**Note:** The power calculation requires the true SNP-heritability, so that the power is the probability of estimating a SNP-heritability that is greater than zero.

**Note:** The default value 2e-5 is obtained from the genetic relatedness between unrelated individuals using genome-wide common SNPs, which is basically the variance of the off-diagonal elements of the GRM. If your GRM is constructed from selected SNPs and/or uses differential weighting of SNPs, you can specify this by the empirical variance of the off-diagonals of the GRM.

**Standard error (SE):** Standard error of the SNP-heritability (\(h^2\)).

**NCP:** Non-centrality paramter of the chi-squared test statistic, which equal to \(h^4 / (SE)^2\).

**Power:** The probability of detecting \(h^2 > 0\) for the given the user-specified type I error rate and the SNP-heritability assumed in the population.

**Note:** The power calculation requires the true SNP-heritability, so that the power is the probability of estimating a SNP-heritability that is greater than zero.

**Note:** The default value 2e-5 is obtained from the genetic relatedness between unrelated individuals using genome-wide common SNPs, which is basically the variance of the off-diagonal elements of the GRM. If your GRM is constructed from selected SNPs and/or uses differential weighting of SNPs, you can specify this by the empirical variance of the off-diagonals of the GRM.

**Standard error (SE):** Standard error of the SNP-heritability (\(h^2\)).

**NCP:** Non-centrality paramter of the chi-squared test statistic, which equal to \(h^4 / (SE)^2\).

**Power:** The probability of detecting \(h^2 > 0\) for the given the user-specified type I error rate and the SNP-heritability assumed in the population.

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the trait.

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the trait.

**Note:** The default value 2e-5 is obtained from the genetic relatedness between unrelated individuals using genome-wide common SNPs, which is basically the variance of the off-diagonal elements of the GRM. If your GRM is constructed from selected SNPs and/or uses differential weighting of SNPs, you can specify this by the empirical variance of the off-diagonals of the GRM.

**Standard error (SE):** Standard error of the genetic correlation (\(r_G\)).

**NCP:** Non-centrality paramter of the chi-squared test statistic, which equals to \(r_G^2 / (SE)^2\).

**Power:** The probability of detecting \(r_G\) for the given user-specified type I error rate, SNP-heritability, and genetic correlation assumed in the population.

**Note:** Here we assume that the genetic and phenotypic correlation is the same

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the disease.

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the disease.

**Note:** The default value 2e-5 is obtained from the genetic relatedness between unrelated individuals using genome-wide common SNPs, which is basically the variance of the off-diagonal elements of the GRM. If your GRM is constructed from selected SNPs and/or uses differential weighting of SNPs, you can specify this by the empirical variance of the off-diagonals of the GRM.

**Standard error (SE):** Standard error of the genetic correlation (\(r_G\)).

**NCP:** Non-centrality paramter of the chi-squared test statistic, which equals to \(r_G^2 / (SE)^2\).

**Power:** The probability of detecting \(r_G\) for the given user-specified type I error rate, SNP-heritability, and genetic correlation assumed in the population.

**Note:** Here we assume that the genetic and phenotypic correlation is the same

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the trait.

**Note:** The calculation of the SE of \(r_G\) requires the true SNP-heritability of the disease.

**Note:** The default value 2e-5 is obtained from the genetic relatedness between unrelated individuals using genome-wide common SNPs, which is basically the variance of the off-diagonal elements of the GRM. If your GRM is constructed from selected SNPs and/or uses differential weighting of SNPs, you can specify this by the empirical variance of the off-diagonals of the GRM.

**Standard error (SE):** Standard error of the genetic correlation (\(r_G\)).

**NCP:** Non-centrality paramter of the chi-squared test statistic, which equals to \(r_G^2 / (SE)^2\).

**Power:** The probability of detecting \(r_G\) for the given user-specified type I error rate, SNP-heritability, and genetic correlation assumed in the population.