Why Clump Variants?
Nearby genetic variants can be correlated because of linkage disequilibrium (LD). As discussed in the earlier material on marginal GWAS effects, correlated variants may carry overlapping association information: a small p-value at one variant does not necessarily represent evidence independent of a nearby variant. LD clumping provides a simple way to retain a set of lead variants while removing nearby variants that are strongly correlated with those leads.
Clumping is a selection rule, not an estimate of causal effects. It uses genomic positions, LD estimates from a reference panel, and association p-values to decide which variants to keep. The rule depends on three settings: the physical distance window around each lead, the maximum LD allowed for a variant to remain alongside that lead, and the ordering used to select leads. Changing any of these can change the retained set, and therefore can change a score constructed from that set.
Specify the Clumping Rule
A reproducible clumping description needs more than the word “clumped.” It should state the eligible variant set, the physical window, the LD statistic and threshold, the p-value ordering, and the LD reference used. For example: “Among eligible variants, sort by discovery-GWAS p-value from smallest to largest; use a 250-kb window on either side of each lead; remove a variant if its reference-panel \(r^2\) with that lead is greater than 0.20.” The reference-panel choice and its checks are covered in the earlier material on choosing and auditing an LD reference panel.
Here, \(r^2\) is the squared correlation between the allelic dosages at two variants in the reference sample. It ranges from 0 to 1, with larger values indicating stronger linear correlation. The window is a physical distance: a 250-kb half-width means that variants up to 250,000 base pairs to the left or right of a lead are considered for removal. The genome build must match the positions used to define that window. This tutorial uses the explicit convention that a candidate is removed when its distance from the lead is at most the stated window and its \(r^2\) is strictly greater than the threshold. Software may use different boundary conventions, so implementations should be checked.
The p-value is an ordering device. The variant with the smallest p-value among those not already removed becomes the next index, or lead, variant. It is not chosen because it has the largest estimated effect or because it is known to be causal. If p-values tie, a deterministic tie-breaking rule, such as variant identifier order, makes the result reproducible. All p-values in a clumping run should come from the same association analysis and use a consistently defined variant set.
Sort them by increasing association p-value. Set aside variants that fail any prespecified eligibility or quality filters.
Make it the next lead. A variant removed by an earlier lead cannot later become a lead.
For each other eligible variant, check its genomic distance from this lead and its \(r^2\) with this lead. Remove it only if it is within the window and exceeds the LD threshold.
Return to the p-value ordering and select the best remaining variant. Stop when every eligible variant is either a lead or has been removed.
Worked Example: Trace the Lead-Variant Selection
Suppose four hypothetical variants have the following positions and discovery p-values. All pass the prespecified quality filters. Use a 250-kb window, an \(r^2\) threshold of 0.20, and the convention that a candidate is removed if \(r^2>0.20\).
| Variant | Position (bp) | p-value | Relevant \(r^2\) |
|---|---|---|---|
| A | 1,000,000 | 1.0 × 10−8 | A–B: 0.64; A–C: 0.12 |
| B | 1,080,000 | 2.0 × 10−6 | B–C: 0.30 |
| C | 1,160,000 | 4.0 × 10−5 | |
| D | 1,500,000 | 0.002 |
Variant A has the smallest p-value, so it is selected first. B is 80,000 bp from A, within the 250-kb window, and \(r^2_{AB}=0.64>0.20\). B is removed. C is 160,000 bp from A, but \(r^2_{AC}=0.12\), which does not exceed the threshold, so C remains eligible. D is 500,000 bp from A, outside the window, so it also remains eligible.
Among the remaining variants, C has the smallest p-value and becomes the next lead. D is 340,000 bp from C, outside the window, so it is not removed by C. The retained lead set is therefore A, C, and D. The result depends on both position and LD: being nearby is not enough for removal, and high LD is not enough if the variants fall outside the specified window.
What the Retained Set Guarantees—and What It Does Not
The algorithm is greedy because each lead is selected in order and its removals are not reconsidered later. Under the stated rule, two retained leads cannot both lie within the window and have \(r^2\) above the threshold. To see why, suppose an earlier lead \(u\) and a later retained lead \(v\) did satisfy both conditions. When \(u\) was selected, \(v\) was still an eligible candidate. The removal rule would then have removed \(v\), contradicting its later selection. Thus, for every retained pair within the specified window, the pairwise \(r^2\) does not exceed the threshold.
This is a local guarantee, not a guarantee that all retained variants are mutually independent. Two retained leads farther apart than the window are not compared by this rule and could still be correlated. Nor does clumping establish statistical independence, identify causal variants, or eliminate all redundancy in a score. “Approximately independent” is a practical description of the retained set under the chosen local rule and reference-panel estimates.
Worked Example: How Window and LD Threshold Change the Set
Consider three hypothetical variants on the same chromosome. Their positions are A at 2,000,000 bp, B at 2,090,000 bp, and C at 2,170,000 bp. Their p-values are \(1.0\times10^{-7}\), \(3.0\times10^{-6}\), and \(2.0\times10^{-5}\), respectively. The reference-panel estimates are \(r^2_{AB}=0.64\), \(r^2_{AC}=0.18\), and \(r^2_{BC}=0.42\).
First use a 250-kb window and threshold 0.20. A is selected first. B is within 90,000 bp and \(0.64>0.20\), so B is removed. C is within 170,000 bp, but \(0.18\) is not greater than \(0.20\), so C remains and is selected next. The retained set is A and C.
Now keep the 250-kb window but lower the threshold to 0.10. Both B and C are within the window of A, and both \(0.64\) and \(0.18\) exceed 0.10. They are both removed, leaving A alone. A more stringent threshold can therefore produce fewer retained variants.
Instead, return to the 0.20 threshold and shorten the window to 100 kb. A removes B because B is only 90,000 bp away and \(r^2_{AB}=0.64\). C is 170,000 bp from A, so it is outside the window and remains. C is then selected; B was already removed, so the retained set is again A and C. To see a window change that alters this set, use a 75-kb window: B is now outside A’s window and remains; C is also outside A’s window. A is selected, then B, and then C. Since B and C are 80,000 bp apart, they are outside the 75-kb window, so all three are retained. This illustrates why window size and LD threshold must be reported together.
Consequences for a Weighted Score
Clumping determines which variants are available to contribute; it does not itself determine their effect weights. The following arithmetic is only a demonstration of how the retained set changes a hypothetical weighted sum. Assume that variant dosages and weights have already been harmonized to the same effect-allele coding, and use the same individual and weights for every comparison. The weight is measured in hypothetical outcome units per effect-allele copy, so the resulting score is in those outcome units. The later material on constructing clumping-and-thresholding scores treats the score method more fully.
Worked Example: Alternative Clumping Settings Change a Score
Use the variants A, B, and C from the previous example and consider a hypothetical individual with dosages \(g_A=1\), \(g_B=2\), and \(g_C=1\). Suppose their fixed weights are \(w_A=0.20\), \(w_B=0.15\), and \(w_C=-0.10\) outcome units per effect-allele copy. For this illustration, add the weighted contributions only for retained variants.
With a 250-kb window and \(r^2\) threshold 0.20, the retained set is A and C. The score is
With the same window and threshold 0.10, only A remains, so the corresponding sum is
With a 75-kb window and threshold 0.20, all three variants remain. The sum is
The sums differ because the retained variants differ, not because their weights or dosages changed. In particular, removing a variant with a negative weight can increase the sum, while adding a positive-weight variant can increase it. A clumping choice therefore changes score values through variant inclusion; it does not guarantee that scores will move in one direction or improve prediction.
Diagnostics, Alternatives, and Limitations
Before interpreting a clumped set, check that the genomic positions use the intended genome build, that alleles and variant identifiers were harmonized, and that the LD estimates came from the chosen reference panel. Inspect the number of variants retained and, where feasible, the distribution of distances and pairwise \(r^2\) among retained variants. An unexpectedly large or small retained set can indicate a window or threshold that differs from what was intended, inconsistent positions, missing LD estimates, or a variant-eligibility problem.
The p-value order also deserves an audit. If p-values are missing, incomparable across analyses, or attached to mismatched variant identifiers, the supposed lead may not be the strongest association among the intended candidates. Tied p-values should not be left to arbitrary file order if reproducibility matters. In addition, LD estimated in a small or poorly matched reference sample can be noisy or differ from LD in the target population; clumping cannot correct that mismatch. Sensitivity analysis across reasonable settings can show whether the retained set, and resulting score, depends heavily on a particular choice.
Clumping is simpler than methods that model correlations among variants, but it discards variants rather than jointly estimating their contributions. A stricter \(r^2\) threshold or a larger window generally removes more candidates, although the exact retained set also depends on p-value order and local LD patterns. Approaches that use LD information to shrink or jointly estimate effects can retain correlated variants, but require additional modeling choices and are not equivalent to clumping. Clumping may be useful as a transparent preprocessing rule; it is not a substitute for evaluating predictive performance in appropriate data.
A common mistake is to say, “A and B are close, so B must be removed.” Clumping requires both the distance condition and the LD condition with the selected lead. Another mistake is to interpret the retained set as a collection of causal, mutually independent variants. The procedure establishes neither claim: it makes a local, lead-centered selection based on observed association ranking and reference-panel LD.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A lead variant has p-value \(2\times10^{-9}\). A second variant is 120 kb away, has p-value \(4\times10^{-7}\), and has \(r^2=0.35\) with the lead. Under a 200-kb window and threshold 0.30, is the second variant removed?
- Why does retaining two variants after clumping not prove they are independent across the genome?
- Three variants have p-values A \(=0.001\), B \(=0.01\), and C \(=0.03\). A removes B under the chosen settings, but does not remove C. Which variant is considered next after A, and why?
- State two checks that can help diagnose an unexpectedly large retained set.
Solutions. (1) Yes. The second variant is within 200 kb and \(0.35>0.30\), so it is removed by the lead. (2) The rule only checks pairs within the chosen window and only establishes that a later retained lead was not removed by an earlier lead. More distant variants can remain correlated. (3) C is considered next: B has already been removed, and C is the smallest-p-value candidate still eligible. (4) Check, for example, that positions use the intended genome build and that reference-panel LD estimates are available and appropriate; also verify the window and threshold actually used and the p-value/variant matching.