Odds Ratio

An odds ratio (OR) is the odds of having a trait among people carrying a variant, divided by the odds among people who do not. OR = 1 means no association. OR > 1 means the allele is more common in cases than controls. OR < 1 means the opposite.

Odds, not probability. If 200 of 1,000 people with a genotype have a condition, the probability is 0.2 and the odds are 200/800 = 0.25. The two diverge as the event gets common, which is why an OR overstates a risk ratio for common outcomes and approximates it closely for rare ones.

How it works

For a biallelic SNP in a case-control study you build a 2×2 table of allele counts:

	Effect allele	Other allele
Cases	a	b
Controls	c	d

OR = (a·d)/(b·c). The standard error of log(OR) is sqrt(1/a + 1/b + 1/c + 1/d), so the 95% CI is exp(log(OR) ± 1.96·SE). Software reports log(OR) because the sampling distribution is roughly normal on that scale. In PLINK, --logistic gives you a beta by default and --or converts it: OR = exp(beta).

The allelic table above assumes a multiplicative model per allele. Genotypic tests compare het and hom-alt against hom-ref separately and give you two ORs, which is how you detect dominance or recessivity. Ignoring the mode of inheritance costs power and biases the summary estimate, which is the motivation behind model-free alternatives like the generalized odds ratio, computed from the full ordered genotype distribution rather than a collapsed 2×2 table.¹²

Now the numbers. For common variants in common disease, per-allele ORs cluster between about 1.1 and 1.5. A meta-analysis of association studies across many traits found the typical replicated common-variant effect sits near an OR of 1.3.³ So an OR of 1.5 is on the strong end for a common SNP and unremarkable for a rare coding variant, where ORs of 3 to 10 appear. An OR of 2.5 for a common allele is rare enough that your first reaction should be to check the sample size and whether it has replicated, not to update your beliefs about yourself.

In your own data

GWAS summary statistics, the GWAS Catalog harmonized TSVs, and per-variant annotations from tools like bcftools +split-vep all carry these numbers. Concretely, when you join your VCF genotypes against a summary-stats file, check four columns before doing anything else:

1. effect_allele vs. your VCF ALT. Strand and allele flips are the single most common error. For A/T and C/G SNPs strand cannot be resolved from the alleles alone, so match on allele frequency or drop them. Getting this wrong inverts the OR (you apply 1/OR without realizing it).
2. Whether the column is OR or beta. Applying sum(dosage * OR) instead of sum(dosage * log(OR)) produces a score that is arithmetically meaningless. Convert once, at load, and name the column log_or.
3. Ancestry of the discovery cohort. An OR estimated in a European cohort transfers poorly when LD structure differs, because the tag SNP and the causal variant are no longer in the same phase.
4. The confidence interval. An OR of 1.6 with a CI of 1.05–2.44 and an OR of 1.6 with a CI of 1.54–1.66 are different objects. Carry the CI through your pipeline.

The practical conversion: absolute risk ≈ baseline odds × OR, converted back to probability. At a 2% lifetime baseline, an OR of 1.5 moves you to roughly 3%. That is the number that matters, and interpreting it for your own health is a conversation with a clinician or genetic counselor, not a spreadsheet operation.

Limitations

Published ORs are biased upward. The variant enters the literature because it crossed a significance threshold in the discovery cohort, so the estimate is conditioned on being large, an effect quantified directly in GWAS data.⁴ Use the replication-cohort estimate when one exists.

Early reports overstate effects in general. Across association studies, the first published result was often substantially larger than the pooled estimate from subsequent studies, with a meaningful fraction failing to replicate at all.⁵ Complex-outcome associations compound this with phenotype heterogeneity and population stratification.⁶

A highly significant, well-replicated OR does not make a good classifier. Markers with ORs in the 1.3 to 1.5 range produce ROC curves barely above chance, because discrimination depends on the variant’s frequency and the distribution overlap, not the p-value.⁷ Reading a GWAS result well means checking sample size, replication, ancestry, and the absolute risk it implies.⁸

Finally, the single-SNP OR is a lower bound on the true genetic effect when the phenotype is dichotomized from an underlying liability, so per-SNP estimates understate the causal variant’s contribution even as selection bias inflates them.⁹ The two biases do not cancel in any predictable way.

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