Effect Size (Beta)

Effect size (beta) is the slope of a regression of a trait on genotype: the average change in the trait per additional copy of the effect allele, expressed in whatever units that trait was measured in. Genotype is coded 0, 1, or 2 copies, so a beta of 0.31 for a height-associated SNP in a model fit on raw centimeters means carriers gain about 0.31 cm per copy, roughly 0.62 cm for homozygotes.

Yes, beta is an effect size. Whether 0.3 is “good” depends entirely on the units. In a GWAS of standardized height it would be enormous, larger than any common variant known. As a Cohen’s d or a correlation it would be middling. As a log odds ratio it is an OR of 1.35, which for a common variant in a complex disease is unusually strong.

How it works

Fit y ~ g + covariates per variant, where g is dosage. The coefficient on g is beta, and its standard error falls roughly as 1/sqrt(2 N f(1-f)), where f is the effect allele frequency. That factor is why rare variants need huge betas to reach significance and why beta and frequency trade off along the detection boundary of every GWAS.

Three conventions decide what the number means:

• Linear traits. Beta is in trait units if the phenotype was left raw, or in standard deviations if it was standardized or inverse-normal transformed. Most modern consortia standardize, so betas are in SD units and a common-variant beta of 0.02 is typical.
• Binary traits. Logistic regression reports log(OR). Exponentiate to get the odds ratio. Some pipelines report OR directly in the beta column, which breaks any downstream tool expecting a log scale.
• Molecular traits. eQTL betas are per-allele changes in log-expression, and here effect sizes are large: a substantial share of expressed genes carry a local eQTL with a clearly measurable per-allele effect, which is why cis-eQTL discovery works in hundreds of samples while disease GWAS needs hundreds of thousands ¹.

Published betas are biased upward at the discovery locus. Winner’s curse means the variants that cross 5e-8 are enriched for those whose noise pushed them up, and replication effect sizes shrink. Methods exist to deconvolve the true effect distribution from summary statistics and to predict how much a replication attempt should shrink ². Mixed architectures are real: for age at maturity in Atlantic salmon, large-scale GWAS found both a few genuinely large-effect loci and a polygenic background underneath them ³.

In your own data

Summary statistics arrive as tab-delimited text: SNP CHR BP A1 A2 FRQ BETA SE P N. Before computing anything, run these checks.

Allele alignment first. A1 in the sumstats must be the allele you are counting in your VCF or PLINK .bim. If they mismatch, flip the sign of beta. For strand-ambiguous SNPs (A/T and C/G), you cannot resolve strand from alleles alone. Compare FRQ against your own cohort frequency and drop ambiguous SNPs with frequency near 0.5, where the comparison is uninformative. This single step is the most common source of silently wrong polygenic scores, and standard QC tutorials treat it as a first-class step rather than an afterthought ⁴.

Then check units. If median(abs(BETA)) for genome-wide significant hits is around 0.02 to 0.05, you are in SD units. If it sits near 1.0 for a case-control study, the column is probably an odds ratio, not a log odds ratio. Confirm with Z = BETA/SE and check that 2*pnorm(-abs(Z)) reproduces the reported P. If it does not, the beta and SE are on different scales or the P came from a different test.

For scoring, plink2 --score sumstats.txt 1 4 7 cols=+scoresums takes SNP, A1, and BETA columns. Use --score-col-nums for multiple betas. Do not use raw genome-wide significant hits alone. Methods that model the full effect size distribution across all variants, rather than thresholding, give better prediction from the same summary statistics ⁵.

Limitations

Betas are estimated in one population and one context. They do not transfer cleanly across ancestries because linkage disequilibrium between the tag SNP and the causal variant differs, and effect heterogeneity across cohorts is common enough that meta-analysis interpretation needs explicit heterogeneity modeling ⁶. Replicability and out-of-sample prediction remain the hard parts of GWAS, not discovery ⁷.

A beta is also not a causal quantity. It is the marginal association of a tag SNP, confounded by LD with everything nearby and by population structure that survived your principal components. Reading a set of betas as evidence about selection or about mechanism requires assumptions that frequently fail ⁸. Nothing in a beta column is clinical information. If a variant or a score prompts a health question, that belongs with a clinician and, where relevant, a clinical-grade confirmatory test.

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