Model-based estimation of the effect of an exposure on an outcome is generally sensitive to the choice of which confounding factors are
included in the model. We propose a new approach, which we call Bayesian Adjustment for Confounding (BAC), to estimate the effect on the outcome
associated with an exposure of interest while accounting for the uncertainty in the confounding adjustment. Our approach is based on
specifying two models: 1) the outcome as a function of the exposure and the potential confounders (the outcome model); and 2) the exposure as a
function of the potential confounders (the exposure model). We consider Bayesian variable selection on both models and link the two by
introducing a dependence parameter omega denoting the prior odds of including a predictor in the outcome model, given that the same
predictor is in the exposure model. In the absence of dependence (omega = 1), BAC reduces to traditional Bayesian Model Averaging
(BMA).  In simulation studies we show that BAC with omega >1 estimates the exposure effect with smaller bias than traditional BMA,
and improved coverage. We then compare BAC and traditional BMA in a time series data set of hospital admissions, air pollution levels and weather variables in
Nassau, NY for the period 1999-2005. Using each approach, we estimate the short-term effects of PM2.5 on emergency admissions for
cardiovascular diseases, accounting for confounding. This application illustrates the potentially significant pitfalls of misusing variable
selection methods in the context of adjustment uncertainty. 

joint work with Chi Wang and Giovanni Parmigiani
This talk is extracted from the following paper

Wang C, Parmigiani G, Dominici F. (2012) Bayesian effect estimation
accounting for adjustment uncertainty Biometrics. DOI:
10.1111/j.1541-0420.2011.