### Post by Jian Yang on Mar 19, 2015 7:42:12 GMT

These options are designed to perform a bivariate REML analysis of two quantitative traits (continuous) from population based studies, two disease traits (binary) from case control studies, or one quantitative trait and one binary disease trait, to estimate the genetic variance of each trait and that genetic covariance between two traits that can be captured by all SNPs.

--reml-bivar 1 2

By default, GCTA will take the first two traits in the phenotype file for analysis. The phenotype file is specified by the option --pheno as described in univariate REML analysis. All the options for univariate REML analysis are still valid here except --mpheno, --gxe, --prevalence, --reml-lrt, --reml-no-lrt and --blup-snp. All the input files are in the same format as in univariate REML analysis.

--reml-bivar-nocove

By default, GCTA will model the residual covariance between two traits. However, if the traits were measured on different individuals (e.g. two diseases), the residual covariance will be automatically dropped from the model. You could also specify this option to exclude the residual covariance at all time.

--reml-bivar-lrt-rg 0

To test for the hypothesis of fixing the genetic correlation at a particular value, e.g. fixing genetic correlation at -1, 0 and 1. By default bivariate GCTA-GREML does not perform a log likelihood test unless this option is specified.

--reml-bivar-prevalence 0.1 0.05

For a bivariate analysis of two disease traits, you can specify the prevalence rates of the two diseases in the general population so that GCTA will transform the estimate of variance explained by the SNPs from the observed 0-1 scale to that on the underlying scale for both diseases.

--reml-bivar-no-constrain

By default, the genetic correlation estimate is constrained between -1 and 1. This option will allow the estimate of genetic correlation > 1 or < -1. Note that not all the analyses can converge with this option.

# With residual covariance

# Without residual covariance

# To test for genetic correlation = 0 or 1

# Case-control data for two diseases (the residual covariance will be automatically dropped from the model if there are not too many samples affected by both diseases)

# Bivariate GREML analysis with multiple GRMs

See gcta.freeforums.net/thread/245/manipulating-grm for the format of multi_grm.txt.

test.hsq (rows are

header line;

genetic variance for trait 1, estimate and standard error (SE);

genetic variance for trait 2, estimate and SE;

genetic covariance between traits 1 and 2, estimate and SE;

residual variance for trait 1, estimate and SE;

residual variance for trait 2, estimate and SE;

residual covariance between traits 1 and 2, estimate and SE;

proportion of variance explained by all SNPs for trait 1, estimate and SE;

proportion of variance explained by all SNPs for trait 2, estimate and SE;

genetic correlation;

sample size).

--reml-bivar 1 2

By default, GCTA will take the first two traits in the phenotype file for analysis. The phenotype file is specified by the option --pheno as described in univariate REML analysis. All the options for univariate REML analysis are still valid here except --mpheno, --gxe, --prevalence, --reml-lrt, --reml-no-lrt and --blup-snp. All the input files are in the same format as in univariate REML analysis.

--reml-bivar-nocove

By default, GCTA will model the residual covariance between two traits. However, if the traits were measured on different individuals (e.g. two diseases), the residual covariance will be automatically dropped from the model. You could also specify this option to exclude the residual covariance at all time.

--reml-bivar-lrt-rg 0

To test for the hypothesis of fixing the genetic correlation at a particular value, e.g. fixing genetic correlation at -1, 0 and 1. By default bivariate GCTA-GREML does not perform a log likelihood test unless this option is specified.

--reml-bivar-prevalence 0.1 0.05

For a bivariate analysis of two disease traits, you can specify the prevalence rates of the two diseases in the general population so that GCTA will transform the estimate of variance explained by the SNPs from the observed 0-1 scale to that on the underlying scale for both diseases.

--reml-bivar-no-constrain

By default, the genetic correlation estimate is constrained between -1 and 1. This option will allow the estimate of genetic correlation > 1 or < -1. Note that not all the analyses can converge with this option.

**Examples**# With residual covariance

`gcta64 --reml-bivar --grm test --pheno test.phen --out test`

# Without residual covariance

`gcta64 --reml-bivar --reml-bivar-nocove --grm test --pheno test.phen --out test`

# To test for genetic correlation = 0 or 1

`gcta64 --reml-bivar --reml-bivar-nocove --grm test --pheno test.phen --reml-bivar-lrt-rg 0 --out test`

`gcta64 --reml-bivar --reml-bivar-nocove --grm test --pheno test.phen --reml-bivar-lrt-rg 1 --out test`

# Case-control data for two diseases (the residual covariance will be automatically dropped from the model if there are not too many samples affected by both diseases)

`gcta64 --reml-bivar --grm test_CC --pheno test_CC.phen --reml-bivar-prevalence 0.1 0.05 --out test_CC`

# Bivariate GREML analysis with multiple GRMs

`gcta64 --reml-bivar --mgrm multi_grm.txt --pheno test.phen --out test`

See gcta.freeforums.net/thread/245/manipulating-grm for the format of multi_grm.txt.

**Output file format**test.hsq (rows are

header line;

genetic variance for trait 1, estimate and standard error (SE);

genetic variance for trait 2, estimate and SE;

genetic covariance between traits 1 and 2, estimate and SE;

residual variance for trait 1, estimate and SE;

residual variance for trait 2, estimate and SE;

residual covariance between traits 1 and 2, estimate and SE;

proportion of variance explained by all SNPs for trait 1, estimate and SE;

proportion of variance explained by all SNPs for trait 2, estimate and SE;

genetic correlation;

sample size).

`Source Variance SE`

V(G)_tr1 0.479647 0.179078

V(G)_tr2 0.286330 0.181329

C(G)_tr12 0.230828 0.147958

V(e)_tr1 0.524264 0.176650

V(e)_tr2 0.734654 0.181146

C(e)_tr12 0.404298 0.146863

Vp_tr1 1.003911 0.033202

Vp_tr2 1.020984 0.033800

V(G)/Vp_tr1 0.477779 0.176457

V(G)/Vp_tr2 0.280445 0.176928

rG 0.622864 0.217458

n 3669

**References**

**The first bivariate GREML example**: Deary et al. (2012) Genetic contributions to stability and change in intelligence from childhood to old age. Nature, 482: 212-215. [Pubmed ID: 22258510]**Bivariate GREML analysis method**: Lee et al. (2012) Estimation of pleiotropy between complex diseases using SNP-derived genomic relationships and restricted maximum likelihood. Bioinformatics, 28: 2540-2542. [PubMed ID: 22843982]**GCTA software**: Yang J, Lee SH, Goddard ME and Visscher PM. (2011) GCTA: a tool for Genome-wide Complex Trait Analysis. Am J Hum Genet, 88: 76-82. [PubMed ID: 21167468]