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Overview

Here we describe an end-to-end RSS-NET analysis of inflammatory bowel disease (IBD) GWAS summary statistics (Liu et al, 2015) and a gene regulatory network inferred for natural killer (NK) cells (ENCODE Project Consortium, 2012). This example illustrates the actual data analyses performed in Zhu et al (2020).

To reproduce results of this example, please use scripts in the directory ibd2015_nkcell/, and follow the step-by-step guide below. Before running any script in ibd2015_nkcell/, please install RSS-NET.

Since a real genome-wide analysis is conducted here, this example is more complicated than the previous simulation example. It is advisable to go through the previous simulation example before diving into the present real-world example.

With the software installed and the input data downloaded, one should be able to run this example by simply typing the following line in shell:

If a different directory is used to store the software, input data and/or output data, please modify file paths in the given scripts accordingly.

Step-by-step illustration

Download data files

All data files required to run this example are freely available at Zenodo DOI. Please contact me (xiangzhu[at]stanford.edu) if you have any trouble accessing these files. After a complete download, you should see the following files.

To help readers confirm if they use the same files as we do, we report 128-bit MD5 hashes of all files in ibd2015_nkcell_data.md5.

To help readers confirm if they can reproduce results of this example, we also provide the full results (ibd2015_nkcell_full_results.zip) and summarized results (ibd2015_nkcell_summary_results.zip) in the same Zenodo deposit.

For simplicity and generality, we introduce the following short-hand notations.

1. ${gwas}_sumstat.mat: processed GWAS summary statistics and LD matrix estimates

This file is large (43G) because it has a LD matrix of 1.1 million common SNPs.

Let’s look at the contents of ibd2015_sumstat.mat.

GWAS summary statistics and LD estimates are stored as cell arrays. RSS-NET only uses the following variables:

  • betahat{j,1}, single-SNP effect size estimates of all SNPs on chromosome j;
  • se{j,1}, standard errors of betahat{j, 1};
  • chr{j,1} and pos{j, 1}, physical positions of these SNPs (GRCh37 build);
  • SiRiS{j,1}, a sparse matrix, defined as repmat((1./se),1,p) .* R .* repmat((1./se)',p,1), where R is the estimated LD matrix of these p SNPs.

2. ${gwas}_snp2gene.mat: physical distance between SNPs and genes

This file contains the physical distance between each GWAS SNP and each protein-coding gene, within 1 Mb. This file corresponds to \({\bf G}_j\) in the RSS-NET model.

In this example, there are 18334 SNPs and 1081481 genes.

The SNP-to-gene distance information is captured by a three-column matrix [colid rowid val]. For example, the distance between gene 1 and SNP 6 is 978947 bps.

3. ${net}_gene2gene.mat: gene regulatory network

This file contains information of gene-to-gene connections in a given regulatory network.

For implementation convenience, this file contains the trivial case where each gene is mapped to itself with val=1.

For a given network, transcription factors (TFs) are stored in rowid and target genes (TGs) are stored in colid. In this example there are 3105 TGs and 376 TFs. Among these TFs and TGs, there are 92399 edges. The edge weights range from 0.61 to 1. These TF-to-TG connections and edge weights correspond to \(\{{\bf T}_g,v_{gt}\}\) in the RSS-NET model.

5. ${gwas}_${cis}_snp2gene_cis.mat: SNP-to-gene cis regulation

This file contains the SNP-to-gene cis regulation scores derived from context-matching cis eQTL studies. This file corresponds to \((c_{jg}-1)\) in the RSS-NET model.

In this example, there are 10790012 SNP-gene pairs with cis regulation scores available, consiting of 829280 SNPs and 18230 genes. The cis regulation scores (val) range from 0 to 0.76. The cis regulation scores used in this example are derived from recently published cis eQTLs in NK cells (Schmiedel et al, 2018).

Run RSS-NET analysis

To facilitate running RSS-NET on real data, I provide a generic script analysis_template.m. For the present example, the RSS-NET analysis is implemented by ibd2015_nkcell.m and ibd2015_nkcell.sbatch.

1. Specify analysis-specific variables

We need to specify a few analysis-specific variables that are required by analysis_template.m, a template script that fits RSS-NET to the given data. For this example, we use ibd2015_nkcell.m for the specification. In brief, the following variables are specified.

  • Data names: gwas_name, net_name, cis_name;
  • GWAS sample size and number of genes: nsam, ngene;
  • Hyper-parameter grid: eta_set, rho_set, theta0_set, theta_set.

In general, if you want to use RSS-NET to analyze a different GWAS and/or network, simply modify ibd2015_nkcell.m and there is no need to change analysis_template.m.

2. Submit job arrays

For a given GWAS and a given regulatory network, all RSS-NET analysis tasks are almost identical and they only differs in hyper-parameter values. To exploit this feature, we run one RSS-NET analysis as a job array with multiple tasks that run in parallel.

To this end, we write a simple sbatch script ibd2015_nkcell.sbatch, and submit it to a cluster with Slurm available.

After the submission, 125 tasks are created. As shown below, multiple tasks should run in different nodes simultaneously.

For each task of this job array, we request 1 node with 8 CPUs and 32 Gb total memory and set the maximum job wall-clock time as 12.5 hours (see ibd2015_nkcell.sbatch for details). The actual memory utilized per task is 26.58 GB (efficiency: 85.06% of 31.25 GB). Across all 125 tasks, the actual running time per task ranges from 5 minutes to 8.9 hours, with median being 2.1 hours.

We request 8 CPUs for each task because RSS-NET takes advantage of parfor in the MATLAB Parallel Computing Toolbox. If this toolbox is not available in your environment, you can still run the same RSS-NET codes on this example (in a serial manner), with longer computation time per task.

Each task of the job array saves results in a Version 7 MAT-file, ${gwas}_${net}_${cis}_out_${id}.mat. Each MAT-file contains variational estimates for a given set of hyper-parameter values. For example, the following MAT-file ibd2015_Primary_Natural_Killer_cells_from_peripheral_blood_NK_out_66.mat stores RSS-NET results based on the 66-th set of hyper-parameter values from the grid.

Here [alpha mu s] correspond to the optimal variational parameters \(\{\alpha_j^\star,\mu_j^\star,(\tau_j^\star)^2\}\) for the given hyper-parameters, logw corresponds to the variational lower bound \(F^\star\) and [theta0 theta sigb sige] corresponds to \(\{\theta_0,\theta,\sigma_0,\sigma\}\). Please see Supplementary Notes of Zhu et al (2020) for definitions.

Summarize RSS-NET results

The RSS-NET result files ${gwas}_${net}_${cis}_out_${id}.mat shown above can be further summarized into both network-level and gene-level statistics as reported in Zhu et al (2020). To facilitate summarizing RSS-NET results, we provide a generic script summary_template.m. For the present example, the RSS-NET summary is implemented by summarize_ibd2015_nkcell.m. If you need to summarize a different RSS-NET analysis, simply modify summarize_ibd2015_nkcell.m and there is no need to change summary_template.m.

For this example, simply run the following line in a Matlab console.

Running summarize_ibd2015_nkcell.m yields two (much smaller) MAT-files: ${gwas}_${net}_${cis}_results_model.mat that stores network-level enrichment results, and ${gwas}_${net}_${cis}_results_gene.mat that stores locus-level association results.

1. ${gwas}_${net}_${cis}_results_model.mat: network-level enrichments

To assess whether a regulatory network is enriched for genetic associations with a trait, we evaluate a Bayes factor (BF) comparing the baseline model (\(M_0:\theta=0~\text{and}~\sigma^2=0\)) in RSS-NET with an enrichment model.

Here log10_bf* are log 10 BFs comparing the flollowing 4 enrichment models against \(M_0\).

  • log10_bf: \(M_1:\theta>0~\text{or}~\sigma^2>0\);
  • log10_bf_ns: \(M_{11}:\theta>0~\text{and}~\sigma^2=0\);
  • log10_bf_nt: \(M_{12}:\theta=0~\text{and}~\sigma^2>0\);
  • log10_bf_ts: \(M_{13}:\theta>0~\text{and}~\sigma^2>0\).

Because \(M_1\) is more flexible than other models, we mainly use log10_bf as recommended by Zhu et al (2020).

By running this example, we reproduce the enrichment BFs of IBD GWAS and NK cell network reported in Zhu et al (2020). The NK cell network shows strong enrichment of IBD genetic associations, which seems consistent with the role of NK cell in autoimmune diseases like IBD.

Let’s perform a more rigorous check of reproducibility. For the same hyper-parameter values, we compare the resulting variational lower bounds from my previous run and from the current run. Differences are numerical negligible.

2. ${gwas}_${net}_${cis}_results_gene.mat: locus-level associations

To summarize association between a locus and a trait, we compute \(P_1^{\sf net}\), the posterior probability that at least one SNP \(j\) in the locus is associated with the trait (\(\beta_j\neq 0\)): \[ P_1^{\sf net}=1-\Pr(\beta_j=0,~\forall j\in\text{locus}~|~\text{data},M_1). \] As in Zhu et al (2020), a locus is defined as the transcribed region of a gene plus 100 kb uptream and downstream. The locus definition is provided in ibd2015_gene_grch37.mat.

Here P1_gene corresponds to \(P_1^{\sf net}\) and [gene_chr gene_start gene_stop] denote physicial position of genes based on GRCh37.

Let’s perform a reproducibility check for gene-level results. Again, my previous analysis and the current analysis yield numerically identical answers.

More examples

The RSS-NET analyses of 18 complex traits and 38 gene regulatory networks reported in Zhu et al (2020) are essentially 684 modified reruns of the example above (with different input GWAS and/or network data, and different hyper-parameter grids). Our full analysis results are publicly available at https://xiangzhu.github.io/rss-peca.

Appendix

Careful readers may notice an optional input data file ibd2015_null_seed_459_squarem_step2.mat specified in ibd2015_nkcell.m and used in analysis_template.m. This file provides the RSS-E baseline model fitting results of IBD GWAS data. If this file is available, analysis_template.m uses the optimal RSS-E baseline model results to initialize RSS-NET. If not, RSS-NET uses a random initialization.

For this example, here are the enrichment BFs based on using the optimal RSS-E baseline model results to initialize RSS-NET.

Here are the enrichment BFs based on random initialization, which are consistent with, but smaller than previous results.

Using optimal RSS-E baseline model results to initialize RSS-NET is not required, but highly recommended in practice, because this often yields a better fit as shown above. Please see this tutorial for more details of fitting RSS-E baseline model on GWAS data.


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