In this paper, we propose a methodological approach to measure the relationship between hospital costs and health outcomes. We propose to investigate the relationship for each condition or disease area using patient-level data. We suggest to examine health outcomes as a function of costs and other patientlevel variables: (1) using two-stage residual inclusion with Murphy-Topel adjustment to address costs being endogenous to health outcomes, (2) using random-effects models in both stages to correct for correlation between observation, and (3) using Cox proportional hazard models in the second stage to ensure the available information is exploited. To demonstrate its application, data on mortality following hospital treatment for acute myocardial infarction (AMI) from a large German sickness was used. Provider reimbursement was used as a proxy for treatment costs. We relied on the Ontario Acute Myocardial Infarction Mortality Prediction Rules as a disease-specific risk-adjustment instrument. 12,284 patients with a treatment for AMI in 2004-2006 were included. Results showed a reduction in hospital costs by 100 to increase the hazard of dying, i.e. mortality, by 0.43%. The negative association between costs and mortality confirms that increased resource input leads to better outcomes for treatment after AMI.