Epistasis

Quantitative epistasis

SUMMIT tests interactions between supplied SNP pairs or between a target SNP and a genetic score. It also estimates target-by-background variance components. Choose targets, backgrounds, and test families before examining confirmation outcomes. These workflows use quantitative traits; binary G×E estimation is described in Generalized G×E PCGC.

Choose a model

Analysis	Model	Interpretation
Supplied pairs or a fixed genetic score	robust_mean	Conditional mean effects with HC3 heteroskedasticity-robust covariance
Independently trained trans score with polygenic adjustment	conditional_polygenic_mean	Conditional mean effect under a declared Gaussian polygenic covariance model; experimental
Target-by-background variance	Default moment estimator	Variance attributed to a supplied interaction kernel, conditional on the other kernels

For pair features H or a target-by-score feature, the finite mean model is

$$Y=C\alpha+H\gamma+\epsilon,\qquad H_i=X_{it}\sum_j w_jX_{ij}.$$

C contains the declared covariates and genetic main effects. The coefficient γ measures association conditional on that design. A detected interaction does not establish a causal mechanism. HC3 allows unequal residual variances across independent people. It does not account for omitted mean effects or residual dependence between people.

Supplied pairs

Use BED or biallelic diploid PGEN with companion files, a selected sample table with FID IID, and phenotype/covariate tables with those identifiers. Selected phenotypes and covariates must be complete. Dominance terms require observed hard calls, because dosage alone does not identify heterozygosity.

Save this as pairs.json, replacing the filenames and SNP IDs:

{
  "kind": "summit.epistasis.prepare",
  "schema_version": 1,
  "genotypes": {"geno": "cohort.bed"},
  "samples": "samples.tsv",
  "phenotypes": {"file": "phenotypes.tsv", "columns": ["trait"]},
  "covariates": {"file": "covariates.tsv", "columns": ["age", "sex", "PC1"]},
  "genotype_scale": "hwe",
  "phenotype_scale": "raw",
  "annotations": {},
  "jobs": [{
    "id": "supplied_pairs",
    "additive_annotations": ["all"],
    "local_variants": ["rsTarget", "rsPartner1", "rsPartner2"],
    "dominance_variants": ["rsTarget", "rsPartner1", "rsPartner2"],
    "pairs": [["rsTarget", "rsPartner1"], ["rsTarget", "rsPartner2"]],
    "inference": {"method": "robust_mean", "save_reference": true}
  }]
}

Paths are relative to the manifest. Pair loci enter the main-effect design; local_variants and dominance_variants allow additional adjustment. Remove monomorphic and all-missing markers before preparation.

summit epistasis prepare pairs.json --out results/pairs \
  --num-threads 4 --block-size 128 --memory-gib 4
summit epistasis fit results/pairs/supplied_pairs.robust-score.npz \
  --out results/pairs.fit.json

Preparation saves scores, information, covariance, and feature definitions. Fitting needs only the saved summary. Results include effect estimates, SEs, their full covariance, a joint test, and supported group tests. Inspect the rank and leverage diagnostics. Redundant features can leave individual coefficients unidentified even when a joint effect is estimable.

Current support checks require at least 1,000 confirmation samples, fitted rank at most 5% of N, maximum leverage at most 0.1, feature effective support at least 100, and normalized condition number at most 10⁶. Passing these checks does not establish calibration for an arbitrary study.

Independently trained trans scores

Training and confirmation samples must be disjoint. Training estimates a target-specific score using a prespecified trans background; confirmation uses its saved weights. All tuning and target selection must respect that separation.

The conditional polygenic procedure includes additive, dominance, and supplied covariate-dependent genetic covariance. For training outcomes Y₀ and confirmation outcomes Y₁, the model uses their joint covariance V:

$$E[Y_1\mid Y_0]=\mu_1+V_{10}V_{00}^{-1}(Y_0-\mu_0),\qquad V_{1\mid0}=V_{11}-V_{10}V_{00}^{-1}V_{01}.$$

The workflow fits the declared nuisance mean and covariance and carries the trained score into the confirmation model. This procedure remains experimental. Coverage under covariance misspecification and calibration at genome-wide significance thresholds have not been established.

For a target on a chromosome other than chromosome 5, save this recipe as trans.json:

{
  "kind": "summit.epistasis.trans_inputs",
  "schema_version": 1,
  "genotypes": {"geno": "cohort.bed", "genome_build": "GRCh37"},
  "target": "rsTarget",
  "background_chromosome": "5",
  "training_samples": "training.tsv",
  "confirmation_samples": "confirmation.tsv",
  "phenotype": {"file": "phenotypes.tsv", "column": "trait", "unit": "cm"},
  "covariates": {
    "file": "covariates.tsv",
    "columns": ["age", "sex", "PC1"],
    "varying_effects": ["PC1"]
  },
  "inference": {"method": "conditional_polygenic_mean"}
}

make-inputs selects complete cases and checks training genotype support. It writes training and preparation manifests, sample lists, and selected local main effects. Use interaction_variants with a SNP-list file in place of background_chromosome for a supplied trans set. varying_effects declares covariates whose genetic slopes enter the model.

summit epistasis make-inputs trans.json --out results/trans --num-threads 4
summit epistasis train-direction results/trans/train.json \
  --out results/trans/trained --num-threads 4 --memory-gib 8
summit epistasis prepare results/trans/prepare.json \
  --out results/trans/prepared --num-threads 4 --memory-gib 8
summit epistasis fit results/trans/prepared/trait.robust-score.npz \
  --out results/trans.fit.json

train-direction --resume and prepare --resume validate compatible completed work or resume solver checkpoints. prepare-traits can reuse a cohort reference for a new phenotype with matched samples and definitions. Conditional polygenic preparation still needs genotypes and a matched training fit for that phenotype.

Variance components and group tests

For target genotype x, background genotypes X, nonnegative annotation weights A, and covariate projection P, the interaction kernel is

$$K=\frac{1}{\sum_j A_j} P\mathrm{diag}(x)X\mathrm{diag}(A)X^T\mathrm{diag}(x)P.$$

The target is excluded from its background. A moment fit estimates the coefficient of K jointly with additive and residual kernels. Replace pairs and inference in a preparation job with a components list, for example [{"name":"interaction","target":"rsTarget","background":"region"}]. Define region in the manifest's annotations mapping from SNP IDs to nonnegative weights, and include relevant additive annotations in additive_annotations. Saved variance summaries use .epistasis.npz.

Moment estimates remain signed. Approximate Wald probabilities from a variance fit need particular care at the zero-variance boundary. Gaussian score and fitted-null procedures are also available through summit.epistasis.score and summit.epistasis.inference_workflow, with their stated covariance assumptions.

combine harmonizes compatible signed pair summaries across cohorts; followup performs conditional tests within a supplied pair family. Preserve allele coding, effect units, feature definitions, and sample-overlap information. Correct multiplicity across all tested targets, backgrounds, traits, and follow-up families.

Computation

Preparation uses SUMMIT's genotype readers and matrix operations. Larger backgrounds use streamed products and randomized reference summaries. Increase --nvecs to assess reference precision; --exact is limited to small numerical examples. Match process thread settings to --num-threads as described in Installation.

Use new output paths. Cohort references and training files can contain sample-aligned information and belong in protected storage. Reuse requires matching samples, genotypes, scaling, features, and nuisance design.