A testrun for MAGMA
Jing Gu
2024-09-16
Last updated: 2024-09-16
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Knit directory: lung_lymph_scMultiomics/
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| Rmd | a2b320f | Jing Gu | 2024-09-16 | test topic enrichment for genetic risks |
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.
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:
- annotate SNPs and genes
- gene-based analysis
- gene-set analysis
Results
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.
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.
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.
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:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=C
[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] data.table_1.15.4 workflowr_1.7.1
loaded via a namespace (and not attached):
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