Estimating enrichment of stratified squared trans-ethnic genetic correlation

This page describes the steps to estimate enrichment of stratified squared trans-ethnic genetic correlation, \(\lambda^2(C) ={ {r^2_g(C)} \over {r^2_g} }\), the ratio between squared trans-ethnic genetic correlation of annotation \( C \) and genome-wide squared trans-ethnic genetic correlation.

Typical command

S-LDXR estimates \(\lambda^2(C)\) with the following command.

python <software directory>/s-ldxr.py \
    --gcor <summary stats directory for EAS>/EAS_sumstats.gz \
           <summary stats directory for EUR>/EUR_sumstats.gz \
    --ref-ld-chr <baseline LD score directory>/EAS_EUR_baseline_chr \
                 <AVGLLD LD score directory>/EAS_EUR_avglld_chr \
                 <BSTAT LD score directory>/EAS_EUR_bstat_chr \
                 <ALLELEAGE LD score directory>/EAS_EUR_alleleage_chr \
    --w-ld-chr <regression weight directory>/EAS_EUR_weight_chr \
    --frqfile <EAS MAF directory>/1000G.EAS. \
              <EUR MAF directory>/1000G.EUR. \
    --annot <baseline annotation directory>/baseline. \
            <AVGLLD annotation directory>/avglld. \
            <BSTAT annotation directory>/bstat. \
            <ALLELEAGE annotation directory>/alleleage. \
    --apply-shrinkage 0.5 \
    --save-pseudo-coef \
    --out TRAIT_EAS_EUR.txt

This command typically takes 10 to 15 minutes to run on a stand alone computer.

Here are the meanings of the flags:

  • --gcor specifies the summary stats files. This flag takes 2 arguments - summary stats for population 1 and summary stats for population 2.

  • --ref-ld-chr specifies prefix of the LD score files. This flag takes one or more arguments – one may put as many LD score files as one wishes.

  • --w-ld-chr specifies prefix of the regression weights. These are standardized LD scores calculated from regression SNPs.

  • --frqfile specifies prefix of minor allele frequency files.

  • --annot specifies prefix of the annotation files. This flags also takes one or more arguments.

Note: The order one specifies the annotation files must be the same as the order one specifies the LD score files. The annotation files must also be the same files that one uses to obtain the LD scores.

  • --apply-shrinkage adjusts the level of shrinkage (the \(\alpha\) tuning parameter in the paper). This should be a number between 0 and 1.

  • --save-pseudo-coef If this flag is specified, jackknife pseudo values of the coefficients will be saved. This flag is optional.

  • --out specifies the output file name.

Note: By default, S-LDXR corrects for bias in ratio estimation analytically. We also provide the option to correct for bias using jackknife. This can be achieved by adding the --use-jackknife-bias-adj flag.

Output

After executing the above command, 5 files will be generated.

  • TRAIT_EAS_EUR.txt output file containing the estimates.

  • TRAIT_EAS_EUR.txt.log log file containing information for debugging.

  • TRAIT_EAS_EUR.txt.pseudo_tau1.gz jackknife pseudo values for \(\tau_C\) coefficients for population 1.

  • TRAIT_EAS_EUR.txt.pseudo_tau2.gz jackknife pseudo values for \(\tau_C\) coefficients for population 2.

  • TRAIT_EAS_EUR.txt.pseudo_theta.gz jackknife pseudo values for \(\theta_C\) genetic covariance coefficients.

Note: The pseudo coefficients will only be saved if the --save-pseudo-coef flag is specified.

Estimating \( \lambda^2(C) \) for continuous-valued annotations

The following command estimates enrichment of stratified squared trans-ethnic genetic correlation for quintiles of continuous-valued annotations.

python <software directory>/cont_annot_gcor.py \
    --coef TRAIT_EAS_EUR.txt \
    --frqfile <EAS MAF directory>/1000G.EAS. \
              <EUR MAF directory>/1000G.EUR. \
    --annot <baseline annotation directory>/baseline. \
            <AVGLLD annotation directory>/avglld. \
            <BSTAT annotation directory>/bstat. \
            <ALLELEAGE annotation directory>/alleleage. \
    --names AVGLLD BSTAT ALLELEAGE \
    --nbins 5 \
    --out TRAIT_EAS_EUR_contannot.txt

This step typically takes 2 to 5 minutes to run on a stand alone computer.

Here are the meanings of the flags.

  • --coef specifies the output from the previous step. The jackknife pseudo coefficients will be loaded automatically.

  • --frqfile specifies prefix of minor allele frequency files.

  • --annot specifies prefix of the annotation files. This flags also takes one or more arguments.

Note: The order one specifies the annotation files must be the same as the order of annotations in TRAIT_EAS_EUR.txt.

  • --names specifies the names of the continuous annotations for which one wishes to compute enrichment at quintiles.

  • --nbins specifies the number of bins to bin the SNPs based on the values of their continuous annotation. The default is 5 (i.e. quintiles).

  • --out specifies the output file name.

Additionally, users may use the --apply-shrinkage flag to adjust the level of shrinkage.

After executing the above command, 2 files will be created.

  • TRAIT_EAS_EUR_contannot.txt contains the estimates.

  • TRAIT_EAS_EUR_contannot.txt.log is the log file for debugging purpose.

Note: By default, S-LDXR corrects for bias in ratio estimation analytically. We also provide the option to correct for bias using jackknife. This can be achieved by adding the --use-jackknife-bias-adj flag.

Expected \(\lambda^2(C)\) from continuous-valued annotations

Estimating expected \(r^2_g(C)\) and \(\lambda^2(C)\) from continuous-valued annotations requires two steps.

The first step gets the coefficients (\(\tau_{1C}\), \(\tau_{2C}\), and \(\theta_{C}\)) of each continuous-valued annotations

python <software directory>/s-ldxr.py \
    --gcor <summary stats directory for EAS>/EAS_sumstats.gz \
           <summary stats directory for EUR>/EUR_sumstats.gz \
    --ref-ld-chr <base LD score directory>/EAS_EUR_allelic_chr \
                 <AVGLLD LD score directory>/EAS_EUR_allelic_chr \
                 <BSTAT LD score directory>/EAS_EUR_allelic_chr \
                 <ALLELEAGE LD score directory>/EAS_EUR_allelic_chr \
    --w-ld-chr <regression weight directory>/EAS_EUR_weight_chr \
    --frqfile <EAS MAF directory>/1000G.EAS. \
              <EUR MAF directory>/1000G.EUR. \
    --annot <base annotation directory>/base. \
            <AVGLLD annotation directory>/avglld. \
            <BSTAT annotation directory>/bstat. \
            <ALLELEAGE annotation directory>/alleleage. \
    --save-pseudo-coef \
    --out ./TRAIT_EAS_EUR_step1.txt

This command typically takes 2 to 5 minutes to run on a stand alone computer.

Note: It is important to include the base (not baseline) annotation.

The output is the same as that of a typical command.

The second step uses the coefficients from the first step to obtain expected \(r^2_g(C)\) and \(\lambda^2(C)\) from continuous-valued annotations.

python <software directory>/pred_binannot_from_contannot.py \
    --coef ./TRAIT_EAS_EUR_step1.txt \
    --frqfile <EAS MAF directory>/1000G.EAS. \
              <EUR MAF directory>/1000G.EUR. \
    --cont-annot <base annotation directory>/base. \
                 <AVGLLD annotation directory>/avglld. \
                 <BSTAT annotation directory>/bstat. \
                 <ALLELEAGE annotation directory>/alleleage. \
    --bin-annot <base annotation directory>/base. \
                <binary annotation directory>/annot_name. \
    --apply-shrinkage 0.5 \
    --out ./TRAIT_EAS_EUR_step2.txt

This command typically takes 2 to 5 minutes to run on a stand alone computer.

Note: It is important to include the base (not baseline) annotation. By default, S-LDXR corrects for bias in ratio estimation analytically. We also provide the option to correct for bias using jackknife. This can be achieved by adding the --use-jackknife-bias-adj flag.

The output is the same as that of the command for continuous-valued annotations.

Interpreting the output

The output files of S-LDXR contain the following columns.

  1. ANNOT name of the annotation

  2. NSNP number of SNPs for binary annotations (sum of annotation values for continuous-valued annotations)

  3. STD standard deviation of the annotation across SNPs

  4. TAU1 heritability annotation coefficient of population 1

  5. TAU1_SE standard error heritability annotation coefficient of population 1

  6. TAU2 heritability annotation coefficient of population 2

  7. TAU2_SE standard error heritability annotation coefficient of population 2

  8. THETA trans-ethnic genetic covariance annotation coefficient

  9. THETA_SE standard error of trans-ethnic genetic covariance annotation coefficient

  10. HSQ1 stratified heritability in population 1

  11. HSQ1_SE standard error of stratified heritability in population 1

  12. HSQ2 stratified heritability in population 2

  13. HSQ2_SE standard error of stratified heritability in population 2

  14. GCOV stratified trans-ethnic genetic covariance

  15. GCOV_SE standard error of stratified trans-ethnic genetic covariance

  16. GCOR stratified trans-ethnic genetic correlation

  17. GCOR_SE standard error for the estimated stratified trans-ethnic genetic correlation

  18. GCORSQ stratified squared trans-ethnic genetic correlation

  19. GCORSQ_SE standard error of stratified squared trans-ethnic genetic correlation

  20. HSQ1_ENRICHMENT heritability enrichment in population 1

  21. HSQ1_ENRICHMENT_SE standard error of heritability enrichment in population 1

  22. HSQ2_ENRICHMENT heritability enrichment in population 2

  23. HSQ2_ENRICHMENT_SE standard error of heritability enrichment in population 2

  24. GCOV_ENRICHMENT genetic covariance enrichment

  25. GCOV_ENRICHMENT_SE standard error of genetic covariance enrichment

  26. GCORSQ_ENRICHMENT estimated enrichment of stratified squared trans-ethnic genetic correlation enrichment

  27. GCORSQ_ENRICHMENT_SE standard error of estimated enrichment of stratified squared trans-ethnic genetic correlation

  28. GCORSQ_ENRICHMENT_P p-value for testing whether enrichment of stratified trans-ethnic genetic correlation is different from 1. Here the p-value is obtained from a t distribution with degree of freedom equal to the number of jackknife blocks minus one, where the test statistic is \( { {\hat{\lambda}^2(C)} \over {s.e.(\hat{\lambda}^2(C)) } }\).

  29. GCOVSQ_DIFF estimated \( \hat{D}^2(C) = \hat{\rho}^2_g(C) - \hat{r}^2_g \hat{h}^2_g(C) \hat{h}^2_g(C) \), the difference between stratified squared trans-ethnic genetic covariance of annotation \( C \), and \( \hat{r}^2_g \hat{h}^2_g(C) \hat{h}^2_g(C) \), the expected squared trans-ethnic genetic covariance based on genome-wide squared trans-ethnic genetic correlation and heritabilities.

  30. GCOVSQ_DIFF_SE standard error for the estimated \( \hat{D}^2(C) \)

  31. GCOVSQ_DIFF_P p-value for testing whether \( \hat{D}^2(C) \) is different from 0, obtained from a t distribution with degree of freedom equal to the number of jackknife blocks minus one, where the test statistic is \( { {\hat{D}^2(C)} \over {s.e.(\hat{D}^2(C)) } }\). This test is equivalent to testing whether \( \lambda^2(C) \) is different from 1. But the p-value is better calibrated.

Note: We recommend to use the column GCORSQ_ENRICHMENT and GCORSQ_ENRICHMENT_SE for meta-analysis of results across traits, and use GCOVSQ_DIFF_P to test for enrichment/depletion.