Econometrics

# What is collider bias?

A paper by Holmberg et al. (2022) in JAMA provides a number of examples of how collider bias can lead to problematic causal inference. The term collider bias is often invoked when using directed acyclic graphs (DAGs) to map the causal pathway. Collider bias occurs when you aim to measure the impact of A on B by controlling for C, but it is the case that A and B both have a causal impact on C. By controlling for C in your regression analysis, you may create a spurious negative relationship between A and B. This is also known as Berkson’s paradox.

Consider the case where we conducted a study examining whether individuals who attend class get good grades. In the data below, 62.5% of students who attend class get good grades, whereas only 37.5% of students who did not attend class got good grades.

As a researcher, however, you do not know these value; you need to estimate them. Consider the case where you did a survey of people regarding whether they attended class and what their grades were. A key issue is that indiivudals with good grades and those who attend class are probably more likely to respond to your survey. Consider the following response rates:

• Attends class and good grades: 80%