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MAGMA

Gene analysis A linear principal component regression model that estimates whether there is genetic effect of gene g on the phenotype Y, conditional on all covariates. The model first projects genotype matrix for a gene g onto its PCs, pruning away PCs with very small eigenvalues. Then it performs F test in the regression of Y on SNP matrix and covariates to estimate genetic effect.

\[ Y = \alpha_{0g}\vec 1 + X_g^*\alpha_g + W\beta_g + \epsilon_g \] When inividual geneotype matrix not available, MAGMA performs gene test with mean \(X^2\) statistics and a gene p-value is then obtained by using a known approximation of the sampling distribution. Please refer to the following paper for details of approximation for the distribution of the weighted combination of p-values. This model requires summary statistics and reference LD panel.

Ref: Hou C (2005) A simple approximation for the distribution of the weighted combination of non-independent or independent probabilities. Stat Probabil Lett 73: 179–187.

Competitive gene-set analysis

One-sided Two-sample T test or linear regression in equivalence is applied to test whether the genes in a gene set are more strongly associated with Y or not.

Let Z denote the association z-score. Let \(\S_s\) be an indicator variable with element \(s_g = 1\) defined as for gene g in gene set s and 0 otherwise. The goal is to test whether \(\beta_s\) is greater than zero, which represents the difference in association between genes in the gene set and genes outside the gene set.

\[ Z = \beta_{0s}\vec 1 + S_s\beta_s + \epsilon \] This also be tested by unpaired two sample T-test, while two samples can have unequal variances and sample sizes.

Testrun

Procedure:

  1. annotate SNPs and genes
  2. gene-based analysis
  3. gene-set analysis

Gene-set associations for topic marker genes that are up-regulated

When corrected for multiple testing, tests will be significant if p-value lower than ~0.005. Around half of the tests show significant p-values, which makes us wonder if p-values are inflated. Then we try using the input genes for topic modeling rather than all genes as background so that they are more comparable.

  • Total number of genes reduced from to 18K to ~16K
  • P values for the reduced background genes are very similar to the full ones.

Version Author Date
ab42a52 Jing Gu 2024-09-16

Test enrichment using top 100 genes from each topic

The supplementary table from MAGMA paper shows the mean type 1 error rates are well controlled for a set of size 100. The MSigDB canonical pathways contains 1320 gene sets from a number of different databases. I can look into the average size of the gene sets. MAGMA controlling for type 1 error rates for gene-set analysis

Instead of all DE genes, I used top 100 up-regulated genes ranked by z scores to test the enrichment for each topic. Now we see only k3, k4, k5 and k12 (4/12) topics show significant enrichment after multiple testing correction.

Check the top genes contributing to topic 5 that have high MAGMA Z-scores

Genes with high Z-scores (p < 0.05) are found to show enrichment in the following gene sets:

  • Regulation of signal transduction (adj.P = 0.01) from GO
    • RORA, GATA3, CDC42SE2, SREBF2
  • Interleukin-2 signaling pathway (adj.P = 0.003) from BioPlanet
    • CD247, RORA, GATA3, TAB2, FOXO1,IL21R, YARS (overlapping genes)
  • Th17 Cell Differentiation (adj.P = 0.0002) and IBD (adj.P = 0.001) from KEGG
    • CD247, RORA, GATA3,IL21R
Joining with `by = join_by(GENE)`

Check the top genes contributing to topic 3 that have high MAGMA Z-scores

Genes with high Z-scores (p < 0.05) are found to show enrichment in the following GO terms:

1 Alpha-Beta T Cell Activation (GO:0046631) 0.00007389 0.007163 204.61 1946.45. 2 Regulation Of Natural Killer Cell Activation (GO:0032814) 0.0001340 0.007163 146.12 1303.03.
3 Regulation Of Lymphocyte Activation (GO:0051249) 0.0001706 0.007163 127.84 1109.13.
4 Stimulatory C-type Lectin Receptor Signaling Pathway (GO:0002223) 0.0001906 0.007163 120.31 1030.52.
5 Cellular Response To Lectin (GO:1990858) 0.0001906 0.007163 120.31 1030.52.
6 Antigen Receptor-Mediated Signaling Pathway (GO:0050851) 0.0002146 0.007163 30.59 258.42.
7 Positive Regulation Of Natural Killer Cell Mediated Cytotoxicity (GO:0045954) 0.0002337 0.007163 107.63 899.96.
8 Natural Killer Cell Mediated Immunity (GO:0002228) 0.0002570 0.007163 102.25 845.24.
9 Positive Regulation Of Natural Killer Cell Mediated Immunity (GO:0002717) 0.0003066 0.007597 92.94 751.89.
10 Innate Immune Response Activating Cell Surface Receptor Signaling Pathway (GO:0002220) 0.0003892 0.008678 81.77 642.05.

Joining with `by = join_by(GENE)`

Check the top genes contributing to topic 4 that have high MAGMA Z-scores

Genes with high Z-scores (p < 0.05) are found to show enrichment in the following GO terms:

1 Regulation Of Blood Vessel Endothelial Cell Migration (GO:0043535) | 0.0006701 | AKT3, PRKCA, TNF, ETS1.
2 Antigen Receptor-Mediated Signaling Pathway (GO:0050851) | 0.006130 | CD28, BCL2, BTN3A3, SKAP1.
3 Positive Regulation Of Leukocyte Cell-Cell Adhesion (GO:1903039)| 0.006130 | TNF, ETS1, SKAP1.

Joining with `by = join_by(GENE)`

Gene-set associations for known immune cell markers

Most immune cell markers were obtained from Gene ontology. The tissue-resident genes were from the single-cell lung paper and ChatGPT. After multiple correction, tissue-resident markers do not show significance for the gene-set association with Asthma. Neither do the genes involved in cell-cell adhesion or cell migration. The gene sets that are significantly enriched for higher association with Asthma risks are activation of T/B cells and differentiation of T cell lineage differentiation.


R version 4.2.0 (2022-04-22)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.3.13-el7-x86_64/lib/libopenblas_haswellp-r0.3.13.so

locale:
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 [4] LC_COLLATE=C         LC_MONETARY=C        LC_MESSAGES=C       
 [7] LC_PAPER=C           LC_NAME=C            LC_ADDRESS=C        
[10] LC_TELEPHONE=C       LC_MEASUREMENT=C     LC_IDENTIFICATION=C 

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] dplyr_1.1.4       data.table_1.15.4 workflowr_1.7.1  

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.12       highr_0.10        compiler_4.2.0    pillar_1.9.0     
 [5] bslib_0.7.0       later_1.3.2       git2r_0.33.0      jquerylib_0.1.4  
 [9] tools_4.2.0       getPass_0.2-2     digest_0.6.35     jsonlite_1.8.8   
[13] evaluate_0.23     lifecycle_1.0.4   tibble_3.2.1      pkgconfig_2.0.3  
[17] rlang_1.1.3       cli_3.6.2         rstudioapi_0.15.0 crosstalk_1.2.1  
[21] yaml_2.3.8        xfun_0.43         fastmap_1.1.1     withr_3.0.0      
[25] httr_1.4.7        stringr_1.5.1     knitr_1.46        htmlwidgets_1.6.4
[29] generics_0.1.3    fs_1.6.4          vctrs_0.6.5       sass_0.4.9       
[33] DT_0.33           tidyselect_1.2.1  rprojroot_2.0.4   glue_1.7.0       
[37] R6_2.5.1          processx_3.8.3    fansi_1.0.6       rmarkdown_2.26   
[41] callr_3.7.3       magrittr_2.0.3    whisker_0.4.1     ps_1.7.6         
[45] promises_1.3.0    htmltools_0.5.8.1 httpuv_1.6.14     utf8_1.2.4       
[49] stringi_1.7.6     cachem_1.0.8