Not always towards the null: reconsidering the direction of overadjustment bias.

Overadjustment bias occurs when adjusting for a variable increases rather than decreases bias. It commonly arises in studies estimating the total causal effect of an exposure on an outcome due to inappropriate adjustment for a mediator. While such inappropriate mediator adjustment can lead to bias in any direction (towards the null, away from the null, or reverse the direction of effect) even in the absence of other relevant unadjusted variables, this type of overadjustment bias is often described as acting towards the null. Using directed acyclic graphs and a simulated example of adjustment for smoking when estimating the total causal effect of education on the risk of breast cancer, we explain how inappropriately adjusting for a mediator can lead to overadjustment bias in any direction. Correspondingly, we provide general guidance to predict the likely direction of overadjustment bias based on the direction of effect of the relevant paths involved. In general, this bias will be away from the null or in the reverse direction when the mediated pathway being closed by inappropriate adjustment acts in the opposite direction to the combined effect of all remaining pathways between the exposure and the outcome. In contrast, this bias will be towards the null when the effects of these paths act in the same direction.