Diagnosing Discordant Individual-Level And Summary Estimates

Why Two Valid Estimates Can Disagree

Individual-level genomic mixed models and cross-trait LD score regression (LDSC) use different data and different sources of information. A mixed model uses phenotypes and a genetic relationship matrix to estimate covariance among traits associated with genomic similarity between individuals. Cross-trait LDSC uses genome-wide summary statistics and linkage disequilibrium patterns to estimate covariance attributable to common variants. Thus, disagreement is not automatically evidence that one analysis is wrong. First ask whether the analyses target the same genetic quantity in comparable populations, on comparable trait scales, and with sufficiently compatible assumptions.

This tutorial focuses on diagnosing such disagreements. It does not treat a numerical difference alone as a test of which method is correct: formal comparison requires the uncertainty of both estimates and their dependence, which can be substantial when analyses share participants or data.

What the Two Approaches Estimate

In an individual-level bivariate genomic mixed model, the observed phenotypes are modeled using fixed effects and random genetic effects. In a simplified form, let \(y_1\) and \(y_2\) be phenotype vectors for the two traits, and let \(K\) be a genomic relationship matrix constructed from measured variants. The additive genetic effects are modeled jointly, with covariance linked to \(K\):

Here \(g_1\) and \(g_2\) are vectors of genetic effects for the analyzed individuals. The model also requires an appropriate residual covariance structure and fixed-effect specification. Restricted maximum likelihood estimates the variance components under the fitted model, and their standardized covariance gives the model-based estimate of \(r_g\). Its interpretation depends on the relationship matrix, included variants, sample, phenotype definitions, covariates, and assumptions about the genetic and residual effects.

Cross-trait LDSC instead relates products of association \(Z\)-statistics across variants to their LD scores. The fitted slope provides an estimate of genetic covariance attributable to the variant set and LD reference represented by the analysis; the intercept accounts for a component not explained by LD scores, including certain effects of sample overlap and confounding. Combining the covariance estimate with compatible single-trait genetic-variance estimates yields an LDSC genetic correlation. These are summary-statistic estimates, not individual-level estimates from the same likelihood.

The comparison is most interpretable when both analyses refer to similar populations, phenotype scales, covariate adjustments, and genetic variation. Even then, the estimates need not match exactly: the two approaches have different sampling variability, model assumptions, and sensitivity to how genetic information is represented.

Compare Estimates Before Explaining Them

Record each estimate together with its standard error, confidence interval, sample size, ancestry composition, phenotype definition, and variant set. A point-estimate difference can be large relative to one method’s uncertainty and small relative to the other’s. Conversely, broad intervals can leave substantial uncertainty even when the point estimates look similar.

For a rough descriptive comparison, calculate the signed difference and state its direction. Do not call that difference statistically significant using the standard errors as if the estimates were independent unless independence is justified. If both methods use overlapping participants or related inputs, the covariance between estimates may be nonzero. The variance of their difference is

Without the covariance term, a formal standard error or test for the difference is not established. Confidence-interval overlap can provide context, but it is not itself a test of equality.

Diagnose the Target Before the Data

A useful first check is whether the two estimates describe the same target. A mixed model’s genetic covariance is defined relative to its relationship matrix and modeled genetic effects. LDSC’s estimate reflects the common-variant signal captured through its summary statistics and LD reference. Differences in variant coverage or allele-frequency distributions can therefore change the genetic component each method captures. A correlation is standardized, but standardization does not make estimates from different components or populations interchangeable.

Trait definitions and scales also matter. “Diagnosed disease,” “self-reported disease,” and a quantitative risk score are not automatically the same phenotype. Transformations can change the scale on which covariance and variances are expressed, and consequently can change the reported genetic correlation. For binary traits, confirm whether estimates are on the observed scale or have been transformed to a liability scale, and check that any transformations are compatible across analyses.

Ancestry and study composition deserve explicit attention. Allele frequencies, LD patterns, environmental exposures, ascertainment, and trait measurement can vary across populations. Mixed-model and LDSC estimates from different ancestry compositions may target different genetic relationships, even if the trait labels match. A discrepancy should not be attributed to ancestry solely because ancestry differs; rather, ancestry differences identify a plausible source to investigate, ideally with analyses on comparable samples and well-matched variant sets.

Check Overlap, Phenotypes, Variants, and Assumptions

Sample overlap can affect both interpretation and uncertainty. In cross-trait LDSC, correlated sampling errors caused by overlapping participants can contribute to the cross-trait intercept. This adjustment does not make arbitrary overlap harmless: the intercept, sample sizes, and the assumptions of the regression must still be appropriate. In an individual-level model, using the same individuals for both traits is a different data structure from using separate samples, and the residual covariance and missingness pattern must be modeled appropriately. When analyses use shared data, their resulting estimates are also generally not independent.

Phenotype checks should establish that case definitions, controls, measurement instruments, covariate adjustments, age ranges, and transformations are as comparable as possible. Differences in case ascertainment or control selection can change the statistical phenotype even when both analyses use the same diagnostic label. Verify that summary-statistic alleles are harmonized and that the individual-level relationship matrix and LDSC analysis use compatible sets of well-measured variants. Variant coverage matters because the two methods need not capture identical genetic effects.

Finally, assess the assumptions behind each fitted model. The mixed model depends on a suitable relationship matrix, a valid specification of fixed effects and residual covariance, and adequate control of population structure and relatedness effects. LDSC depends on suitable LD scores and reference information, reliable summary statistics, and the regression assumptions used to separate the LD-dependent signal from the intercept. A failed assumption can shift an estimate or make its uncertainty unreliable; merely obtaining a numerical answer does not verify the model.

A Practical Diagnostic Sequence

Keep the investigation ordered. Start with the target and data before tuning models or interpreting biological explanations.

Common Mistake and Why the Comparison Matters

Wrong reasoning: “The mixed-model estimate is larger, so LDSC must be biased downward.” This treats the estimates as measurements of one identical quantity and assumes their difference has only one possible explanation. It ignores differences in samples, variant coverage, phenotype scale, model assumptions, and uncertainty.

Correction: First determine whether the estimates target comparable genetic correlations. Then investigate design and input differences, model diagnostics, and sensitivity to harmonized choices. Report estimates with uncertainty and describe the limits of any comparison. If the methods use overlapping participants, do not test their difference as though the estimates were independent unless their covariance has been accounted for.

Careful diagnosis matters because genetic correlations are often used to summarize shared genetic architecture across traits. A discrepancy may reflect different genetic components or populations rather than a contradiction about biology. Equally, apparent agreement does not guarantee valid estimation: two analyses can agree while sharing a phenotype mismatch or an unexamined assumption.