Bayesian Inference for Causal Quantities via the Instrumental Variable Approach with a Binary Outcome and a Binary Treatment

• Activity Number: 653
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Rodney Sparapani*+ and Purushottan Laud and Jessica Pruszynski and Robert E. McCulloch
• Companies: Medical College of Wisconsin and Medical College of Wisconsin and Medical College of Wisconsin and The University of Chicago Booth School of Business
• Keywords: Bayesian inference ; bivariate probit regression ; causal inference ; comparative effectiveness research ; instrumental variable ; Markov chain Monte Carlo

Abstract

In biostatistical investigations, randomized controlled clinical trials are often the gold standard of evidence for determining the safety and efficacy of a treatment. However, clinical trials are often performed on a fairly restricted population; in some cases these trials cannot be performed at all. Non-randomized, observational studies are another type of evidence. In non-randomized studies, the treatment may be confounded with the patient's diagnostic/prognostic information. The Instrumental Variable (IV) approach was invented in classical econometrics to adjust for such confounding, although, typically for a continuous outcome. Many biostatistical investigations require a binary outcome and a binary treatment. We will present a Bayesian approach that adapts IV to this case which facilitates the computation of causal quantities such as the local average treatment effect and the average treatment effect. We will compare the performance of this model with classical econometric methods via repeated data simulation and standard measures such as bias, mean square error and length/coverage of interval estimates.