Two Workflows, Different Data Representations
Trans-ancestry fine-mapping uses association evidence and ancestry-specific linkage disequilibrium (LD) to assess which variants could account for signals at a locus. The analysis can start from summary statistics—such as marginal effect estimates, standard errors, or score statistics—or from individual-level data, where genotypes and phenotypes are available for each participant. These approaches can target related questions, but they do not use interchangeable inputs: each represents the genotype information differently and depends on different data being correctly matched.
In either workflow, variants must be aligned to the same genomic positions and effect-allele convention across ancestry groups. The data also need compatible phenotype definitions and sample descriptions. For summary-statistic methods, the crucial additional input is an LD representation for each ancestry. For individual-level methods, LD can be calculated from the analyzed genotypes, while the genotypes, phenotypes, covariates, and ancestry assignments must be accessible and correctly coordinated.
Neither label specifies a single algorithm. A summary-statistic analysis may use estimated LD from the study participants or an external reference panel. An individual-level analysis may fit a joint model or construct ancestry-specific components within a broader model. In both cases, the interpretation depends on the model and its assumptions, not just on whether the input file contains rows for people or rows for variants.
What the Summary-Statistic Likelihood Needs
A summary-statistic fine-mapping method needs association evidence for the variants under study and an LD matrix that describes correlations among those variants in each ancestry. It also needs harmonized variant identifiers and alleles, sample sizes, and enough information to put association statistics on the scale assumed by the likelihood. Depending on the method, this may mean effect estimates and standard errors, or score and covariance information. Sample size alone does not determine the precision of every variant if missingness or imputation quality differs.
The role of LD can be seen in a simple linear-model setting. Consider one ancestry, a quantitative phenotype, and genotypes that have been centered and scaled to variance one. Suppose covariates have been accounted for, the residuals have variance \(\sigma^2\), and the genotype columns are measured in the same participants. Let \(G\) be the genotype matrix, with \(n\) rows and \(p\) variants, and let \(R=G^\mathsf{T}G/n\) be its sample LD matrix. Under the model \(y=G\beta+\epsilon\), assume independent normal residuals \(\epsilon\sim N(0,\sigma^2 I)\). Here \(\beta\) contains joint effects per standard-deviation change in genotype.
To justify this summary representation, substitute \(y=G\beta+\epsilon\) into \(U\). Its conditional mean is \(G^\mathsf{T}G\beta/(\sigma\sqrt{n})=\sqrt{n}R\beta/\sigma\). Its conditional covariance is \(G^\mathsf{T}(\sigma^2 I)G/(\sigma^2n)=R\). Thus, under these assumptions, the score vector has an expected pattern determined by both the joint effects and LD, and its uncertainty is also related to LD. Across ancestries, the corresponding \(R\) matrices can differ. A summary-statistic method therefore needs LD that represents the analyzed ancestry and variant set well; association summaries do not, by themselves, supply that information.
This derivation is for a simplified quantitative-trait model with standardized genotypes and known residual variance. Logistic models, estimated nuisance parameters, imputation, and variant-specific sample sizes require suitable score or likelihood approximations. A method’s stated likelihood determines which summary inputs and scaling are appropriate; it is not safe to insert any reported effect estimate and LD matrix without checking those conventions.
Worked Example: Checking the Role of Ancestry-Specific LD
Suppose a hypothetical ancestry group has \(n=1{,}000\) participants, residual standard deviation \(\sigma=1\), and two standardized variants. Its LD matrix is \(R=\begin{pmatrix}1&0.30\\0.30&1\end{pmatrix}\). For illustration, suppose the joint effects are \(\beta=(0.10,0)\), in phenotype units per standard-deviation increase in genotype. What score pattern does the model expect?
First multiply LD by the joint-effect vector: \[ R\beta= \begin{pmatrix}1&0.30\\0.30&1\end{pmatrix} \begin{pmatrix}0.10\\0\end{pmatrix} = \begin{pmatrix}0.10\\0.03\end{pmatrix}. \] Then multiply by \(\sqrt{n}/\sigma=\sqrt{1{,}000}\approx31.62\): \[ E(U\mid G)\approx 31.62 \begin{pmatrix}0.10\\0.03\end{pmatrix} = \begin{pmatrix}3.162\\0.9487\end{pmatrix}. \] The second variant has a nonzero expected marginal score even though its joint effect is zero: it is correlated with the first variant. This is an expected value under the stated model, not a claim that an observed score must equal these numbers. The calculation shows why summary association evidence must be interpreted together with the correct LD.
What Individual-Level Analysis Adds
An individual-level workflow uses genotype data for the participants and their phenotype and covariate records. In the simple quantitative-trait model above, it can evaluate the likelihood of \(y\) conditional on \(G\) directly. The analyzed genotypes contain the sample’s LD, so a separate reference panel is not required to obtain that LD. The model still needs appropriate genotype quality control, ancestry assignment or ancestry-specific modeling, a suitable phenotype model, and valid handling of missing data and relatedness where relevant.
Participant-level analysis can make it easier to use the same individuals’ genotype and phenotype records, accommodate covariates or sample-specific missingness, and model overlap explicitly when the necessary identifiers and data are available. These are capabilities, not automatic guarantees of validity: a poorly specified model can still confound effects or misrepresent dependence. Nor does individual-level access automatically make the estimates more informative; precision is constrained by the sample and the model.
The computational burden is also different in form. Individual-level methods must access and process genotype and phenotype records, which can be large and subject to privacy or governance restrictions. Summary-statistic methods can be easier to share and may reduce data-transfer needs, but a dense LD matrix for many variants can itself be large. Memory use, runtime, and numerical stability depend on the number of participants, variants, ancestry groups, model, and implementation. Neither workflow is universally cheaper.
| Consideration | Summary-statistic workflow | Individual-level workflow |
|---|---|---|
| Genetic input | Association summaries plus LD information for each ancestry | Participant-level genotypes, from which analyzed-sample LD can be calculated |
| Other inputs | Allele alignment, sample sizes, effect and uncertainty scales, variant coverage | Phenotypes, covariates, ancestry information, and aligned genotype records |
| Access and sharing | Often easier to share, but summaries and LD still require careful governance | Requires access to sensitive participant-level records |
| Important vulnerability | LD reference mismatch, incorrect scaling, or unmodeled cohort dependence | Incorrect model or phenotype handling; duplicate or dependent participants still need attention |
Worked Example: Comparing Storage Requirements
Consider a hypothetical analysis of \(10{,}000\) variants in one ancestry group with \(2{,}000\) participants. For a rough storage comparison, suppose both genotype and LD matrices are stored as double-precision numbers using 8 bytes per entry, with no compression or other overhead.
The dense participant-by-variant genotype matrix has \(2{,}000\times10{,}000=20{,}000{,}000\) entries, requiring \(20{,}000{,}000\times8=160{,}000{,}000\) bytes, or about 160 MB in decimal units.
The dense \(10{,}000\times10{,}000\) LD matrix has \(100{,}000{,}000\) entries, requiring \(100{,}000{,}000\times8=800{,}000{,}000\) bytes, or about 800 MB. Under these assumptions, the full LD matrix is five times the size of the genotype matrix. This is only a storage illustration: software can use compression, exploit matrix structure, or analyze smaller variant sets, and actual computation also involves intermediate data. It would be incorrect to conclude from this example that one workflow is always less computationally demanding.
Overlap and Reference Mismatch
Summary statistics from different ancestry analyses are not automatically independent. If participants appear in more than one analysis, their association estimates can share sampling noise. Combining them as if independent can make the evidence appear more precise than it is. The size and direction of this dependence depend on the shared participants, phenotypes, genotypes, and analysis models; it is not always captured by a single overlap count. Appropriate methods may use a cross-analysis covariance model, use nonoverlapping samples, or otherwise account for the dependence.
Individual-level data can make shared participants easier to identify and model, but overlap is not automatically resolved by having genotypes. If the same person is inadvertently included twice as if they were independent, the analysis can still overstate information. A joint model must represent the actual sampling structure.
A separate vulnerability is LD-reference mismatch. An external reference panel may differ from the analyzed cohort in ancestry composition, variant coverage, imputation, or allele handling. Since LD determines how correlated association signals are attributed across variants, substituting an inappropriate matrix can change the fitted evidence and the resulting fine-mapping probabilities. A reference panel labeled with a broad ancestry category is not necessarily a close match to every cohort assigned that label. When available and appropriate, LD estimated from the analyzed participants avoids this particular reference-sample substitution, but it has its own uncertainty, especially in small samples.
Worked Example: Quantifying Dependence From Shared Participants
For a simple illustration, suppose two hypothetical analyses estimate the same standardized effect with \(n_1=1{,}000\) and \(n_2=800\) participants, with \(m=200\) people shared. Assume equal per-person information, and suppose the covariance between the estimates is \(\operatorname{Cov}(\hat\beta_1,\hat\beta_2)=m/(n_1n_2)\). Then their variances are \(1/n_1\) and \(1/n_2\). What happens if one forms the sample-size-weighted average?
The weighted average is \[ \hat\beta_{\mathrm{w}}=\frac{n_1\hat\beta_1+n_2\hat\beta_2}{n_1+n_2}. \] If the estimates were independent, its variance would be \(1/(n_1+n_2)=1/1{,}800\approx0.0005556\).
With the stated covariance, its actual variance is \[ \operatorname{Var}(\hat\beta_{\mathrm{w}}) = \frac{n_1^2(1/n_1)+n_2^2(1/n_2)+2n_1n_2\{m/(n_1n_2)\}}{(n_1+n_2)^2} = \frac{n_1+n_2+2m}{(n_1+n_2)^2}. \] Substituting the values gives \(2{,}200/1{,}800^2\approx0.0006790\), larger than the independence-based variance. Under this simplified setup, treating the estimates as independent overstates precision. Real trans-ancestry analyses need a covariance appropriate to their actual overlap and score construction; this calculation illustrates the issue rather than providing a universal correction.
Choosing and Checking a Workflow
A practical choice depends on access, analysis goals, and whether the needed inputs can be validated. Summary-statistic analysis can be suitable when participant-level records cannot be centralized, provided the association summaries, LD matrices, allele conventions, and dependence structure are compatible with the method. Individual-level analysis can be attractive when the data are available and the model needs participant-level covariates, sample-specific details, or explicit handling of shared participants. Both approaches require careful harmonization and a model whose assumptions fit the data.
Before interpreting fine-mapping evidence, check the following:
- Are variants identified consistently, and are effect alleles aligned across ancestry groups?
- Does each LD matrix represent the relevant ancestry group and the same variants and allele coding as its association summaries?
- Do sample sizes and variant-specific coverage match the assumptions used to scale the association evidence?
- Are cohorts independent, or is overlap represented in the model or covariance information?
- For individual-level analysis, do genotypes, phenotypes, covariates, and ancestry labels refer to the same participants and the intended analysis samples?
These checks matter because workflow choice does not eliminate data mismatch. Summary statistics can be valid inputs only when their associated LD and uncertainty information support the likelihood; individual-level records can support a richer model only when participant inclusion and model specification are correct.
Common Mistake
Wrong reasoning: “The summary statistics have large sample sizes, so any reasonable LD panel will be adequate, and analyses from separate cohorts can be treated as independent.”
Correction: Large sample size does not repair an LD matrix that poorly represents the analyzed cohort, nor does it remove dependence caused by shared participants. LD and covariance are parts of the statistical model, not optional annotations. Verify ancestry and variant matching, identify possible sample overlap, and use a likelihood that accounts for the data structure. If the required inputs are not available or cannot be validated, the resulting fine-mapping evidence should be treated cautiously.
Check Your Understanding
Answer each question by referring to the data representation and assumptions of the workflow.
- What LD information does a summary-statistic trans-ancestry analysis require, and why does it need to correspond to the analyzed ancestry and variants?
- In the simplified linear model, why can a variant with zero joint effect have a nonzero expected marginal score?
- What is one computational or access advantage of summary statistics, and one limitation that remains even when they are easy to share?
- How can shared participants make an independence-based combination of association evidence overstate precision?
- Does analyzing participant-level genotypes automatically eliminate concerns about overlap or model misspecification? Explain.