1. Power Calculations for GWAS

2. What is Power?
Power is the probability that we will detect a true association between a SNP and a phenotype
It is common to use a power of 80% or 90% for study design
An 80% power means that there is a 80% chance that the association will be discovered given the assumptions that you have made
The main assumptions are about the p value that is significant, the sample size and the odds ratio or relative risk

3. Relative Risk RR = (DR/TR) (DP/TP) Disease Healthy Total
Risk Allele Count DR HR TR
Protective Allele Count DP HP TP
Probability of Disease With Risk Allele
Probability of Disease With Protective Allele
Disease
Healthy
Total
Risk allele
220
180
400
Protective Allele
780
820
1600
1000
2000
220/400
0.550
DR/TR
780/1660
0.488
DP/TP
1.128
Relative Risk

4. Odds Ratio OR = (DR/HR) (DP/HP) Disease Healthy Total
Risk Allele Count DR HR TR
Protective Allele Count DP HP TP
Ratio of Diseased to Healthy with Risk Allele
Ratio of Diseased to Healthy With Protective Allele
Disease
Healthy
Total
Risk
220
180
400
Protected
780
820
1600
1000
2000
220/180
1.222
DR/HR
780/820
0.951
DP/HP
1.285
Odds ratio
1.128
Relative Risk

5. Comparison of Relative Risk and Odds Ratio
Minor Allele frequency = 0.3
The exact relationship will depend on MAF
Odds Ratio will always give a larger estimate of effect than Relative Risk

6. Assumptions required for Power calculation
Power depends on
Inheritance model
Sample size
Number of Independent tests (SNP tested)
Minor Allele Frequency
Probability of having phenotype if you have the risk allele (odds ratio)
Linkage disequilibrium between marker SNP and causative SNP

7. Inheritance Models Mendelian trait Quantative trait
Phenotype controlled by a single locus.
Easiest to detect.
All affected will have the risk allele
Some unaffected may have risk allele (<100% penetrance) eg Huntingdons’ Disease
Easily discovered in small sets of families
Quantative trait
Phenotype controlled by multiple loci. Eg hundreds of loci have been found associated with height.
Not all individuals with phenotype will have the causative allele at a particular locus
A critical mass of causative loci may be required before phenotype develops.
Eg an individual might need 50 risk alleles to develop cancer out of many hundred possible risk alleles
We need to discover a statistically significant excess of an allele in the affected population over the control population
We are measuring the increased risk of exhibiting the phenotype associated with each variant

8. Inheritance model Dominant Additive (Co-dominant) Recessive
These are the easiest to detect as the contribution to risk from a heterozygote will the same as homozygotes. Therefore the association with the locus will be stronger.
These were made famous by Mendel’s peas but I am not aware of any examples associated with Quantative traits and we will ignore them
Additive (Co-dominant)
Both alleles contribute approximately the same amount to risk of disease.
This is the commonest mode of inheritance and the one that we will assume.
Recessive
This is the hardest to detect since only homozygotes will be at risk of disease and these may be rare in the population.
Eg An allele present at 10% frequency will be homozygous in only 1% of the population (Hardy Weinberg)
Can be maintained by balancing selection Eg sickle cell anaemia

9. Population size
Increasing population size will increase power to detect a given Odds Ratio
This shows how power increase with population size for a small Odds ratio.
The plot is highly dependent on the particular Odds Ratio Chosen

10. Multiple Testing
We will be testing 1,000s of SNP loci which are assumed to have independent effects
If we test 100 loci using a 5% alpha then we would expect to get 5 positive associations even if all the data was completely random.
We will use the Bonferroni correction to control for this
Divide the alpha by the number of loci tested
If we use 100 SNP loci then we would set the required alpha to 0.05/100 =

11. Effect of Number of Tests on Power
Hong, E. P. & Park, J. W. Sample Size and Statistical Power Calculation in Genetic Association Studies. Genomics Inform 10, 117 (2012).

12. Effect of Minor Allele Frequency on Power
Hong, E. P. & Park, J. W. Sample Size and Statistical Power Calculation in Genetic Association Studies. Genomics Inform 10, 117 (2012).

13. Effect of Disease Prevalence on Power
Hong, E. P. & Park, J. W. Sample Size and Statistical Power Calculation in Genetic Association Studies. Genomics Inform 10, 117 (2012).

14. Effect of linkage disequilibrium on Power
Hong, E. P. & Park, J. W. Sample Size and Statistical Power Calculation in Genetic Association Studies. Genomics Inform 10, 117 (2012).

15. Excercise
In the folder “Power Analysis” in your Flash disk there is a word doc “Power Analysis.docx”. Please open it and follow the instructions