Covariate selection criteria for controlling confounding bias in a causal study

It is important to control confounding bias when estimating the causal effect of treatment in an observational study. We illustrated that the covariate selection in the causal inference is different from the variable selection in the ANCOVA model. We then investigated the three criteria of covariate selection for controlling confounding bias, which can be used when we have inadequate information to draw a complete causal graph. VanderWeele and Shpitser (2011) proposed one of them and claimed it was better than the other two. We show by example that their criterion also has limitations and some disadvantages. There is no clear winner; however, their criterion is better (if some correction is made on its condition) than the other two because it can remove the confounding bias.