Odds Ratios and Relative Risk
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Odds ratios (OR) and relative risk (RR) quantify the strength of association between an exposure (e.g., a genetic variant) and an outcome (e.g., disease). They are commonly encountered in GWAS results, pharmacogenomics, and multifactorial disease risk assessment.
- Relative Risk (RR) = (risk in exposed) / (risk in unexposed) = [a/(a+b)] / [c/(c+d)]
- Odds Ratio (OR) = (odds in exposed) / (odds in unexposed) = (a x d) / (b x c)
Using a 2x2 table:
| Disease+ | Disease- | |
|---|---|---|
| Exposed | a | b |
| Unexposed | c | d |
- Relative Risk: Used in cohort studies and clinical trials. Directly interpretable as "how many times more likely."
- Odds Ratio: Used in case-control studies (where you cannot calculate RR because the prevalence is set by study design). Also used in logistic regression.
- When disease is rare (<10% prevalence), OR approximates RR.
| Value | Meaning |
|---|---|
| OR or RR = 1 | No association |
| OR or RR > 1 | Increased risk with exposure |
| OR or RR < 1 | Decreased risk (protective) |
Problem: A GWAS finds that carriers of a specific SNP have a disease prevalence of 5%, while non-carriers have a prevalence of 2%. What is the relative risk?
Solution:
- RR = 5% / 2% = 2.5
- Carriers are 2.5 times more likely to develop the disease
Odds ratio:
- Odds in carriers = 0.05 / 0.95 = 0.0526
- Odds in non-carriers = 0.02 / 0.98 = 0.0204
- OR = 0.0526 / 0.0204 = 2.58
- Note: OR is close to RR because the disease is rare (<10%)
- A 95% confidence interval that includes 1.0 means the association is not statistically significant
- Example: OR = 1.8 (95% CI: 0.9-3.6): not significant (CI crosses 1)
- Example: OR = 1.8 (95% CI: 1.2-2.7): significant (CI does not cross 1)
- P-value < 0.05: Conventionally considered statistically significant
- In GWAS: P < 5 x 10^-8 is the genome-wide significance threshold (correcting for ~1 million independent tests)
- GWAS SNPs: Most common variant associations have small effect sizes (OR 1.1-1.5). Not clinically actionable individually but can be combined into polygenic risk scores.
- Pharmacogenomics: Some variant-drug associations have large ORs (e.g., HLA-B*57:01 and abacavir hypersensitivity, OR > 100)
- Multifactorial conditions: Risk is the product of multiple small ORs across many loci