In this work, we characterize the doctor-patient relationship using a machine learning-derived trust score. We show that this score has statistically significant racial associations, and that by modeling trust directly we find stronger disparities in care than by stratifying on race. We further demonstrate that mistrust is indicative of worse outcomes, but is only weakly associated with physiologically-created severity scores. Finally, we describe sentiment analysis experiments indicating patients with higher levels of mistrust have worse experiences and interactions with their caregivers. This work is a step towards measuring fairer machine learning in the healthcare domain.