Tractor-Mix

Summary¶

Tractor-Mix is a generalized linear mixed model (GLMM) for genome-wide association studies (GWAS) in admixed cohorts that also contain related individuals. It extends the earlier Tractor framework — which requires unrelated samples — by fitting a genetic relationship matrix (GRM) as a random effect alongside local-ancestry-partitioned genotype dosages, similar to GMMAT. This yields well-calibrated joint and ancestry-specific P values and effect sizes for admixed samples with high degrees of relatedness, such as biobanks recruited via household- or family-based sampling.

Background¶

Admixed individuals make up a large share of the global population but are underrepresented in GWAS, in part because standard analytic pipelines assume approximately homogeneous ancestry or unrelated samples.[1] The Tractor method addressed the admixture problem by using local-ancestry deconvolution to partition each individual's genotype dosage by ancestral background, producing ancestry-specific effect sizes and boosting power to detect ancestry-enriched loci.[1][2] However, because Tractor is a generalized linear model, it requires independent samples — a growing limitation as biobanks and targeted cohorts in non-Western settings increasingly include closely or cryptically related admixed individuals.[1]

Tractor-Mix closes this gap by combining Tractor's local-ancestry partitioning with a mixed-model framework (as used in GMMAT, SAIGE, and BOLT-LMM) that models relatedness via a GRM random effect, rather than requiring sample exclusion.[1] It was developed by the Atkinson Lab at Baylor College of Medicine, which also created the original Tractor method.[1]

Statistical Model¶

For a 2-way admixed individual i, Tractor-Mix models the trait as a function of ancestry-specific genotype dosages g_iA, g_iB (partitioned by local ancestry) plus covariates X_i and a random effect b_i ~ MVN(0, τ²Φ), where Φ is the GRM/kinship matrix and τ² is the additive genetic variance.[1] The joint null hypothesis H0: βA = βB = 0 is tested with a 2-degree-of-freedom Rao score test, fit once per cohort (shared across variants) using GMMAT's penalized quasi-likelihood approach for computational efficiency.[1]

Ancestry-specific effect sizes and P values are approximated from the score-test null model without fitting the full model per variant, making genome-wide scanning tractable; a slower but more robust Wald test (directly fitting the full mixed model) is also implemented for confirming top hits.[1] Across simulations the two approaches gave concordant P values under the null and similar effect-size estimates, with a small reported downward bias for the score-test approach on dichotomous traits (consistent with prior reports for GMMAT).[1]
Low allele-count handling: partitioning risk alleles by local ancestry can leave some ancestry-specific dosages with very low allele counts, which can inflate false positives for dichotomous traits. Tractor-Mix addresses this with a default minimum allele-count threshold (AC > 50): ancestries failing the threshold are dropped from the joint model and only marginal P values/effect sizes are reported for the ancestries retained, with the model used tracked per variant in the output.[1]
Unlike the original Tractor, Tractor-Mix does not condition on total local-ancestry ("hapcount") at a site by default, primarily to avoid fitting a separate null model per local-ancestry segment (computationally expensive under a score-test framework); this trades some effect-size interpretability and locus resolution for tractable genome-wide computation and slightly higher power to detect ancestry-specific loci.[1]

Pipeline¶

Per the published version's Extended Data Figure 1, a full Tractor-Mix analysis proceeds in six steps: (1) haplotype phasing (SHAPEIT5) and local ancestry inference (RFMix2); (2) local-ancestry dosage computation with Tractor's ExtractTracts.py; (3) global-ancestry PC estimation with PC-AiR (GENESIS); (4) GRM estimation with PC-Relate (GENESIS); (5) null-model fitting with GMMAT; and (6) computation of joint and ancestry-specific P values and effect sizes with Tractor-Mix.[3]

Simulation Results¶

Using simulated 2-way AFR-EUR admixed cohorts with pedigree-based relatedness (2,500 independent + 2,500 related individuals across 250 families for false-positive evaluation; 1,000 independent + 1,000 related individuals for power evaluation), the authors compared 8 model configurations spanning standard regression, original Tractor, GMMAT, and Tractor-Mix, each with either standard PCA/GRM estimators, PC-AiR/PC-Relate estimators, or the ground-truth simulated admixture proportions and kinship matrix.[1]

False positive control: standard linear/logistic regression (with or without Tractor-style ancestry partitioning) showed inflated type I error under relatedness, as expected. Mixed-model approaches (GMMAT, Tractor-Mix) controlled false positives well for dichotomous traits; continuous traits showed small residual inflation when admixture proportions/kinship were estimated rather than known exactly. A larger-scale run (~120M P values for continuous traits, ~22M for dichotomous traits) found no false-positive inflation for common variants (MAF > 0.05) at α = 5×10⁻⁶ when using Tractor-Mix with true covariates and GRM.[1]
Statistical power: Tractor-Mix gains substantial power over a standard mixed model (GMMAT) when ancestry-specific effect sizes are highly heterogeneous (effect present in one ancestry only), is roughly comparable under moderate heterogeneity (βA = 2βE), and is less powerful than GMMAT when effects are identical across ancestries (βA = βE) — because partitioning dosages by ancestry adds no discriminating information in that case while reducing effective sample size per term.[1]

Empirical Validation¶

UK Biobank¶

Applied to 9,220 2-way AFR-EUR admixed UK Biobank participants (first PC correlated 0.998 with inferred global ancestry; KING-robust identified 315 first-degree and 489 second-degree relative pairs), Tractor-Mix replicated known GWAS hits for total cholesterol (missense variant rs7412 in APOE) and sickle cell anemia (missense variant rs334 in HBB).[1]

For total cholesterol, Tractor-Mix reached P ≈ 1×10⁻⁸⁰ at rs7412, versus P ≈ 1×10⁻²⁵ for the original (relatedness-excluding) Tractor — attributed largely to the larger effective sample size once related individuals are retained. The signal was AFR-specific (AFR P = 1×10⁻⁸⁰; not significant in EUR), consistent with the risk allele's higher frequency in the AFR-ancestry background (AFR MAF = 0.120 vs. EUR MAF = 0.068). Genomic control was well-behaved (λGC = 0.997 joint, 1.024 AFR-specific, 0.964 EUR-specific).[1]
For sickle cell anemia, both GMMAT and Tractor-Mix recovered rs334 (MAF = 0.091 in AFR vs. 0.0008 in EUR) as the top hit. Tractor-Mix additionally flagged several variants genome-wide not identified by GMMAT (rs67525852, rs2075208, rs12553528, rs79407438, rs606926, rs12483053); the authors note the biological relevance of these variants has not been characterized.[1]

Mexico City Prospective Study¶

Tractor-Mix was applied to body mass index (BMI) in 33,500 participants of the Mexico City Prospective Study with <2.5% East Asian/African global ancestry, modeled as 2-way Indigenous American (IAM, mean 85.1%) and European (EUR, mean 14.9%) admixture.[1]

Genomic-control inflation was 1.40 for unadjusted PLINK regression, 1.24 for GMMAT, and 1.27 for the Tractor-Mix joint test (IAM-specific λ = 1.23, EUR-specific λ = 1.27).[1]
The FTO locus — the strongest known European BMI association — was significant only in the EUR-specific Tractor-Mix analysis (index variant rs11647020, P = 9.36×10⁻⁹), the sole genome-wide-significant hit in that ancestry background. All other genome-wide-significant ancestry-decomposed associations were IAM-specific and largely mirrored the joint/GMMAT profile, with most mapping within 250 kb of BMI loci previously reported in European-ancestry studies — suggesting the IAM-specific power gain reflects shared effect alleles segregating differently by ancestry background rather than IAM-private causal variants.[1]
Tractor-Mix's joint test additionally detected a locus near the ZNF646P1 pseudogene (index variant rs9568859, P = 7.67×10⁻⁹) that did not reach genome-wide significance in the GMMAT analysis. This variant had not previously been linked to BMI itself but has been associated with waist circumference, and nearby SNPs have been linked to adiposity traits. It was IAM- but not EUR-specific in the ancestry-stratified analysis, despite the effect allele being common in all three ancestries examined (IAM AF = 0.485, EUR AF = 0.113, AFR AF = 0.239).[1]

Yale-Penn Cohort¶

Tractor-Mix was also applied to alcohol-related traits in the Yale-Penn cohort, identifying AFR-ancestry-specific associations for alcohol use disorder (AUD); this analysis is reported only in the paper's Supplementary Information, so the wiki notes its existence without reproducing unverified supplementary-only detail.[1]

Limitations¶

Systematically evaluated only for 2-way admixture; the authors advise limiting modeled ancestries to those contributing a sizeable share (e.g. ≥10% average global ancestry) of a cohort and caution that 3-way-or-higher admixture (more free parameters, sparser partitioned dosages) has not been benchmarked.[1]
Implemented in R with large matrix operations; despite a sparse GRM implementation and multi-core parallelization, the authors expect it to be slow at very large scale (tens of thousands of samples and tens of millions of markers).[1]
Inherits GMMAT's known sensitivity to highly imbalanced case/control ratios and low ancestry-specific allele counts; Tractor-Mix mitigates this with the AC > 50 dosage-dropping rule described above rather than a full saddle-point approximation (SPA), which the authors flag as a direction for future work.[1]

Software Dependencies¶

The reference pipeline composes several existing tools: SHAPEIT5 (phasing), RFMix2 (local ancestry inference), Tractor (ancestry dosage extraction), GENESIS (PC-AiR/PC-Relate), GMMAT (mixed-model null-model fitting), and — for empirical comparisons in the manuscript — PLINK 2.0, REGENIE, and SAIGE.[3]

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. Source: 2025.05.27.25328444v1.full.md. Supports: statistical model, simulation results, and all UKBB/MCPS/Yale-Penn empirical findings above. Location: Full text — Introduction, Results, Discussion, Methods sections.

[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 (peer-reviewed version of record). DOI: 10.1038/s41588-026-02689-6. Supports: publication status, author list, Extended Data Figure descriptions, code/data availability. Location: Abstract, Extended Data Figs. 1–6, Data/Code availability (only the abstract, extended-data captions, and metadata of this version were accessible; full published body text was not independently inspected — see note below).

[3] Extended Data Figure 1 (Tractor-Mix pipeline) and Code availability statement, Nature Genetics version [2].

Note on sourcing: At the time of ingestion, the Nature Genetics version of record [2] was paywalled beyond its abstract and extended-data captions. The claims in this page are drawn from the openly accessible medRxiv preprint [1], which appears to be the same study; specific numbers have not been cross-checked against the final peer-reviewed text, which may differ in minor respects. Confidence is set to medium accordingly.