Cross trait analysis

Cross-trait genetic response models

This research extension estimates covariance between two traits' genetic responses to environmental contexts. It reports baseline genetic correlation, response correlations, and paired differences between them. Ordinary additive --rg remains available through the h²/rg guide.

For [1, age, BMI], the cross-trait matrix contains nine ordered entries. Trait X's age response can covary with trait Y's BMI response differently from X's BMI response with Y's age response. Reversing the trait pair transposes the matrix. Each SNP annotation has its own matrix.

Workflow

1. Define a common genotype scale and saved context coding, including an intercept coordinate. Each trait retains its own observed sample rows, fixed effects, and phenotype normalization.
2. Prepare chromosome reference moments with the generalized G×E machinery. Keep the reference context definitions and sample identities with the files.
3. Use CrossTraitBatch around MaskedTraitBatch to collect the requested pairs in one study genotype traversal. The batch shares decoded genotypes and within-trait scores, and computes overlap residual moments.
4. Assemble compatible within-trait and ordered cross-trait equations from the saved summaries. Fit them on the same SNP blocks.
5. Derive correlations and contrasts using the joint covariance of both within-trait estimates and the cross-trait estimate.

The API modules are summit.ldscore.generalized_gxe_cross_trait_batch, summit.context.cross_trait_gram, and summit.context.cross_trait_fit. CrossTraitMomentPlan and fit_cross_trait perform the summary-based fit. write_cross_trait_fit adds derived quantities and paired uncertainty when the matching within-trait fits are supplied. Across chromosomes, the full same-person Gram must be formed from the summed person-level diagonals; summing chromosome Grams would omit cross-chromosome diagonal products.

There is no general summit cross-trait G×E command yet. The research drivers scripts/generalized_gxe/cross_trait_study.py and cross_trait_pilot_fit.py show the complete workflow, including input checks and checkpoint resume. These scripts use a study-specific directory layout; adapting them requires preparing the same input files. They do not accept ordinary GWAS summaries.

Reference modes

Mode	Treatment of reference genotype–context dependence
factorized	Uses population LD and cohort exposure moments; default
factorized_plus_residual	Adds the nonfactorized reference remainder
legacy_transport	Transfers the reconstructed ordered reference moment
legacy_transport_exact	Transfers an ordered moment repaired with additional reference Z summaries

All modes account for each trait's sample mask and actual overlap. Their differences assess reference assumptions; close agreement on one dataset does not establish calibration for every sampling design. The last mode needs compatible Z summaries. Reference-mode choice does not change the scientific definition of the ordered cross-trait covariance.

Uncertainty and interpretation

baseline_rg uses the original context origin; centered_baseline_rg uses each trait's mean context. Orthogonalization uses the centered baselines. Retain the saved exposure units and covariance metric with the results.

The default is directional target-moment deletion with full-estimate delta propagation. It retains covariance among XX, YY, and XY estimates. Comparisons such as response correlation minus baseline correlation use paired uncertainty; subtracting two independent confidence intervals is incorrect.

The research fitter also exposes --uncertainty-method jackknife for nonlinear delete-block estimates. Both methods use the paired SNP blocks.

The aggregate orthogonal-response correlation measures shared response after removing each trait's genetic association with its baseline, under the recorded context covariance metric. It is not an average of exposure-specific correlations and does not describe the direction of an environmental intervention.

Weak or nonpositive genetic-variance denominators can make correlations and intervals undefined. Raw values outside [-1, 1] are retained and flagged. Uncertainty is conditional on the supplied reference. It excludes reference sampling, random-vector error, and error from transferring reference moments to a different study cohort.

The method description gives the equations and reference approximations. Binary cross-trait PCGC is a separate research path with its own ascertainment and overlap assumptions.