Figure 1. Relationship among power, GRR (multiplicative inheritance) and sample size.

The graphs show expected power (91) for a disease with 1% population prevalence (p - 5 × 10⁻⁸), depending on minor (less frequent) allele frequency of the tested SNP, sample size (assuming the N of cases shown in the graph legend, and the same N of controls (power is similar for the same N of case-parent trios), and genotypic relative risk (GRR), which is the ratio of the risk of disease to carriers of a particular genotype vs. non-carriers (thus, if GRR is 1.2, risk is increased by 20%). The calculations assume indirect association between a tested SNP allele and a risk allele at a correlation (r²) of 0.8, so that the effective sample sizes are approximately 80% of those shown. A sample of 8,000 cases and 8,000 controls will miss most associated alleles that confer much less than a 20% increase in risk (GRR << 1.2), whereas 20,000/20,000 would detect most associated alleles with GRR = 1.12 and frequency > 15-20%. Factors that affect power include:

• GRR. Power increases with GRR.
• Allele frequency and LD. Power increases with the minor allele frequency of the associated SNP and with stronger LD between than SNP and an untested risk allele.
• Mode of transmission. Power is greater for dominant and multiplicative (log additive) genetic effects, and less for recessive effects (particularly for rare alleles).
• Selection of controls. For diseases with higher prevalence (e.g., >> 5%), power increases if controls with the disorder/trait of interest are excluded.(40)
• Technical artifacts of all kinds can reduce power.