# GCTA-GREML Power Calculator

written by Gibran Hemani and Jian Yang at the Centre for Neuroscience and Statistical Genomics

#### Calculate the power of univariate or bivariate GREML analysis as implemented in GCTA

This tool is designed to calculate the statistical power of estimating genetic variance or genetic correlation using genome-wide SNPs (GREML analysis as implemented in GCTA). For full details on the methods please refer to:

Visscher et al. (2014) Statistical power to detect genetic (co)variance of complex traits using SNP data in unrelated samples. PLoS Genetics, 10(4): e1004269.

For more information about GCTA analyses, please visit the GCTA webpage

### Note on browsers

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### Options

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.

### Results

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.

### Options

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.

### Outputs

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.

### Options

#### Trait #1

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the trait.

#### Trait #2

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the trait.

#### Other details

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.

### Outputs

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.

### Inputs

#### Other details

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

### Options

#### Trait #1

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the disease.

#### Trait #2

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the disease.

#### Other details

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.

### Outputs

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.

### Inputs

#### Other details

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

### Options

#### Quantitative trait

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the trait.

#### Case-control study

Note: The calculation of the SE of $$r_G$$ requires the true SNP-heritability of the disease.

#### Other details

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.

### Outputs

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.