Extending the Bayesian Adjustment for Confounding algorithm to binary treatment covariates to estimate the effect of smoking on carotid intima-media thickness: the Multi-Ethnic Study of Atherosclerosis.

We illustrate the application of the Bayesian Adjustment for Confounding (BAC) algorithm when the treatment covariate is binary. Using data from the Multi-Ethnic Study of Atherosclerosis, we estimate the effect of ever smoking on common carotid artery intimal medial thickness among adult Caucasian participants (n=1378). Our novel implementation of the BAC algorithm is performed first from an outcome model perspective and second from a treatment model perspective with both inverse probability weighting and doubly-robust estimation techniques. The BAC results are compared with the results obtained using standard model averaging and full model strategies, giving a range of adjusted estimates between 45.50 and 65.30 μm for increased common carotid artery intimal medial thickness among ever smokers. For both perspectives, we observe that BAC offers similar performance to using the fully specified outcome and/or treatment model (the full outcome model ever smoking effect is 48.61 μm; 95% CI: (0.62, 96.60)). We then redo the analyses for the African American, Hispanic, and Chinese adult participants to study the robustness of these findings with reduced sample size. For the Chinese subcohort, which corresponds to the smallest sample size (n=436), we find that, from a treatment model perspective, BAC reduces the variability of the estimates in comparison with using a full model approach. This suggests that the use of BAC in conjunction with inverse probability weighting and doubly-robust estimation can be advantageous when applied to relatively small sample sizes. This conjecture is subsequently verified on the basis of three simulated experiments.