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A paper by Holmberg et al. (2022) in JAMA Numerous examples are provided of how collider bias can lead to problematic causal inference. The term collider bias is often called when directed acyclic graphs (DAGs) are used to map causal paths. Collider bias occurs when your goal is to measure the effect of A on B by controlling C, but the case is A and B both has a causal effect on C. By controlling for C in the regression analysis, you may create a spurious negative relationship between A and B.This is also called Berkson’s paradox.
Consider the case where we conducted a study examining whether people who took classes were getting good grades. In the data below, 62.5% of the students who attended the class achieved good grades, while only 37.5% of the students who did not attend the class achieved good grades.
| Attendance | % Get good grades | Good results | Poor performance |
| Attend class | 62.5% | 20 | 12 |
| Do no Attend class | 37.5% | 12 | 20 |
However, as a researcher, you don’t know these values; you need to estimate them. Consider a situation where you surveyed people about whether or not they attended classes and their grades. A key issue is that individuals with high grades and those in class may be more likely to respond to your survey. Consider the following response rates:
- class and OK Grade: 80%
- Poor attendance and grades: 50%
- Do no class and OK Grade: 50%
- Do no Poor class and grades: 10%.
In this case, the data we will collect is as follows:
| Attendance | % Get good grades | Good results | Poor performance |
| Attend class | 72.7% | 16 | 6 |
| Do no Attend class | 75.0% | 6 | 2 |
In this example, if we look at the relationship between attendance and grades, we would mistakenly assume that no Taking classes increases your chances of getting good grades. However, this relationship exists because survey response rates are both influenced by whether a person gets good grades and whether they attend classes. Since both the intervention variable and the outcome affect the third factor (response rate), this is the collider bias. Because we excluded people who responded to the survey (because if we didn’t have the data, we had no choice), this would lead to a collider bias.The DAG for this causal path is shown below, you can find the math behind the above example in the spreadsheet here.
In fact, there is a whole video on how to fix the collider bias. The video also explains why some people (wrongly) think attractive people are more likely to be mean.
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