Contrasting evidence within and between institutions that supply treatment in an observational study of alternative forms of anesthesia
Mark D. Neuman, Department of Anesthesiology and Critical Care, School of Medicine, University of Pennsylvania  
Paul R. Rosenbaum, Department of Statistics, The Wharton School, University of Pennsylvania 
Jeff H. Silber, Center for Outcomes Research, The Children’s Hospital of Philadelphia 
*Jose R. Zubizarreta, Department of Statistics, The Wharton School, University of Pennsylvania 

Keywords: Assignment algorithm, combinatorial optimization, evidence factor, fine balance, observational study, optimal matching of an optimal subset, sensitivity analysis

In many observational studies, subjects find their way to treatment or control in two steps, either or both of which may lead to biased comparisons. By a vague process perhaps affected by proximity or sociodemographic issues, subjects find their way to institutions that provide treatment. Once at such an institution, a second process, perhaps thoughtful and deliberate, assigns individuals to treatment or control. In the current paper, the institutions are hospitals, and the treatment under study is the use of general anesthesia alone versus some use of epidural or regional anesthesia during surgery. For a specific operation, the use of regional anesthesia may be typical in one hospital and atypical in another. A new matched design is proposed for studies of this sort. Using a new extension of optimal matching with fine balance, pairs of the first type exactly balance treatment assignment across institutions, so differences between institutions that affect everyone in the same way cannot bias this comparison. Pairs of the second type compare institutions that assign most subjects to treatment and other institutions that assign most subjects to control, so each institution is represented in the treated group if it typically assigns subjects to treatment or alternatively in the control group if it typically assigns subjects to control. The design provides two evidence factors, that is, two tests of the null hypothesis of no treatment effect that are independent when the null hypothesis is true, where each factor is largely unaffected by certain unmeasured biases that could readily invalidate the other factor. The two factors permit separate and combined sensitivity analyses, where the magnitude of bias affecting the two factors may differ. The case of knee surgery in the study of regional versus general anesthesia is considered in detail.