1 Collider Bias

  • Collider Variable is caused INDEPENDENTLY by an exposure and an outcome

  • If we control for this Collider Variable, then we introduce Collider Bias.

  • When control for the Collider Variable we induce a distorted association between the exposure and outcome.

  • Colliders undermine attempts to test causal theories.

  • Collider bias can be induced by sampling.

  • Selection bias can sometimes be considered to be a form of collider bias.

ref: https://catalogofbias.org/biases/collider-bias/

1.1 Confounding Bias vs Collider Bias

  • confounder
    • exposure more likely
    • independently modifies the outcome
    • appear as if an association between the exposure and the outcome when there is none
      • or masking a true association
  • how to avoid?
    • randomisation
    • stratification

1.2 Examples

1.2.1 e.g. “admission rate bias” (1979)

  • data from 257 hospitalised individuals
    • detected an association between locomotor disease and respiratory disease
      • (odds ratio 4.06)
  • sample of 2783 individuals from the general population
    • found no association
      • (odds ratio 1.06)
  • bias:
    • BOTH diseases caused individuals to be hospitalised
      • in the original 257 (i.e. focusing on the stratum of hospitalised individuals)
        • observed a DISTORTED association
          • because of selection bias: due to controlling for collider by study design
    • general population
      • locomotor disease and respiratory disease are NOT associated
  • locomotor disease and respiratory disease are independent causes of:
    • hospitalisation = the collider (the TWO arrowheads “collide” into hospitalisation)
  • Using the general population:
    • any form of controlling for “hospitalisation” (via statistics etc), will induce collider bias (through statistical error).

ref: page 3 of https://www.jameslindlibrary.org/wp-data/uploads/2014/06/Sackett-1979-whole-article.pdf

1.2.2 e.g. obesity paradox (2016)

  • general population (with and without cardiovascular disease)
    • obesity increases mortality rates (risk of early death)
  • conditions on cardiovascular disease (by design or analysis)
    • resulting in:
      • a distorted association between obesity and unmeasured other factors
      • i.e. collider bias
    • if sample only has patients with cardiovascular disease:
      • then obesity falsely appears to protect against mortality

1.2.3 e.g. selective school

LEFT

  • Assume: sporting ability and academic ability are both normally distributed and independent (no influence on each other) in the population

  • Suppose: prestigious/selective school chooses to enrol children who have high sporting OR academic ability

RIGHT

  • Assume (for simplicity) capacity of school to enrol = top 10% of pupils from the general population, based on their COMBINED sporting and academic scores.

  • independence => enrolled pupils are:
    • likely to be EITHER sporting OR academic
    • unlikely to be BOTH
  • in the school: sporting and academic ability appear NEGATIVEly correlated (inversely related)
    • (even though, no relationship in the general population)

ref: Collider bias undermines our understanding of COVID-19 disease risk and severity

1.2.4 e.g. NHS vs COVID-19

  • being a health worker is a risk factor for severe COVID-19 symptoms
    • target population is all adults in the general population
    • study sample restricted only to those who are tested for active COVID-19 infection
      • tests performed on health worker or public with symptoms severe enough to require hospitalisation
      • partipants selected for BOTH:
        • hypothesised risk factor (being a healthcare worker)
        • outcome of interest (severe symptoms)

  • BIAS: healthcare workers will generally appear to have relatively low severity (inducing a negative observational association)

  • being a healthcare worker has occupational hazards relating to infectious disease
    • true causal effect is likely to be in the opposite direction
      • healthcare workers are likely exposed to higher viral loads

ref: Collider bias undermines our understanding of COVID-19 disease risk and severity

1.2.5 Further examples:

  • Collider example: simulation in R

  • Cole SR, Platt RW, Schisterman EF, Chu H, Westreich D, Richardson D, et al. Illustrating bias due to conditioning on a collider. Int J Epidemiol. 2010 Apr;39(2):417-20.

  • Elwert F, Winship C. Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable. Annu Rev Sociol. 2014 Jul;40:31-53.

  • Luque-Fernandez MA, Schomaker M, Redondo-Sanchez D, Jose Sanchez Perez M, Vaidya A, Schnitzer ME. Educational Note: Paradoxical collider effect in the analysis of noncommunicable disease epidemiological data: a reproducible illustration and web application. Int J Epidemiol. 2019 Apr 1;48(2):640-53.

1.3 How to Avoid?

1.4 Further Reading