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After each association test, the case-control labels were randomly permutated and the association test was performed again to evaluate the number of significant results under H0.

Given that, as in Sandionigi et al.16, significance was obtained by comparing the original dataset with results from a permuted data set in which grouping labels were randomly re-assigned to observations.

In the first model (label removal, Additional file 1: Figure S1A), individual activity labels were randomly chosen and removed.

The class labels were randomly permuted and the entire LOOCV process was repeated.

The expression labels were randomly shuffled to obtain a permutated dataset.

The case and control labels were randomly permuted 10,000 times to obtain the distribution of the expected difference in average deleteriousness under the null hypothesis.

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In Multiple Hypothesis Testing, prognostic group labels are randomly permuted.

Figure 1B shows the distribution of p-values when class labels are randomly permuted once across all loci and are representative of what we would see under the null distribution of no group effect.

In each permutation Y k, the phenotype labels are randomly reassigned to individuals with no replacement.

In the second scenario (referred to as Permuted in Bins), gene labels are randomly permuted within bins of 100 genes sorted by locus length.

Within a gene, we will control the family-wise type I error rate at 5%: case labels are randomly permuted (possibly within subgroups to control for potential confounders) against all genotypes – this procedure maintains the correlational structure of the tests under all permuted replicates, and so is not conservative as the Bonferroni correction which assumes tests are independent.

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