This study quantifies health outcome disparities in invasive Methicillin-Resistant Staphylococcus aureus (MRSA) infections by leveraging a novel artificial intelligence (AI) fairness algorithm, the Fairness-Aware Causal paThs (FACTS) decomposition, and applying it to real-world electronic health record (EHR) data. We spatiotemporally linked 9 years of EHRs from a large healthcare provider in Florida, USA, with contextual social determinants of health (SDoH). We first created a causal structure graph connecting SDoH with individual clinical measurements before/upon diagnosis of invasive MRSA infection, treatments, side effects, and outcomes; then, we applied FACTS to quantify outcome potential disparities of different causal pathways including SDoH, clinical and demographic variables. We found moderate disparity with respect to demographics and SDoH, and all the top ranked pathways that led to outcome disparities in age, gender, race, and income, included comorbidity. Prior kidney impairment, vancomycin use, and timing were associated with racial disparity, while income, rurality, and available healthcare facilities contributed to gender disparity. From an intervention standpoint, our results highlight the necessity of devising policies that consider both clinical factors and SDoH. In conclusion, this work demonstrates a practical utility of fairness AI methods in public health settings.