Using Inverse Probability Weighting to Address Post-Outcome Collider Bias

We consider the problem of bias arising from conditioning on a post-outcome collider. We illustrate this with reference to Elwert and Winship (2014) but we go beyond their study to investigate the extent to which inverse probability weighting might offer solutions. We use linear models to derive expressions for the bias arising in different kinds of post-outcome confounding, and we show the specific situations in which inverse probability weighting will allow us to obtain estimates that are consistent or, if not consistent, less biased than those obtained via ordinary least squares regression.