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Title: High-dimensional confounding adjustment using continuous spike and slab priors Authors:  Joseph Antonelli - University of Florida (United States) [presenting]
Giovanni Parmigiani - Dana-Farber Cancer Institute (United States)
Francesca Dominici - Harvard University (United States)
Abstract: In observational studies, estimation of causal effects relies on proper adjustment for confounding. If the number of the potential confounders ($p$) is larger than the number of observations ($n$), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are for the most part aimed at predicting the outcome, and are not suited for estimation of causal effects. We propose continuous spike and slab priors on the regression coefficients $\beta_j$ corresponding to the potential confounders $X_j$ when $p\geq n$. If $X_j$ is associated with the treatment, then we increase the prior probability that $\beta_j$ is included in the slab component of the prior. This reduces the degree of shrinkage of $\beta_j$ towards zero. Using theoretical considerations and a simulation study we compare our proposed approach to alternatives and show its ability to adjust for confounding across a range of data generating mechanisms. Finally, we estimate the causal effects of persistent pesticide exposure on triglyceride levels, which highlights the key important features of our approach: 1) the ability to identify the true confounders, and 2) the ability to exclude instrumental variables, therefore minimizing bias and improving efficiency of effect estimates.