Comparing Colocalization Models With eCAVIAR and enloc

Why Compare Colocalization Models?

Two traits can both have strong association signals in the same genomic region without sharing a causal variant. Fine-mapping helps describe uncertainty about which variants may be causal for each trait; colocalization methods then combine that evidence to assess whether the traits may share a causal variant. When a region contains multiple candidate signals, the result depends not only on which variants have high posterior support, but also on how the method represents multiple causal variants and calibrates sharing.

eCAVIAR and enloc both use fine-mapping evidence, but their reported quantities are not interchangeable. eCAVIAR reports variant-level joint evidence called the colocalization posterior probability (CLPP). enloc reports a regional colocalization probability (RCP), using fine-mapping probabilities together with an estimated enrichment of colocalization. Reading either output requires knowing what it summarizes and what assumptions lie behind it.

Definition: For trait \(t\) and variant \(j\), the posterior inclusion probability (PIP), written \(\mathrm{PIP}_{tj}\), is the posterior probability that variant \(j\) is causal for trait \(t\), under the fine-mapping model and its assumptions. A PIP is not the probability that an association is real without qualification, nor does it establish a biological mechanism.

Both traits must be represented by comparable variants and appropriately aligned association evidence. Variant harmonization, the linkage disequilibrium (LD) reference, the fine-mapping model, and the set of variants analyzed can all affect the PIPs supplied to a colocalization method. The calculations below take those inputs as given; they do not remove errors or uncertainty in those inputs.

eCAVIAR: Variant-Level Joint Evidence

For each variant, eCAVIAR combines the two traits’ PIPs by multiplying them. If the two traits’ causal-variant identities have independent posterior distributions given their respective data, then the product is the posterior probability that variant \(j\) is causal for both traits. This independence is an assumption about the posterior distributions, not a consequence of conditioning on the causal-variant identities.

Definition: The eCAVIAR CLPP for variant \(j\) is \(\mathrm{CLPP}_j=\mathrm{PIP}_{1j}\mathrm{PIP}_{2j}\). Under posterior independence of the traits’ causal-variant identities given their respective data, \(\mathrm{CLPP}_j\) is the probability that variant \(j\) is causal for both traits. Without that independence, the product is an approximation to the joint posterior probability.

The formula is local to a variant: it quantifies joint support for that same variant. A large CLPP requires support for the variant in both traits. If one trait’s PIP is small, the product will be small even when the other trait’s PIP is large.

Worked Example: Calculating CLPP Across Three Variants

Suppose hypothetical fine-mapping results for two traits give the following PIPs at three shared variants. Assume the two traits’ causal-variant posterior distributions are independent given their respective data.

Variant	Trait 1 PIP	Trait 2 PIP
A	0.60	0.25
B	0.10	0.70
C	0.05	0.08

For each variant, multiply its two PIPs:

\begin{aligned} \mathrm{CLPP}_A &= 0.60 \times 0.25 = 0.150,\\ \mathrm{CLPP}_B &= 0.10 \times 0.70 = 0.070,\\ \mathrm{CLPP}_C &= 0.05 \times 0.08 = 0.004. \end{aligned}

Variant A has the largest variant-level joint support, with CLPP 0.150. This is not the same as saying the region has a 15% probability of colocalization: the calculation concerns variant A. Nor does it show that A causes a downstream molecular change that causes the second trait.

What Changes When There Are Multiple Signals?

Fine-mapping models that allow multiple causal variants can assign substantial PIP to more than one variant for the same trait. In that setting, summing variant-level CLPPs needs care. Let \(I_j\) equal 1 when variant \(j\) is causal for both traits and 0 otherwise. Under the posterior-independence condition above, the expected number of shared causal variants across the analyzed set is the sum of the CLPPs:

E\left[\sum_j I_j\mid D_1,D_2\right] = \sum_j P(I_j=1\mid D_1,D_2) = \sum_j \mathrm{PIP}_{1j}\mathrm{PIP}_{2j}.

This follows from the linearity of expectation: the expected value of a sum of indicators is the sum of their probabilities. It does not require the indicators to be independent of one another. But the sum is generally an expected count, not a probability of at least one shared variant; it can exceed 1 when multiple shared variants are possible.

If each trait is constrained to have exactly one causal variant in the region, the events “variant \(j\) is causal for both traits” are mutually exclusive across variants. In that special case, summing their probabilities gives the probability that the traits select the same variant. That interpretation should not be carried over automatically to a multi-causal-variant model.

Worked Example: A CLPP Sum Is Not Necessarily a Probability

Consider a hypothetical locus with three variants. A multi-signal fine-mapping analysis gives trait 1 PIPs of 0.70, 0.50, and 0.10, and trait 2 PIPs of 0.20, 0.60, and 0.30. These PIPs need not sum to 1 because the model allows multiple causal variants. Assume posterior independence between the two traits’ causal-variant identities.

The variant-specific products are:

\begin{aligned} \mathrm{CLPP}_1 &= 0.70 \times 0.20 = 0.140,\\ \mathrm{CLPP}_2 &= 0.50 \times 0.60 = 0.300,\\ \mathrm{CLPP}_3 &= 0.10 \times 0.30 = 0.030. \end{aligned}

Their sum is \(0.140+0.300+0.030=0.470\). Under the stated independence assumption, 0.470 is the expected number of variants in this three-variant set that are causal for both traits. Since that count could be 0, 1, 2, or 3, the sum is not automatically the probability that at least one variant is shared. Variant 2 has the strongest individual CLPP, but the regional interpretation requires a model for how the variant-level events relate.

enloc: Enrichment-Calibrated Regional Evidence

enloc also uses fine-mapping evidence and is designed to handle loci with multiple signals. Its RCP summarizes regional evidence for colocalization rather than reporting only the product for one variant. In addition to the fine-mapping probabilities, enloc uses an estimated enrichment of colocalization: broadly, whether variants implicated for one trait are more likely than expected under a baseline model to be implicated for the other trait. This calibration is informed by colocalization patterns across loci, so the result depends partly on that estimated enrichment and the model used to obtain it.

Definition: enloc’s regional colocalization probability (RCP) is a model-based posterior probability that a region contains at least one shared causal variant for the two traits. It aggregates fine-mapping evidence for the region and incorporates an estimated colocalization-enrichment parameter. It is not a variant-specific PIP or a direct rescaling of one eCAVIAR CLPP.

The RCP’s regional scope makes it useful when several candidate signals are present, but it does not identify the shared variant by itself. Variant-level fine-mapping results are still needed to see which candidates contribute support. As with other posterior quantities, an RCP is conditional on the model, its priors and enrichment calibration, the input data, and the analyzed region. A high RCP is not a guarantee that the region truly contains a shared causal variant.

Worked Example: Interpreting a Hypothetical enloc RCP

Suppose an enloc analysis of a hypothetical molecular-trait and disease-trait pair reports an RCP of 0.82 for a region containing several fine-mapped signals. Under the fitted model, this is a posterior probability of 0.82 that the region contains at least one shared causal variant. The complementary posterior probability assigned to no shared causal variant is \(1-0.82=0.18\).

The corresponding posterior odds for sharing versus no sharing are:

\frac{0.82}{0.18}=4.56.

Thus, under this model and its inputs, the posterior odds are about 4.56 to 1 in favor of at least one shared causal variant. The RCP does not say that each candidate variant has probability 0.82 of being shared, and it does not establish which signal is shared. That requires inspecting variant-level evidence and the fine-mapping results.

Comparing Results Without Treating Them as the Same Quantity

A direct numerical comparison between an eCAVIAR CLPP and an enloc RCP can be misleading. A CLPP refers to a particular variant; an RCP refers to the region and incorporates enloc’s enrichment calibration. Even a sum of CLPPs may represent an expected number of shared variants rather than the probability of any sharing. Differences can therefore arise without either result being an arithmetic error.

Worked Example: Explaining a Difference Between Methods

Imagine that two hypothetical analyses of the same harmonized region report a maximum eCAVIAR CLPP of 0.18 at variant A and an enloc RCP of 0.76. The values answer different questions: 0.18 is variant A’s joint support under eCAVIAR’s calculation, while 0.76 is enloc’s model-based regional probability of at least one shared causal variant.

For a simple descriptive comparison, the numerical difference is \(0.76-0.18=0.58\), but that subtraction is not an estimate of a single scientific effect. It compares quantities with different scopes and calibration. The results could be compatible with several moderate variant-level signals contributing to regional evidence, or with differences in the fine-mapping inputs or model assumptions. The analyst should inspect the full PIP patterns, number of signals, LD inputs, and enloc’s enrichment calibration before interpreting the discrepancy.

If the region instead had one dominant candidate and little support elsewhere, a high regional probability alongside a low maximum CLPP would warrant especially careful checking. It might reflect different assumptions or inputs, rather than independent confirmation that the same variant is shared.

Assumptions, Diagnostics, and Common Mistakes

A useful comparison starts by checking that both methods analyze the same biological traits, variant set, genomic region, and aligned alleles. Then examine whether the fine-mapping models had suitable LD information and whether the candidate signals are represented adequately. The interpretation should also state the scope of the output: variant-level for CLPP, regional for RCP.

Do not call any overlap in fine-mapping support colocalization. Two traits can have high PIPs for nearby variants in LD without sharing the causal variant.
Do not read a CLPP sum as a probability by default. With multiple causal variants, the sum is an expected shared-variant count under the stated independence condition; it can exceed 1.
Do not interpret the product as a joint posterior without its condition. Multiplication represents the joint probability only when the traits’ causal-variant posterior distributions are independent given their respective data, or when the modeling procedure otherwise justifies that joint calculation.
Do not compare CLPP and RCP as if they were identically defined. They differ in scope and calibration, so their numerical values need not agree.
Do not translate colocalization into causation between traits. Shared genetic evidence does not by itself show that one trait mediates an effect on the other or identify the biological mechanism.

These distinctions matter when prioritizing loci for follow-up. Variant-level evidence can focus attention on candidate shared variants, while a regional quantity can summarize evidence across multiple signals. Neither substitutes for careful review of the underlying fine-mapping results and assumptions. The strongest interpretation is the one that remains stable when plausible changes to LD inputs, fine-mapping uncertainty, and enrichment assumptions are considered.

Key takeaway: eCAVIAR’s CLPP is a variant-level product of two traits’ PIPs; under posterior independence, it is the probability that the specific variant is causal for both. enloc’s RCP is an enrichment-calibrated regional posterior probability of at least one shared causal variant. In multi-signal loci, do not confuse a CLPP sum with a regional probability or treat the two methods’ outputs as interchangeable.

Check Your Understanding

Answer using the scope and assumptions of each quantity.

Under what condition does the product of two traits’ PIPs give the posterior probability that a particular variant is causal for both?
Why can the sum of variant-level CLPPs exceed 1 when multiple causal variants are allowed?
What does an enloc RCP of 0.70 refer to, and what does it not identify by itself?
Why is it misleading to compare a maximum CLPP directly with an RCP as though both were probabilities for the same event?
Name two input or modeling features that should be checked before explaining a disagreement between eCAVIAR and enloc.