Fig 1.
Significance threshold curves in the one element case for the product-normal (dashed) and Fisher’s method (dotted) for various p-values.
The diagonal is indicated by a gray dash-dotted line and corresponds to equal −log10 p-values.
Fig 2.
QQ-plots of observed p-values resulting from the index I for 1000 pairs of samples of against uniform p-values.
A: Off-diagonal elements of Σ set to 0.2. B: Off-diagonal set to 0.8. The blue curve is obtained using the variance-gamma distribution to perform the statistical test, while the orange curve is obtained via the weighted χ2 distribution. The latter corrects for the correlation and therefore is well calibrated.
Fig 3.
Interpretation of the ratio test.
The test detects potential gene-wise causal relations between a GWAS trait viewed as exposure (E) and a GWAS trait viewed as outcome (O). The association of the exposure has to be confirmed independently via a standard gene enrichment test. Potential confounders (C) have to be excluded by other means.
Fig 4.
Resulting p-values for cross-scoring 23 drug classes GWAS against very severe COVID-19 GWAS for anti-coherence (A) and coherence (B).
Each data point corresponds to a gene. The dotted red line marks a Bonferroni significance threshold of 1.18×10−7 (0.05 divided by the 18453 genes tested and 23 drug classes). Note that the drug class M05B shows the most significant enrichment in coherence with severe COVID-19.
Fig 5.
Manhattan plot for cross scoring very severe confirmed COVID-19 with medication class M05B for coherence.
Data points correspond to genes. The dotted red line marks a Bonferroni significance threshold of 1.18 × 10−7 (0.05 divided by the 18453 genes tested and 23 drug classes). The inlay plot shows a zoom into the relevant locus chr3p21.31.
Fig 6.
Left: SNP p-values after rank transform for the CCR3 gene.
The x-axis is numbered according to the ith SNP in the gene window ordered by increasing position. The dotted black lines indicate the transcription start and end positions (first and last SNP). Up bars correspond to M05B and down bars to severe COVID-19. Green indicates positive and violet negative association with the trait. Right: SNP-SNP correlation matrix inferred from the 1KG reference panel. The color scale is shown on the right with dark red (+1) corresponding to perfect SNP-SNP correlation and dark blue (−1) to perfect anti-correlation over the reference population.
Table 1.
Bonferroni significant pathways for cross-scored severe COVID-19 genes.
We only tested the six listed traits for pathway enrichment as these traits possess significant or close to significant genes under the coherence test. The coherent case corresponds to the right (R) tail, the anti-coherent case to the left (L) tail. The number of genes in the pathway is given in the fourth column. We tested against the 32284 gene sets of MSigDB 7.4. We list Bonferroni significant (p < 0.05/32284/6 ≃ 2.6 × 10−7) pathways and close to significant pathways.
Fig 7.
Resulting p-values for cross-scoring several GWAS related to osteoporosis against the severe COVID-19 GWAS.
The top figure (A) shows the anti-coherent case and the bottom figure (B) the coherent case. The red dotted line marks the Bonferroni significance threshold of 3.9 × 10−7 (0.05 divided by the 18453 genes tested and 7 traits). We observe Bonferroni significant enrichment for RA plus enrichments in vitamin D and calcium with p-values < 10−5.
Fig 8.
Manhattan plot for cross-scoring severe confirmed COVID-19 with rheumatoid arthritis for anti-coherence.
Data points correspond to genes. The dotted red line marks a Bonferroni significance threshold of 3.9 × 10−7 (0.05 divided by the 18453 genes tested and 7 traits). The labels denote the leading gene hit for the corresponding peak.
Table 2.
Table of genes detected via the coherence test for COVID-19 against RA, vitamin D, and calcium (with p < 6.0 × 10−6).
The column D indicates the direction of the test with + for coherent and − for anti-coherent.
Table 3.
Table of genes of significance (p < 10−6) detected via ratio tests against COVID-19.
The column E lists the exposure, the outcome, and
the test direction, with + for coherent and − for anti-coherent. We confirmed that all listed genes are pV significant under the exposure, but not the outcome.
Fig 9.
Manhattan plot for ratio scoring Vitamin D concentration against severe COVID-19 in the coherent case, with ratio denominator given by COVID-19.
The Bonferroni significance threshold of p = 3.4 × 10−7 is indicated by the red dotted line (0.05 divided by the 18453 genes and 2 times 4 traits tested).
Table 4.
Bonferroni significant pathways for the ratio test.
We tested against the 32284 gene sets of MSigDB 7.4. We list Bonferroni significant pathways (p < 0.05/32284/7 ≃ 2.2 × 10−7) and pathways close to significance.
Fig 10.
GWAS gene scores, obtained separately for two GWAS using joint qq-normalization and standard χ2 based enrichment test, plotted against each other.
Each point corresponds to a gene. The gray dotted line marks the diagonal corresponding to equal −log10 p-values. The orange and red dashed curves mark the simple gene-wise product-normal threshold curves for significance of p < 10−6 and Bonferroni significance, respectively. The color of a gene (orange and red) indicates the full SNP-wise cross scored p-value (p < 10−6 and Bonferroni significant, respectively).