blocking the direct sex to ventricular volume path yielded the most fairness gain per unit accuracy cost across algorithms. Spurious effect (SE) generally showed negative CFUR, suggesting interventions on confounder paths increased loss with little fairness benefit.

Heart Failure Clinical Records Ground Truth Graph Overview

For the heart failure clinical records dataset, a benchmark causal graph (Figure 3 in the original paper) was established through collaboration with a domain expert and extensive literature review. This graph captures complex interdependencies between demographic variables (age, gender), comorbidities (anaemia, diabetes, hypertension, smoking), physiological measurements (serum creatinine, ejection fraction), and the mortality outcome. It serves as a crucial benchmark for evaluating causal discovery algorithms in a real-world clinical context.

FCI achieved the best structural recovery on the HFCR dataset with an F1 score of 0.38 and a lowest SHD of 20, recovering more true edges with fewer false positives compared to PC and GES.

Total variation (TV) was consistent across graphs at approximately -0.4%. FCI and GES successfully recovered indirect and spurious components, whereas PC collapsed to direct effect only.

Ejection fraction was the most significant contributor to Ctf-IE at 3.37%, highlighting its mediating role. Age, platelets, and serum sodium contributed to Ctf-SE.

Under the ground truth, indirect and spurious effects showed positive CFUR, suggesting potential benefits from interventions on mediators and confounders. FCI had the most negative direct-effect CFUR.

Key Insights from Discussion

Our study demonstrated that graph choice significantly influences fairness decomposition. Discovered graphs often collapse indirect and spurious components or recover them with varying fidelity. For instance, PC often reduced decomposition to direct effects only, while GES and FCI showed better recovery of indirect and spurious components, particularly FCI on the heart failure dataset due to its ability to handle latent confounders. The Causal Fairness Utility Ratio (CFUR) profiles varied by graph and dataset, providing fine-grained insights into the fairness-utility trade-off.

The findings highlight the critical need for graph-aware fairness evaluation and path-specific analysis in clinical applications. Limitations include relying on expert-defined ground truths, potential violations of faithfulness and Markov equivalence with observational data, and the sample size of the HFCR dataset impacting confidence intervals. Future work will focus on expanding the suite of causal discovery algorithms, datasets, and evaluation metrics, developing methods for multiple protected attributes, and extending the framework to broader health data domains.