Project meetings Aug 7 & Aug 14

[gaow]

with @NKweiwang

Aug 7

Discussion on multivariate, multiple regression version of ASH extension, i.e., extending the mash model with mvash. This issue summarizes these projects.

Action items

• The extended model, temporarily called m2ash, will be ready in the form of an R package taking both raw data and summary statistics. The VB procedure will be implemented in C++ for now (without squarem boost).
• The mvash package will share the core code as a special case. The m2ash can be a standalone statistical package which will be integrated in the OmicsBMA framework for real world applications.
• Next step of m2ash is to analyze eQTL and GWAS data. We will identify scenarios in eQTL study where mash's independent SNP assumption is problematic, then we analyze GTEx data with m2ash model and comment on results from this "fine mapping":
  • We should show difference in results compared to mash. Potentially mash will result in wrong sign of effect size due to LD which m2ash model will fix.
  • A potentially interesting case: what if one SNP is at enhancer another at repressor but are in positive LD? mash will fail and we will not realize it without fine mapping.

    Discussions

    mash and mvash are special case of m2ash

The m2ash model reads:

\hat{\beta}_{P, J} | \beta_{P, J}, V_{P, P}, \Sigma_{J, J} ~ N_{P,J} (\beta, V, \Sigma)

where V is proportional to X'X. Replacing V with identity matrix results in mash.

Aug 14

Discussion on m2ash model and wrapping up mvash.

Action items

• Putting together in writing the existing results from mvash. What we have so far include:
  1. Write-up of the model
  2. Comparison with ash on simulated data (MSE of beta estimates). We may compare with varbs down the line.
  3. Simulation based on GTEx data, and justification the choice of method to estimate correlation struction on real data (the \Omega) via results learned from dscr_omega
• Analyze GTEx data with mvash, of blood/non-blood and brain/non-brain for starters
  • At this point we hope to validate the usefulness of mvash by being able to identify valid groups of diferentially expressed genes that other methods (ash) fails to identify. By "valid" we mean that the groups identified will have clear biological interpretation.
• In the context of GSEA, instead of creating a mvash based method that accounts for correlations, we may simply use mvash to obtain new ranks of signals and perform any existing GSEA method on it, and compare the results with their original paper where the enrichment analysis is based on ranking by conventional methods.
  • In order to do this we need to find a data-set from published work.

The paper follows the logic that practical application of mvash method has two components: estimate \Omega and perform shrinkage via the mvash model. We justify the first component by benchmarking a range of \Omega estimation methods, and the second component by comparing with ash which does not model correlations. We then show mvash on real data, by first identifying biologically valid groups of differentially expressed genes, then apply it in combination with GSEA methods.

[gaow]

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