Approximate Bayesian Inference for Double-Robust Estimation

• Activity Number: 364
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Daniel Graham*+ and David A Stephens and Emma McCoy
• Companies: Imperial College London and McGill University and Imperial College London
• Keywords: Bayesian inference ; Double-robust ; Propensity Score ; treatment effect

Abstract

Double-robust (DR) estimators are typically constructed as solutions to estimating equations based on a set of moment restrictions. Standard Bayesian methods are difficult to apply because restricted moment models do not imply fully specified likelihood functions. This paper uses a Bayesian bootstrap approach to derive approximate posterior predictive distributions that are DR for average treatment effect (ATE) estimation. This is achieved by specifying Dirichlet prior weights for the parameters of an outcome regression (OR) model augmented with inverse propensity score (PS) covariates, and by repeatedly estimating the weighted model to build up the posterior distribution. Simulations show that the predictive posterior distributions for ATEs can provide a good approximation to linear or nonlinear dose-response functions under various sources of misspecification of the OR or PS models. The estimator is applied in a public health case study of the effect of speed cameras on the incidence of road casualties in Britain.