Efforts to understand the relationship between market structure and the quality of health services are complicated by the non-random character of patients' choices of where to receive care. To address this problem, I construct an empirical model of health outcomes for dialysis patients that accounts for the endogenous selection of which facility patients choose to receive treatment from. The model's estimates of facilities' average quality are robust to both unobservable variation in condition severity and heterogeneous responses to different facilities' treatment regimes. I estimate the model using data from 2004-2008 for all hemodialysis patients in Atlanta, Georgia. Decompositions of the recovered facility quality estimates show that the average treatment effect is substantially higher in areas characterized by greater competition. Overall, the results suggest that the idiosyncratic match between patient and facility is an important determinant of outcomes, helping to explain the mixed findings in the prior literature.