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Selection bias and colliders

Selection bias arises when who ends up in the analysis depends on something that both the exposure and the outcome influence, which manufactures an association that does not exist in the population.

The structural idea

Confounding comes from a COMMON CAUSE of exposure and outcome. Selection bias comes from conditioning on a COMMON EFFECT. That single distinction unifies a long list of named biases: inappropriate control selection, informative censoring, loss to follow-up related to both treatment and prognosis, and adjustment for a variable affected by the exposure.

What a collider looks like

A causal diagram in which exposure and outcome both cause selection into the study. Selection is drawn in a square box, meaning the analysis is restricted to it or adjusted for it, and a dashed line between exposure and outcome shows the association that conditioning creates.Selection bias: conditioning on a common effectAssociation created byconditioningExposureOutcomeSelected into theanalysisSquare box: conditioned on, by restriction, selection or adjustment. Dashed line: an associationwith no causal arrow behind it.
Conceptual diagram. It shows the structure of the idea, not data from any study.

Why a collider is counter-intuitive

Two genuinely unrelated causes of the same event become associated once you restrict to people in whom that event occurred. Among hospitalised patients, two independent conditions can appear correlated simply because either one raises the chance of admission. Nothing about the underlying biology changed; the restriction created the pattern.

Where it enters an analysis rather than a study

This is not only a recruitment problem. Restricting to survivors, dropping people whose exposure could not be measured, or adjusting for a post-exposure variable are all conditioning on a common effect. The last two look like data cleaning, which is what makes them dangerous.

Why Mallard warns about it

Mallard flags exclusion of participants whose exposure could not be measured, and prefers retaining them with multiple imputation, because that exclusion is selection on a variable the exposure affects.

Key assumptions and design requirements

  • The selection process into the study is described, and its relationship to exposure and outcome considered.
  • Loss to follow-up is reported BY GROUP, because differential loss is the common route to this bias.
  • No variable affected by the exposure is used as a covariate without an explicit argument.
  • Exclusions are justified against the causal structure, not only against data quality.
  • A causal diagram is drawn, since the bias is visible in the structure and often invisible in the numbers.

What to watch out for

Selection bias can be created by an analysis choice, not only by recruitment: restricting to survivors, excluding people with missing exposure, or adjusting for a variable affected by both exposure and outcome all condition on a common effect. Excluding participants because their exposure could not be measured is the version most easily mistaken for tidying.

Clinical example

A study of a discharge intervention excludes patients whose medication list was incomplete. If both the intervention and the outcome influence whether the list was completed, the exclusion conditions on a common effect and biases the estimate. Retaining those patients and imputing the missing exposure is usually the better route.

Recent studies that used this
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Part of the learning path Make a causal claim carefully (step 3 of 7).
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Sources & further reading
  1. A structural approach to selection bias (opens in a new tab) · Epidemiology · doi 10.1097/01.ede.0000135174.63482.43
  2. Tutorial on directed acyclic graphs (opens in a new tab) · J Clin Epidemiol · doi 10.1016/j.jclinepi.2021.08.001
The first paper is where the common-effect classification is set out. The second is the practical guide to drawing the diagram in which a collider becomes visible.
Last source review: 2026-09-06
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