Choosing LD Windows and Clumping Reference Panels

Why Clumping Settings Matter

Clumping reduces redundancy among candidate variants by retaining association lead variants and removing sufficiently correlated variants within a specified genomic range. Its outcome depends not only on the association results but also on two choices: how far from a lead variant to look, and how much linkage disequilibrium (LD) is enough to remove another variant. The reference panel used to estimate LD matters as well, because correlations between genotypes can differ across ancestry groups.

These settings are not interchangeable. A wide physical window can include distant variants, but they are removed only if their LD meets the chosen cutoff. Conversely, a stringent LD cutoff can leave moderately correlated variants in the same window. A clumped set should therefore be understood as less redundant according to a particular window, cutoff, reference panel, and clumping procedure—not as a set of statistically independent variants.

Window and LD Threshold

For clarity, this tutorial uses a symmetric-window convention: a window of \(W\) kilobases around a lead variant includes variants no more than \(W\) kilobases away on either side. Software can define or label its window differently, so the software documentation must be checked before translating a setting. The LD quantity used here is \(r^2\), the squared correlation between the genotype dosages of two variants in a reference panel.

Definition: Suppose a lead variant \(i\) is at genomic position \(x_i\), and a candidate variant \(j\) is at \(x_j\). Under the symmetric-window convention, their physical distance is \(d_{ij}=|x_i-x_j|\). Let \(r^2_{ij}\) be the squared genotype correlation estimated from a specified reference panel. Given window radius \(W\) and LD threshold \(c\), variant \(j\) meets the clumping removal rule for lead \(i\) when \(d_{ij}\leq W\) and \(r^2_{ij}\geq c\). A variant outside the window is not removed by that lead under this rule, regardless of its \(r^2\).

For dosage variables \(G_i\) and \(G_j\), the population quantity represented by \(r^2_{ij}\) is

r^2_{ij}=\operatorname{Corr}(G_i,G_j)^2 =\frac{\operatorname{Cov}(G_i,G_j)^2} {\operatorname{Var}(G_i)\operatorname{Var}(G_j)}.

The squared correlation is between 0 and 1. A value near 1 indicates strong correlation in the reference data; a value near 0 indicates little linear correlation. Squaring removes the sign, so variants with positive or negative genotype correlation are treated alike by an \(r^2\)-based rule. In practice, the value is estimated from the reference sample, and finite sample size can make that estimate uncertain.

The two parts of the removal rule have different jobs. Increasing \(W\) makes more distant variants eligible for removal. Lowering \(c\) makes the LD criterion easier to meet, so more variants within the window can be removed. Neither change guarantees that every variant in a genomic region will be removed: both the distance and LD conditions must hold.

Worked Examples: Applying the Settings

Worked Example: A Local Window Excludes a Correlated Variant

Consider three hypothetical variants at positions 10 kb, 35 kb, and 82 kb. Call them A, B, and C, respectively. Suppose A is the association lead variant, the window radius is 50 kb, and the LD threshold is \(c=0.20\). The reference panel gives \(r^2_{AB}=0.64\) and \(r^2_{AC}=0.27\).

For B, the distance from A is \(|35-10|=25\) kb, which is within the 50 kb window. Its LD also meets the cutoff because \(0.64\geq0.20\). B is therefore removed by A.

For C, the distance is \(|82-10|=72\) kb, which exceeds the window radius. Although its LD meets the cutoff, \(0.27\geq0.20\), it is outside the specified window and is not removed by A under these settings.

If the window radius were increased to 100 kb while the threshold remained 0.20, C would be within range and would meet the LD criterion, so it would be removed by A. This illustrates why a short window can leave correlated variants behind: the LD condition cannot compensate for a failed distance condition.

Worked Example: Changing the LD Threshold

Suppose lead variant D and candidate variant E are 30 kb apart, and their reference-panel estimate is \(r^2_{DE}=0.42\). The window radius is 80 kb, so the distance condition is satisfied: \(30\leq80\).

With threshold \(c=0.50\), E is retained relative to D because \(0.42<0.50\). With threshold \(c=0.30\), E is removed because \(0.42\geq0.30\). The positions and estimated LD have not changed; only the removal rule has changed.

Thus, a higher threshold is more conservative about removing variants: it requires stronger LD. A lower threshold removes variants with weaker LD as well, potentially reducing redundancy more but also discarding more distinct signals. Neither choice is automatically best; it depends on the purpose of the clumped set and should be assessed as a design decision.

Worked Example: Ancestry Changes the Estimated LD

Suppose lead variant F and candidate variant G are 40 kb apart, within a 100 kb window. In a hypothetical reference panel representative of ancestry group 1, their estimated \(r^2\) is 0.48. In a panel representative of ancestry group 2, it is 0.11. Use \(c=0.20\) in both cases.

With group 1 as the reference, \(0.48\geq0.20\), so G is removed by F. With group 2 as the reference, \(0.11<0.20\), so G is not removed by F. The physical distance and threshold are identical; the different LD estimates change the outcome.

This is not evidence that one panel is universally correct. It shows that clumping encodes the LD structure represented by its reference panel. If the goal is to reduce redundancy for prediction in a particular target population, a reference panel that adequately represents that population's ancestry composition is generally more relevant than one that does not. Panel size and variant coverage also matter because they affect the stability and availability of LD estimates.

Worked Example: A Long-Range LD Pair

Consider hypothetical variants H and J separated by 900 kb. Suppose their reference-panel estimate is \(r^2_{HJ}=0.35\), and the threshold is 0.20. With a 250 kb window radius, the distance condition fails: \(900>250\), so J is not removed by H. With a 1,000 kb radius, the distance condition is met and \(0.35\geq0.20\), so J is removed by H.

Long-range LD can arise in particular genomic regions and need not be captured by a window intended mainly for local LD. A broader window can account for a known long-range correlation, but it also allows more distant variants to be considered for removal. The example does not imply that every pair 900 kb apart is correlated; the LD estimate must still meet the threshold.

Why the Two Conditions Work Together

The removal rule can be viewed as the intersection of two requirements: physical proximity and sufficient estimated LD. Define an indicator \(I_{ij}\) that equals 1 when variant \(j\) meets the removal rule for lead \(i\), and 0 otherwise. The rule is

I_{ij} = \mathbf{1}\{d_{ij}\leq W\} \mathbf{1}\{r^2_{ij}\geq c\}.

Here, \(\mathbf{1}\{\cdot\}\) equals 1 when its condition is true and 0 otherwise. Since the product is 1 only when both indicators are 1, a variant must be within the window and meet the LD threshold to be removed by that lead. This gives a direct way to reason about parameter changes: increasing \(W\) can add pairs that pass the distance condition, while decreasing \(c\) can add pairs that pass the LD condition.

In an actual clumping procedure, multiple lead variants may be considered in sequence. Which variants remain can therefore depend on the association ranking and the procedure's rules for assigning variants to leads. The calculations above isolate each stated lead-candidate comparison; they do not assert that every candidate will remain after all leads have been processed.

Choosing and Reporting Settings

There is no single window radius or LD threshold that is optimal for every score. A defensible choice reflects the intended use, the genomic regions being analyzed, the reference data available, and the degree of redundancy the analyst is willing to tolerate. A local window may be suitable when the aim is to address nearby LD, but it can miss long-range pairs. A very broad window can capture more distant LD but may remove variants across a larger physical span.

The reference panel should be chosen in relation to the LD structure the clumping is meant to represent. Ancestry labels are useful summaries, but real datasets can contain individuals with diverse or admixed ancestry. A panel that poorly represents the relevant population can yield LD estimates—and therefore removal decisions—that do not transfer well. Small panels can also produce noisier estimates. Where feasible, examine whether the panel contains the variants required and whether its sample size and ancestry composition are appropriate.

Sensitivity analysis can reveal whether conclusions depend heavily on a particular setting. For example, compare retained variants under a narrower and broader window, or under a more and less stringent LD threshold, while holding the other choices fixed. These comparisons are diagnostics, not a search for a setting that guarantees the best prediction. Prediction performance must be evaluated separately in data appropriate to the intended use.

For reproducibility, report the window convention and size, the LD measure and threshold, the reference panel and its ancestry composition, and the software or procedure used. State any special handling of regions with known long-range LD. Without these details, another analyst cannot determine exactly which variants were eligible for removal or what LD structure governed the result.

Common Mistakes

Assuming a wide window removes every variant inside it. The window only makes a pair eligible; the pair must also meet the LD threshold.
Reversing the threshold direction. A larger \(r^2\) cutoff requires stronger correlation and removes fewer variants, all else equal. A lower cutoff allows weaker correlations to trigger removal.
Calling the retained variants independent. Clumping applies a specified pairwise rule; variants can remain correlated because they fall outside the window or below the cutoff.
Assuming LD estimates are the same across reference panels. Ancestry composition, sample size, and variant coverage can change the estimated correlations and the resulting retained set.
Reporting a window without defining its convention. A software setting may describe a radius or another window definition. State the actual genomic span used and check the implementation.

Key takeaway: A clumping decision depends jointly on distance, an LD cutoff, and LD estimates from a particular reference panel. Choose and document all three in relation to the population and purpose for which the retained variants will be used.

Check Your Understanding

Use the stated window and LD rule to answer each question.

A candidate variant is 45 kb from a lead variant, has \(r^2=0.31\), and the settings are a 50 kb radius and a 0.25 threshold. Is it removed by that lead? Explain both conditions.
What happens to the set of pairs eligible for removal if the window radius is increased while the LD threshold and reference panel remain fixed?
For a pair within the window with \(r^2=0.18\), compare its status under thresholds of 0.10 and 0.25.
Why might the same pair be removed using one ancestry reference panel but retained using another?
A pair has high estimated LD but lies outside the chosen window. What does the stated clumping rule imply, and what limitation might this reveal?