Sensitivity to Annotation Definitions and LD References

Why Sensitivity Analysis Matters

A partitioned heritability estimate depends on how the analysis represents genomic regions. A functional mask may include variants selected by one annotation definition but exclude those selected by another. An allele-frequency threshold changes which variants are analyzed, and an LD reference panel changes the estimated relationship between variants through linkage disequilibrium. These are not merely formatting choices: they can alter the fitted partition and the interpretation of its estimate.

Sensitivity analysis asks whether the substantive pattern persists under a set of reasonable alternative specifications. It does not ask which specification produces the most favorable result. A large change can indicate that attribution depends on a boundary, reference panel, or SNP set; a small change is reassuring only when the alternatives are scientifically defensible and the analysis remains adequately supported.

For an annotation set \(C\), let \(\hat h^2_C\) denote its estimated contribution to SNP heritability, and let \(\hat h^2\) denote the estimated total SNP heritability on the same scale. The estimated share is \(\hat h^2_C/\hat h^2\). An enrichment measure can compare that share with the fraction of analyzed SNPs in the annotation. These summaries are meaningful for cross-specification comparison only if their definitions, denominators, and analysis populations are made explicit. In models with overlapping annotations, the fitted coefficient for one annotation is conditional on the other annotations in the model; it is not automatically an isolated causal contribution.

Plan Comparisons Before Fitting

A useful comparison begins with a primary specification and a short list of alternatives that answer a scientific question. For example, compare two biologically defensible boundaries for a regulatory annotation, or compare LD references that differ in ancestry composition. Avoid changing several parts of the analysis at once if the aim is to identify what drives a difference.

Whenever possible, hold the phenotype summary statistics, sample size and covariates, model structure, weighting choices, and analysis SNP set fixed while changing one feature. If a feature cannot be varied independently—for example, an allele-frequency threshold necessarily changes the SNP set—state the coupled changes. Use the same target definition in every fit, or explain why the target itself changes. A difference between estimates from different targets is not a like-for-like comparison.

Comparing Functional Masks

A functional mask is a rule that determines which SNPs receive an annotation label. Alternative definitions can differ in genomic boundaries, evidence criteria, or whether nearby regions are included. If two masks are fitted in otherwise identical models, their estimates address closely related—but not necessarily identical—sets of SNPs. Check how many SNPs each mask contains, how much they overlap, and whether the model includes the same accompanying annotations. A difference in estimated contribution may reflect the added or removed SNPs, altered overlap with other annotations, or both.

Changing Allele-Frequency Thresholds and SNP Sets

An allele-frequency threshold defines which variants enter a frequency-restricted analysis. Tightening the threshold may remove low-frequency variants, change the number and distribution of analyzed SNPs, and alter the annotation coverage. Consequently, the estimate can change because the included variants differ, even when the annotation rule itself is unchanged. Report the threshold, the resulting SNP count, and the resulting annotation fraction. Do not present the two estimates as if they described precisely the same SNP population when they do not.

SNP-set sensitivity has a related issue. A quality-control filter, imputation restriction, or intersection of available variants can change both the observations used to fit the model and the denominator used in partition summaries. If comparing SNP sets, either define a common target set and refit both analyses on it, or explicitly describe how the target differs. A change in the estimate is evidence of sensitivity to the analysis set, not proof that one set has recovered the true biological partition.

Changing the LD Reference Panel

Stratified LD score regression uses LD information to relate association statistics to annotation-specific genetic contributions. An LD reference panel supplies estimated LD patterns for this calculation. Differences between panels can arise from ancestry composition, sample size, variant availability, or other properties. If the reference is not well matched to the study population, LD estimates may be less representative of the study's linkage disequilibrium, which can affect partition estimates.

For an informative comparison, use the same GWAS summary statistics, model terms, SNP set, and fitting procedure when changing the LD panel, to the extent possible. Check variant coverage and allele harmonization. Report the reference panels and their relevant population characteristics rather than describing one simply as “better.” A shift may flag dependence on the LD reference; it does not by itself diagnose which panel is responsible or establish that either estimate is unbiased.

Uncertainty for Differences Between Fits

Separate standard errors for two estimates are not enough to determine the uncertainty of their difference when the fits use the same GWAS data. The estimates are usually correlated. For estimates \(A\) and \(B\), the variance identity is

Ignoring the covariance can therefore misstate the uncertainty. A matched block jackknife accounts for the shared genomic data by recomputing both fits after removing the same block each time, then taking their difference. Let \(\hat\Delta\) be the full-data difference, let \(\hat\Delta_{(-b)}\) be the difference after omitting block \(b\), and let \(\overline{\Delta}_{(-)}\) be the mean of the \(B\) leave-one-block-out differences. The jackknife standard error is

This calculation gives a direct uncertainty estimate for the contrast, provided the blocks are defined consistently and the same blocks are omitted from both fits. It is generally preferable to subtract point estimates and then use a paired uncertainty procedure than to infer the uncertainty of the difference from two separate intervals.

What Makes an Attribution Look Fragile?

A pattern is more concerning when a modest, defensible change in one analysis choice produces a large shift in the target estimate, reverses the direction of a contrast, or changes which annotations appear to carry the signal. Instability across plausible masks can suggest that attribution depends on boundary choices. Instability across frequency thresholds or SNP sets can indicate that the result is driven by the included variant population. Instability across LD references can indicate dependence on the LD representation.

Interpret each shift alongside its uncertainty and the feature changed. A change that is small relative to its uncertainty may be consistent with sampling variation, while a large paired difference with a narrow interval suggests a reproducible specification dependence. Neither pattern alone tells whether the underlying biological interpretation is correct. Sensitivity analysis diagnoses dependence on modeling choices; it does not replace biological validation or resolve model misspecification.

Common Mistake

• Wrong reasoning: “The estimate is larger with the alternative mask, so that mask reveals a stronger biological effect.”
• Correction: A larger estimate may arise because the mask includes more SNPs, overlaps differently with other annotations, or changes the fitted partition. Compare the same defined target where possible, report mask size and overlap, and quantify the paired difference and its uncertainty. A specification-dependent estimate is not, by itself, evidence of a stronger causal effect.