The process for estimating confounding bias is almost identical to that for estimating SNP Heritability, except that when using --sum-hers to regress the test statistics onto the tagging file, you should add either the option --genomic-control YES or --intercept YES.

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In the absence of confounding bias, E[S_{j}] = 1 + n_{j} v^{2}_{j}, where S_{j} is the test statistic for Predictor j, n_{j} is its sample size and v^{2}_{j} is the expected amount of heritability it is expected to tag under the assumed heritability model. When estimating confounding bias, our aim is to determine how much test statistics deviate from these expectations.

We recommend using the model E[S_{j}] = C (1 + n_{j} v^{2}_{j}), where C indicates the multiplicative inflation of test statistics due to confounding. We prefer this model as it naturally allows for the impact of genomic control, which is often the major source of confounding in a GWAS). To specify this model, add the option --genomic-control YES.

The alternative is to use the model E[S_{j}] = 1 + A + n_{j} v^{2}_{j}, where A indicates the additive inflation of test statistics due to confounding. This is the model used by LDSC, and is specified by adding the option --intercept YES.

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Example: for this we use the file height.txt constructed in the example for Summary Statistics and the file sumldak.tagging created in the example for Tagging File.

To estimate the multiplicative inflation of test statistics due to confounding, use

../ldak.out --sum-hers sumldak_gcon --tagfile sumldak.tagging --summary height.txt --genomic-control YES

In most cases, this command will fail because LDAK finds predictors with inconsistent alleles. However, provided there are not too many, we can proceed regardless using

../ldak.out --sum-hers sumldak_gcon --tagfile sumldak.tagging --summary height.txt --genomic-control YES --check-sums NO

The estimate of the scaling factor C will be in sumldak_gcon.extra, while sumldak_gcon.hers will provide a revised estimate of SNP heritability. To instead estimate the additive inflation of test statistics due to confounding, use

../ldak.out --sum-hers sumldak_cept --tagfile sumldak.tagging --summary height.txt --intercept YES

Again, you will likely have to add --check-sums NO. Once completed the file sumldak_cept.extra will contain the estimate of the intercept 1+A, while sumldak_cept.hers will report a revised estimate of SNP heritability.