Adjustment uncertainty in effect estimation

The selection of confounders and their functional relationship with the out- come affects exposure effect estimates. In practice, there is often substantial uncertainty about this selection, which we define here as “adjustment uncertainty.” We address the problem of estimating the effect of exposure on an outcome with focus on quantifying the effect of unknown confounders from a large set of potential confounders. We propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation, a specific implementation called "Structured Estimation under Adjustment Uncertainty (STEADy)", and associated visualization tools. Theoretical results and simulation studies show that STEADy consistently estimates the exposure of interest and its associated variability. An important by-product of our methodology is that it reveals that the standard version of Bayesian Model Averaging (BMA) can fail to estimate the effect of scientific interest and can over or underestimate statistical variability of the exposure effect estimate. This is essentially due to the fact that BMA averages parameter estimates, only a subset of which can actually be interpreted as being the adjusted effect of interest. While this has been previously acknowledged, our methodology provides the theoretical platform for performance analysis of BMA estimation. We compare our approach (STEADy) to BMA on time series data on levels of fine particulate matter (PM10, PM2.5) and mortality and hospitalization counts.