Polygenic power calculator: Statistical power and polygenic prediction accuracy of genome-wide association studies of complex traits

Power calculation is a necessary step when planning genome-wide association studies (GWAS) to ensure meaningful findings. Statistical power of GWAS depends on the genetic architecture of phenotype, sample size, and study design. While several computer programs have been developed to perform power calculation for single SNP association testing, it might be more appropriate for GWAS power calculation to address the probability of detecting any number of associated SNPs. In this paper, we derive the statistical power distribution across causal SNPs under the assumption of a point-normal effect size distribution. We demonstrate how key outcome indices of GWAS are related to the genetic architecture (heritability and polygenicity) of the phenotype through the power distribution. We also provide a fast, flexible and interactive power calculation tool which generates predictions for key GWAS outcomes including the number of independent significant SNPs, the phenotypic variance explained by these SNPs, and the predictive accuracy of resulting polygenic scores. These results could also be used to explore the future behaviour of GWAS as sample sizes increase further. Moreover, we present results from simulation studies to validate our derivation and evaluate the agreement between our predictions and reported GWAS results.