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Tractor-Mix

Summary

Tractor-Mix is a local-ancestry-informed generalized linear mixed model (GLMM) developed by Tan, Atkinson et al. (2025/2026) in the Atkinson Lab for genome-wide association studies (GWAS) in admixed populations with sample relatedness.[1] It extends the original Tractor framework—which required strictly unrelated individuals—by fitting a genetic relationship matrix (GRM) random effect alongside local-ancestry-partitioned dosage terms.[1] This enables high-powered association testing across family-based or biobank cohorts (such as the UK Biobank and Mexico City Prospective Study) while controlling for both global/local ancestry population stratification and cryptic relatedness.[1]

Statistical Model & Score Test Formulation

For a 2-way admixed individual $i$, Tractor-Mix models trait $Y_i$ using a generalized linear mixed model framework:[1]

$$g(\mathbb{E}[Y_i]) = \mathbf{X}i \boldsymbol{\alpha} + \beta + b_i$$} G_{i,A} + \beta_{B} G_{i,B

where: - $\mathbf{X}i \boldsymbol{\alpha}$: Fixed covariates (age, sex, global ancestry principal components estimated via PC-AiR).[1] - $G$: Ancestral-allele copy dosages (0, 1, or 2) assigned to local ancestry components $A$ and $B$, extracted via local ancestry deconvolution.[1] - $\beta_A, \beta_B$: Ancestry-specific effect sizes for ancestry components $A$ and $B$.[1] - $b_i \sim \mathcal{N}(0, \sigma_g^2 \mathbf{\Phi})$: Random effect capturing sample relatedness, where $\mathbf{\Phi}$ is the kinship matrix estimated via PC-Relate and $\sigma_g^2$ is the additive genetic variance.[1]}, G_{i,B

Tractor-Mix Model Architecture
  Individual i Trait (Y_i)
          │
          ├── Fixed Covariates (Age, Sex, PC-AiR Global PCs)
          ├── Local Ancestry Component A Dosage (G_i,A * β_A)
          ├── Local Ancestry Component B Dosage (G_i,B * β_B)
          └── Cryptic Kinship Random Effect (b_i ~ N(0, σ²_g * Φ))

2-Degree-of-Freedom Joint Score Test

To scan millions of variants efficiently, Tractor-Mix tests the joint null hypothesis $H_0: \beta_A = \beta_B = 0$ using a 2-DoF score test statistic ($Q$):[1]

$$Q = \mathbf{U}^T \mathbf{V}^{-1} \mathbf{U} \sim \chi^2_2$$

where $\mathbf{U} = [\mathbf{U}_A, \mathbf{U}_B]^T$ is the score vector derived from the null model fit once per cohort using Penalized Quasi-Likelihood (PQL), and $\mathbf{V}$ is the variance-covariance matrix of score statistics accounting for GRM relatedness.[1]

Low Allele-Count Thresholding Rule

Partitioning risk alleles by local ancestry reduces the effective allele count per ancestral term.[1] To prevent false-positive inflation on low-count terms, Tractor-Mix enforces an explicit threshold:[1] - Threshold: Minimum ancestry-specific allele count $AC_{\text{anc}} > 50$.[1] - Filtering Logic: If an ancestral dosage term fails $AC_{\text{anc}} > 50$, it is dropped from the joint model, and Tractor-Mix falls back to reporting single-ancestry marginal test statistics for the valid ancestry term.[1]

Six-Step Pipeline Workflow

A standard Tractor-Mix analysis proceeds through six computational modules:[1][3]

  1. Haplotype Phasing: Phase genotype arrays/WGS using SHAPEIT5.[3]
  2. Local Ancestry Inference: Deconvolve local ancestry across haplotypes using RFMix2.[3]
  3. Ancestry Dosage Extraction: Run Tractor's ExtractTracts.py script to generate ancestral dosage matrices ($G_{i,A}, G_{i,B}$).[3]
  4. Unconfounded Principal Components: Estimate global ancestry PCs using PC-AiR (GENESIS package).[3]
  5. Kinship Matrix Estimation: Compute the genetic relationship matrix ($\mathbf{\Phi}$) using PC-Relate to handle admixture-aware relatedness.[3]
  6. GLMM Null & Score Scanning: Fit the null mixed model in GMMAT via PQL, followed by genome-wide 2-DoF joint score testing in Tractor-Mix.[1][3]

Empirical Performance & Validation Benchmarks

1. UK Biobank ($N = 18,375$ AFR-EUR Admixed Participants)

Evaluating total cholesterol and sickle cell anemia across 18,375 admixed UK Biobank participants (containing 315 1st-degree and 489 2nd-degree relative pairs):[1]

  • Total Cholesterol (APOE rs7412):
  • Standard Tractor GLM (excluding relateds): $P = 1.2 \times 10^{-25}$.[1]
  • Tractor-Mix GLMM (retaining relateds): $P = 4.1 \times 10^{-80}$ (AFR-specific $P = 4.1 \times 10^{-80}$; non-significant in EUR).[1]
  • Power Gain: $+55$ orders of magnitude boost in $P$-value due to sample preservation and local ancestry partitioning.[1]
  • Genomic Control: Joint $\lambda_{\text{GC}} = 0.997$, AFR-specific $\lambda_{\text{GC}} = 1.024$, EUR-specific $\lambda_{\text{GC}} = 0.964$.[1]
  • Sickle Cell Anemia (HBB rs334): Replicated strong AFR-specific association ($MAF_{\text{AFR}} = 0.091$ vs $MAF_{\text{EUR}} = 0.0008$).[1]

2. Mexico City Prospective Study ($N = 139,944$ IAM-EUR Admixed Participants)

Evaluating BMI across 139,944 participants with high degrees of household relatedness (mean $85.1\%$ Indigenous American [IAM], $14.9\%$ European [EUR]):[1]

  • Genomic Control Calibration:
  • Unadjusted PLINK linear regression: $\lambda_{\text{GC}} = 1.40$ (severe inflation).[1]
  • Standard GMMAT (no local ancestry): $\lambda_{\text{GC}} = 1.24$.[1]
  • Tractor-Mix Joint Model: $\lambda_{\text{GC}} = 1.27$ (IAM $\lambda_{\text{GC}} = 1.23$, EUR $\lambda_{\text{GC}} = 1.27$).[1]
  • Locus Discoveries:
  • FTO rs11647020: Significant strictly in the EUR-specific term ($P = 9.36 \times 10^{-9}$), reflecting European risk-allele origin.[1]
  • ZNF646P1 rs9568859: Detected as a novel genome-wide hit in the joint test ($P = 7.67 \times 10^{-9}$) and driven by IAM local ancestry ($AF_{\text{IAM}} = 0.485$ vs $AF_{\text{EUR}} = 0.113$).[1]

Model Comparison: Tractor vs. Tractor-Mix vs. GMMAT / SAIGE

Feature / Dimension Original Tractor GMMAT / SAIGE Tractor-Mix
Model Type Generalized Linear Model (GLM) Generalized Linear Mixed Model Local-Ancestry GLMM
Sample Relatedness Requires unrelateds (excludes families) Handles relatedness via GRM Handles relatedness via GRM
Local Ancestry Dosage Partitioned ($G_{A}, G_{B}$) Standard unpartitioned dosage Partitioned ($G_{A}, G_{B}$)
Joint Test Stat 2-DoF Score/Wald 1-DoF Score 2-DoF Score ($Q$)
Heterogeneous Power High power for ancestry-private hits Reduced power High power for ancestry-private hits

See Also

  • Tractor — original GLM predecessor for unrelated admixed samples.
  • GMMAT — GLMM engine utilized by Tractor-Mix for null model fitting.
  • UK Biobank — validation cohort for AFR-EUR admixture testing.
  • Mexico City Prospective Study — validation cohort for IAM-EUR admixture testing.

Citations

[1] Tan, T., Vergara-Lope, A., Martínez-Magaña, J.J., et al. (2025). Extending Genome-Wide Association Studies to admixed cohorts with high degrees of relatedness. medRxiv preprint. DOI: 10.1101/2025.05.27.25328444 Supports: GLMM statistical model, 2-DoF score test $Q$, low AC thresholding ($AC > 50$), UK Biobank APOE rs7412 ($P = 4.1 \times 10^{-80}$), and MCPS FTO / ZNF646P1 findings. Location: Methods ("Tractor-Mix Model", "Score Test Formulation"); Results ("UK Biobank Analysis", "Mexico City Prospective Study Analysis").

[2] Tan, T., Vergara-Lope, A., Martínez-Magaña, J.J., et al. (2026). Extending genome-wide association studies to admixed cohorts with high degrees of relatedness. Nature Genetics, 58, 204–215. Supports: peer-reviewed version of record and pipeline specifications. Location: Main Text; Extended Data Figs. 1–6.

[3] Extended Data Figure 1 (Tractor-Mix pipeline workflow) in Tan et al. (2026). Supports: six-step analysis workflow (SHAPEIT5, RFMix2, ExtractTracts, PC-AiR, PC-Relate, GMMAT).