Bias

Bias refers to a systematic (non-random) deviation of an estimator's expected value from the true parameter.

For a statistic \(T\) estimating a parameter \(\theta\):

where: - \(T\): statistic used to estimate \(\theta\) - \(E(T)\): expected value of \(T\)

Conceptual classification of bias

In genetic epidemiology and GWAS, biases can be broadly grouped into:

1. Confounding
2. Measurement / information bias
3. Selection bias
4. Analysis-induced bias (modeling and statistical selection)

1. Confounding

Confounding occurs when an exposure and outcome share a common cause, creating a non-causal association.

Common confounders in GWAS

• Population structure: Systematic differences in allele frequencies across subpopulations that can induce spurious genotype–phenotype associations.

• Cryptic relatedness: Unrecognized familial relationships among participants that violate independence assumptions and bias effect estimates.

• Assortative mating: Non-random mating based on phenotypes (or correlated traits, such as education or socioeconomic status) can induce correlations between genotypes and shared family environments. This creates family-level (dynastic) confounding, leading to biased genotype–phenotype associations, inflated heritability estimates, and distorted genetic correlations.

2. Measurement / information bias

Measurement (information) bias arises from errors in measuring exposures, outcomes, or covariates.

Examples in GWAS

• Phenotype misclassification (e.g. ICD codes, self-reported traits)
• Batch effects in genotyping or imputation
• Differential measurement error across cohorts in meta-analysis

3. Selection bias

Selection bias occurs when inclusion in the study depends on factors related to the exposure, outcome, or their causes, making the analyzed sample non-representative of the target population.

3.1 Collider bias

Collider bias arises when both the exposure and outcome affect a common variable and that variable is conditioned on (e.g. adjusted for or used as a selection criterion).

In other words, conditioning on a collider can induce a spurious association between exposure and outcome.

3.2 Participation (ascertainment) bias

Participation (ascertainment) bias is a form of selection bias in which inclusion in the study depends on traits that are genetically correlated with the outcome.

In biobank-scale GWAS, this can: - Distort SNP–trait associations - Bias heritability estimates - Affect downstream analyses such as PRS and Mendelian randomization

4. Analysis-induced bias

These biases arise after data collection, due to modeling assumptions or statistical procedures.

4.1 Model misspecification bias

Model misspecification bias occurs when the assumed statistical model does not match the true data-generating process.

Examples in GWAS include: - Ignoring non-additive genetic effects (dominance, epistasis) - Using linear models for binary traits without appropriate correction - Incorrect variance assumptions in mixed models

4.2 Winner’s curse

Winner’s curse refers to the upward bias in estimated effect sizes for variants that pass a significance threshold.

In GWAS, this occurs because: - Only variants with large observed effects are selected - Effect sizes are conditional on extreme sampling variation

References

• Holmberg, M. J., & Andersen, L. W. (2022). Collider bias. JAMA, 327(13), 1282–1283.
• Schoeler, T., Speed, D., Porcu, E., Pirastu, N., Pingault, J. B., & Kutalik, Z. (2023). Participation bias in the UK Biobank distorts genetic associations and downstream analyses. Nature Human Behaviour, 7(7), 1216–1227.
• Griffith, G. J., Morris, T. T., Tudball, M. J., Herbert, A., Mancano, G., Pike, L., et al. (2020). Collider bias undermines our understanding of COVID-19 disease risk and severity. Nature Communications, 11(1), 5749.