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Homework 7

Task 1: Estimating colocalisation between gene expression and disease associations (2 points).

Based on the colocalisation tutorial available here and using the default prior probabilities of coloc (p1 = p2 = 1e-4, p12 = 1e-5), estimate the colocalisation of genetic associations for the following traits:

  1. Expression of PTK2B gene in the naive condition and Alzheimer's disease (AD)
  2. Expression of ICOSLG gene in the naive condition and ulcerative colitis (UC).
  3. Expression of the TRAF1 gene in the IFNg + Salmonella condition and rheumatoid arthritis (RA).

You can find all of the data here:

  1. eQTL summary statistics
  2. Disease associations for the three loci

In all three cases, use the region +/- 200 kb from the lead eQTL variant. For all three analyses, report the posterior probabilities for all 5 hypothesis (H0-H4). To remind yourself what the hypotheses were, have a look at the original paper. Which of these three gene expression signals colocalise with the disease association?

In all three cases, make also Manhattan plots for both the disease and gene expression associations. On both plots, mark the lead eQTL variant in red and the lead GWAS variant in blue. Also, report the p-values for these two variants for both of the traits (4 p-values in total). For a given trait (gene expression or disease) are the p-values similar or different? Does this reflect the colocalisation posterior probabilities (PP4)?

Task 2: How do the prior probabilities influence colocalisation results? (1.5 points)

Repeat the colocalisation analyses that you did in Task 1, but now change the prior probabilites to the ones recommended in the paper (p1 = p2 = 1e-4, p12 = 1e-6). Note that although the paper and the software were written by the same authors, they recommend different prior probabilities. How can this new lower p12 prior probability be interpreted? (HINT: Read the original paper).

How do the results for the three colocalisations from Task 1 change? Are the TRAF1 and PTK2B associations influenced differently the the change in prior probabilities? If yes, can you understand why? (HINT: Reading case studies in the original paper) might again be helpful.

Task 3: How does the length of the genomic region influence colocalisation results? (1.5 points)

Repeat the colocalisation analysis with the priors that you used in Task 2 but now instead of using the +/- 200kb region around the lead eQTL variant, try three progressively smaller regions (+/- 100kb, +/- 50kb and +/- 5kb). How do the colocalisations results change for the three loci (PTK2B, TRAF1 and ICOSLG)? Can you explain why the changes happen? Redrawing the Manhattan plots from Task 1 in progressively smaller regions might help you to understand why.