Introduction to Selection Bias

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What is Selection Bias?

When Our Sample Doesn't Represent the Population

Selection bias occurs when the association observed in the selected sample differs from the association in the target population we wish to make inferences about. Unlike confounding, which arises from common causes, selection bias arises from the process of who gets included in our analysis.

Selection Bias Defined

Selection bias occurs when the probability of being included in the study (or remaining in follow-up) depends on both the exposure and the outcome, or their causes. This creates a spurious association or distorts the true causal relationship.

Sources of Selection

Selection into an analysis can happen at multiple stages:

Stage	Mechanism	Example
Study enrollment	Eligibility criteria, willingness to participate	Only volunteers in health studies
Loss to follow-up	Dropout during study	Sicker patients stop attending visits
Analysis restriction	Conditioning on post-treatment variables	Analyzing only "responders"
Survival	Only living individuals observable	Studying only heart attack survivors

The Graphical Structure

The classic selection bias structure involves conditioning on a collider:

A → S ← Y

Where S represents selection into the study. If both treatment A and outcome Y (or their causes) affect who gets selected, conditioning on S (by only analyzing selected individuals) opens a biasing path.

Selection vs. Confounding

Confounding arises from common causes of A and Y. Selection bias arises from conditioning on common effects of A and Y. Both create spurious associations, but through different mechanisms.

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