The Impact of Collider Bias due to Confounder Measurement Error: Observations on the Dilemma between Collider Bias and Confounding Control

Abstract

This study focuses on cases when confounder measurement error leads to collider bias. In the context of causal inference, when confounding factor cannot be perfectly measured, the usual way is to construct a proxy as accurate as possible in order to exclude the bias partially. However, when we try to control a proxy variable which is constructed from the confounding factor and a error term that somehow occurred endogenously, the collider bias occurs. So that, in such situation, there will be a dilemma between partially controlling of the confounding factor and the risk of collider bias. This study clarifies the trade-off between partially controlling and collider bias of such proxies. The result showed that considering the risk of collider bias, a more unbiased causal inference is not always available by using more accurate proxies, actually, in some cases, the causal effect is very likely to be underestimated.