Dealing with endogeneity in non-randomized medical studies: a study of acute kidney injury following cardiopulmonary bypass surgery

Many medical studies have used non-randomized sampling, which tends to be the case in research that involves a surgical procedure. Intra-operative procedures and actions conducted by the attending surgical team may be based on pre-operative conditions of the patient, which can introduce endogeneity. Using acute kidney injury (AKI) following cardiopulmonary bypass surgery as a research setting, the present study uses a control function approach to explain why two perfusionist-directed principle components of delivered oxygen (DO₂) while the patient is on pump—hemoglobin and cardiac index—need to be treated as endogenous variables rather than exogenous ones. We further show conditions in which the exogenous model understates and overstates the predicted probability of AKI.