Ambiguous Colocalization from Trait-Specific Effects
In colocboost: Multi-Context Colocalization Analysis for QTL and GWAS Studies

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This vignette demonstrates an example of ambiguous colocalization from trait-specific effects using the colocboost. Specifically, we will use the Ambiguous_Colocalization, which is output from colocboost analyzing GTEx release v8 and UK Biobank summary statistics (see more details of the original data source in Acknowledgment section).

library(colocboost)
# Run colocboost with diagnostic details
data(Ambiguous_Colocalization)
names(Ambiguous_Colocalization)

1. The `Ambiguous_Colocalization` Dataset

The Ambiguous_Colocalization dataset contains results from a colocboost analysis of a real genomic region showing ambiguous trait-specific effects between eQTL (expression quantitative trait loci) and GWAS (genome-wide association study) signals. Ambiguous colocalization occurs when there appears to be shared causal variants between traits, but the evidence is complicated by the presence of trait-specific effects. This ambiguity typically arises when some trait-specific boosting learners are updating very similar, yet not the same sets of variants as these traits did not share coupled updates.

This dataset is structured as a list with two main components:

ColocBoost_Results: Contains the output from running the ColocBoost algorithm.
SuSiE_Results: Contains fine-mapping results from the SuSiE algorithm for both eQTL and GWAS data separately.
COLOC_V5_Results: Contains colocalization results from COLOC, which is directly from two susie output objects.

2. ColocBoost results

In this example, there are two trait-specific effects for the eQTL and GWAS signals, respectively. But two uCoS have overlapping variants, which indicates that the two uCoS are not independent. ColocBoost identifies two uCoS:

ucos1:y1: eQTL trait-specific effect has 6 variants.
ucos2:y2: GWAS trait-specific effect has 22 variants.
There are 3 variants that are overlapping between the two uCoS.

# Trait-specific effects for both eQTL and GWAS
Ambiguous_Colocalization$ColocBoost_Results$ucos_details$ucos$ucos_index

# Intersection of eQTL and GWAS variants
Reduce(intersect, Ambiguous_Colocalization$ColocBoost_Results$ucos_details$ucos$ucos_index)

After checking the correlation of variants between the two uCoS, we can see the high correlation between the two uCoS.

The minimum absolute correlation between the two uCoS is 0.636 (off-diagonal purity$min_abs_corr).
The median absolute correlation between the two uCoS is 0.837 (off-diagonal purity$median_abs_corr).
The maximum absolute correlation between the two uCoS is 1 (off-diagonal purity$max_abs_corr), indicating overlapping variants exists.

# With-in and between purity
Ambiguous_Colocalization$ColocBoost_Results$ucos_details$ucos_purity

Based on the results, we can see that the two uCoS are not independent, but they are not fully overlapping.

n_variables <- Ambiguous_Colocalization$ColocBoost_Results$data_info$n_variables
colocboost_plot(
  Ambiguous_Colocalization$ColocBoost_Results, 
  plot_cols = 1,
  grange = c(2000:n_variables),
  plot_ucos = TRUE,
  show_cos_to_uncoloc = TRUE
)

2. Fine-mapping results from SuSiE and colocalization with COLOC

In this example, we also have fine-mapping results from SuSiE for both eQTL and GWAS data separately.

For eQTL, SuSiE shows 40 variants in 95% credible set (CS).
For GWAS, SuSiE shows 57 variants in 95% credible set (CS).
There are 24 variants are overlapping between the two credible sets.

susie_eQTL <- Ambiguous_Colocalization$SuSiE_Results$eQTL
susie_GWAS <- Ambiguous_Colocalization$SuSiE_Results$GWAS

# Fine-mapped eQTL
susie_eQTL$sets$cs$L1

# Fine-mapped GWAS variants
susie_GWAS$sets$cs$L1

# Intersection of fine-mapped eQTL and GWAS variants
intersect(susie_eQTL$sets$cs$L1, susie_GWAS$sets$cs$L1)

To visualize the fine-mapping results,

susieR::susie_plot(susie_eQTL, y = "PIP", pos = 2000:n_variables)
susieR::susie_plot(susie_GWAS, y = "PIP", pos = 2000:n_variables)

We also show the colocalization results from COLOC method. For this ambiguous colocalization, COLOC shows

A high posterior probability of colocalization (PP.H4) of 0.85.
Two hits are corresponding to variants with highest PIP in SuSiE for eQTL and GWAS, separately.

Note that SuSiE-based COLOC has a relatively high confidence of this as a colocalization event because each of SuSiE 95% CS as shown above cover substantially larger region (containing more variants) compared to the trait-specific effects identified by ColocBoost, although at a lower purity (SuSiE purity = 0.56 and 0.64, ColocBoost uCoS purity = 0.67 and 0.70). With larger overlap between the SuSiE 95% CS across traits, the high probability of colocalization is expected. But for this particular data application without knowing the ground truth, it is difficult to determine which method is more precise.

# To run COLOC, please use the following command:
# res <- coloc::coloc.susie(susie_eQTL, susie_GWAS)
res <- Ambiguous_Colocalization$COLOC_V5_Results
res$summary

3. Get the ambiguous colocalization results and summary

ColocBoost provides a function to get the ambiguous colocalization results and summary from trait-specific effects, by considering the correlation of variants between the two uCoS.

3.1. Get the ambiguous colocalization results

The get_ambiguous_colocalization function will return the ambiguous results in ambigous_ucos object, if the following conditions are met:

The two uCoS should have at least one overlapping variant.
The minimum absolute correlation between the two uCoS is greater than min_abs_corr_between_ucos (default is 0.5).
The median absolute correlation between the two uCoS is greater than median_abs_corr_between_ucos (default is 0.8).

colocboost_results <- Ambiguous_Colocalization$ColocBoost_Results
res <- get_ambiguous_colocalization(
  colocboost_results, 
  min_abs_corr_between_ucos = 0.5, 
  median_abs_corr_between_ucos = 0.8
)
names(res)
names(res$ambiguous_cos)
names(res$ambiguous_cos[[1]])

Explanation of results For each ambiguous colocalization, the following information is provided:

ambiguous_cos: Contains variants indices and names of the original trait-specific uCoS used to construct this ambiguous colocalization.
ambiguous_cos_overlap: Contains the overlapping variants information across the uCoS used to construct this ambiguous colocalization.
ambiguous_cos_union: Contains the union of variants information across the uCoS used to construct this ambiguous colocalization.
ambiguous_cos_outcomes: Contains the outcomes indices and names for uCoS used to construct this ambiguous colocalization.
ambiguous_cos_weight: Contains the trait-specific weights of the uCoS used to construct this ambiguous colocalization.
ambiguous_cos_puriry: Contains the purity of across uCoS used to construct this ambiguous colocalization.
recalibrated_cos_vcp: Contains the recalibrated integrative weight to analogous to variant colocalization probability (VCP) from the ambiguous colocalization results.
recalibrated_cos: Contains the recalibrated 95% colocalization confidence set (CoS) from the ambiguous colocalization results.

3.2. Get the summary of ambiguous colocalization results

To get the summary of ambiguous colocalization results, we can use the get_colocboost_summary function.

summary_level = 1 (default): get the summary table for only the colocalization results, same as cos_summary in ColocBoost output.
summary_level = 2: get the summary table for both colocalization and trait-specific effects if exists.
summary_level = 3: get the summary table for colocalization, trait-specific effects and ambiguous colocalization results if exists.

# Get the full summary results from colocboost
full_summary <- get_colocboost_summary(colocboost_results, summary_level = 3)
names(full_summary)

# Get the summary of ambiguous colocalization results
summary_ambiguous <- full_summary$ambiguous_cos_summary
colnames(summary_ambiguous)

recalibrated_*: giving the recalibrated weights and recalibrated 95% colocalization confidence sets (CoS) from the trait-specific effects.

See details of function usage in the Functions.

4. Take home message

In this vignette, we have demonstrated how post-processing of ColocBoost results may be use to reconciliate ambiguous colocalization scenarios where trait-specific effects share highly correlated and overlapping variants.

Through simulation studies, we have found that the minimum absolute correlation cutoff of 0.5 and median absolute correlation cutoff of 0.8 produce reasonable results when merging two uCoS, which in this example will furnish a colocalization event. Still, we mark such colocalization events as ambigous_cos. We recommend users not to lower these thresholds further without strong justification.
We suggest treating this scenario with caution and distinct such merged CoS from typical colocalization events as a result of coupled updates between traits, if researcher decides to investigate these ambiguous colocalization events.
As such,
- While we provide recalibrated weights as a suggested approach for interpreting ambiguous results, users can still choose between recalibrated weights and trait-specific weights based on their research context.
- The colocboost_plot function will not consider it as colocalized but still showing them as uncolocalized events, with overlapping variants color labeled.

Acknowledgment

The eQTL data used for the analyses described in this example results were obtained from GTEx release v8 from GTEx Portal.
The GWAS summary statistics used for the analyses described in this example results were obtained from UK Biobank (UKBB) from UK Biobank and downloaded from Nealelab.