Poisson Mixed Model Tool Accelerates Single-Cell Expression Quantitative Trait Locus Discovery

Researchers have developed SAIGE-QTL, a Poisson generalized linear mixed model framework that directly models single-cell RNA sequencing read counts to substantially expand expression quantitative trait locus mapping across diverse cell populations. In a comprehensive evaluation analyzing 1.2 million peripheral blood mononuclear cells from 982 donors within the OneK1K cohort, SAIGE-QTL identified 48.8 percent more genes with significant expression quantitative trait loci than standard pseudobulk analysis using TensorQTL. Traditional single-cell association studies frequently aggregate cellular measurements into pseudobulk profiles or apply Gaussian models poorly suited to discrete count data. SAIGE-QTL overcomes these limitations by directly evaluating read counts while simultaneously accounting for donor covariates, cell covariates, relatedness among individuals, and unequal cell numbers per donor. Benchmarking across simulations and three distinct real-world datasets demonstrated that the framework achieves improved statistical power while maintaining computational efficiency and strict calibration. The open-source platform also accommodates genome-wide trans-eQTL mapping and rare-variant set tests, uncovering signals independent of common regulatory loci.

The development of SAIGE-QTL addresses fundamental statistical and computational bottlenecks that have long constrained association analysis in single-cell transcriptomics. Existing approaches generally collapse cell-level heterogeneity by aggregating read counts into donor-level pseudobulk summaries, discarding cell-to-cell variability and obscuring differences in donor cell numbers. Furthermore, standard pseudobulk implementations rely on Gaussian models that are poorly aligned with the non-negative, discrete, and zero-inflated distributions characteristic of sequencing read counts. While generalized linear mixed models such as glmer directly model counts using Poisson distributions, their reliance on iterative Wald tests imposes prohibitive computational burdens that prevent execution on cohort-scale datasets. Other mixed model packages, including CellRegMap, were formulated primarily to map dynamic expression quantitative trait loci along trajectories rather than providing scalable association screening across entire genomes. By combining a Poisson mixed model with efficient score testing, SAIGE-QTL establishes a mathematically rigorous bridge between single-cell count resolution and cohort-scale computational feasibility.

The analytical architecture of SAIGE-QTL is structured into three discrete sequential steps executed for each tested gene. In the first step, the tool fits a null Poisson mixed model relating read counts to donor-level and cell-specific covariates without genotype variables. Fixed effects incorporate individual-level factors, such as chronological age, sex, and ancestry principal components, alongside cell-level factors like expression-based PEER factors derived within specific lineages. Intra-individual cell-to-cell variability and potential sample relatedness are accommodated through random effects. In the second step, SAIGE-QTL conducts association testing across the genetic spectrum using score statistics derived under the fitted null model. For common single-nucleotide polymorphisms, single-variant score tests assess phenotypic association. For less frequent and rare genetic variants with minor allele frequencies of five percent or less, the framework executes set-based association tests, including Burden tests, SKAT, and ACAT-V, combined through ACAT-O. Finally, in the third step, variant-level p-values across cis-regions are combined into gene-level significance values using Cauchy combinations.

To achieve computational tractability across millions of cells and hundreds of donors, SAIGE-QTL implements key mathematical optimizations during null model fitting. Parameter estimation employs penalized quasi-likelihood paired with the average information restricted maximum likelihood algorithm. To eliminate the standard cubic computational complexity of inverting an N-by-N variance matrix across N cells, SAIGE-QTL applies the Sherman-Morrison-Woodbury formula by exploiting the low-rank structure of the random-effects design matrix. This algebraic transformation converts the inversion problem into solving an n-by-n linear system based on the donor count n, reducing computational complexity from O(N cubed) to operations bounded by the non-zero elements in the relatedness matrix, n squared, and N. For unrelated donors, calculations reduce to closed-form block-wise operations with linear complexity O(N). For larger donor cohorts where memory demands increase, an alternative preconditioned conjugate gradient algorithm solves linear systems through consecutive matrix-vector multiplications without forming the dense cell-level variance matrix.

Score test evaluations are similarly accelerated through a two-stage variance ratio estimation strategy and saddlepoint approximation. In conventional mixed model score testing, evaluating test statistic variances requires matrix manipulations scaling with the square of cell counts. SAIGE-QTL circumvents this by calculating variance ratios that remain approximately constant across genetic markers with minor allele counts of twenty or greater. The algorithm first computes an unadjusted variance ratio using mean-centered genotypes, reducing computation costs from quadratic order down to order n for approximately 95 percent of tested genetic variants. For the remaining candidate variants that achieve nominal significance with p-values below 0.05, SAIGE-QTL applies a second, highly accurate variance ratio incorporating the inverse variance matrix. To prevent type I error inflation caused by the breakdown of asymptotic normality in low-frequency variants or low count rates, the framework incorporates saddlepoint approximation. In simulations across three representative immune cell types spanning diverse sparsity levels, these procedures demonstrated well-calibrated false-positive control.

Direct performance comparisons against existing statistical packages highlighted dramatic gains in processing speed and analytical power. In a benchmark evaluation of one hundred genes in innate and naive B cells, SAIGE-QTL executed 244 times faster than glmer while yielding virtually identical results, exhibiting a Pearson determination coefficient of 0.991 for negative log p-values and 0.998 for effect size estimates. The software also showed high concordance with CellRegMap-association, achieving an R-squared of 0.982. When evaluated against pseudobulk tools including TensorQTL and jaxQTL, SAIGE-QTL demonstrated superior empirical power across all simulated scenarios, with advantages most pronounced in less abundant cell types and uneven cell designs. While TensorQTL and jaxQTL completed tests faster in specific subsets, SAIGE-QTL maintained a smaller memory footprint, requiring between 0.3 and 1.6 gigabytes across cell types. Furthermore, SAIGE-QTL and TensorQTL maintained well-controlled false-positive rates down to significance thresholds of 5 times 10 to the negative fifth power.

Application of SAIGE-QTL to real data from the OneK1K study demonstrated significant increases in expression quantitative trait locus discovery. The OneK1K cohort comprises single-cell data covering 14 peripheral blood cell types from 982 individuals, encompassing 16,250 expressed genes and over 12 million genetic variants. Across all 14 cell types, SAIGE-QTL identified 17,218 significant eGenes at a false discovery rate below five percent, corresponding to 5,894 unique genes. This represents a 48.8 percent increase over the 11,569 eGenes discovered by TensorQTL applying beta permutation. Among the unique eGenes identified, 2,447 were detected in only one cell type, underscoring pronounced cellular specificity. Top single-variant test statistics in SAIGE-QTL were 3.8 to 19.2 percent higher than those in TensorQTL across all tested lineages. Downsampling experiments in CD4-positive naive and central memory T cells confirmed that SAIGE-QTL consistently detected approximately 7.5 to 8.0 percent more eGenes across cellular and donor subsampling fractions.

Integration of SAIGE-QTL summary statistics with autoimmune genome-wide association studies through summary-data-based Mendelian randomization provided functional insights into disease etiology. Examining four complex autoimmune disorders—Crohn’s disease, inflammatory bowel disease, rheumatoid arthritis, and systemic lupus erythematosus—SAIGE-QTL mapped more putative causal loci than the original pseudobulk Matrix eQTL analysis across every disease. Specifically, SMR identified 58 gene-trait pairs for Crohn’s disease compared to 55 with Matrix eQTL, 152 versus 123 for inflammatory bowel disease, 299 versus 249 for rheumatoid arthritis, and 9 versus 4 for systemic lupus erythematosus. Notably, SAIGE-QTL captured ninety percent of associations discovered by Matrix eQTL while revealing novel disease-associated regulatory mechanisms. For instance, the 9q21 genomic locus was linked to altered risk for both Crohn’s disease and inflammatory bowel disease through regulation of CARD9 expression in classical monocytes. Similarly, the 20q13 locus was identified as contributing causally to rheumatoid arthritis through CD40 expression changes in plasma cells, pinpointing a well-documented therapeutic target.

The computational efficiency of SAIGE-QTL further unlocked genome-wide scans for trans-acting expression quantitative trait loci across representative immune lineages. Testing over 5.3 million common genetic variants across autosomes required between 630 and 1,013 CPU hours per cell type, enabled by parallel gene testing and batched genotype processing. In trans-eQTL mapping across naive T cells, naive B cells, and plasma cells, investigators evaluated common variants located over two megabases away from gene bodies or on separate chromosomes, excluding the major histocompatibility complex region. At the standard genome-wide significance threshold of 5 times 10 to the negative eighth power, SAIGE-QTL identified 413 trans-eQTLs influencing 390 unique genes across the three cell types. At a threshold of 5 times 10 to the negative sixth power, 94,795 trans-eQTLs were detected across 13,159 unique genes. A representative multi-chromosome association involved the variant rs3924376 on chromosome 16, which acted as a cis-eQTL regulating SPNS1 expression while simultaneously serving as a trans-eQTL regulating MRPL32 expression on chromosome 7.

SAIGE-QTL also expanded the characterization of rare genetic variation and demonstrated robust replication across external datasets. Analyzing 6.78 million rare single-nucleotide polymorphisms with minor allele frequencies of five percent or less, set-based testing identified 5,541 rare-variant eGenes across 14 immune cell types, encompassing 2,317 unique genes. Crucially, 483 of these unique genes were completely independent of common regulatory signals, retaining statistical significance after conditioning on all common cis-eQTLs. Weighting variants by distance to the transcription start site enhanced discovery by 68 percent over equal weighting. External replication in the California Lupus Epidemiology Study confirmed that SAIGE-QTL identified more eGenes than TensorQTL in both B cells and natural killer cells, with over 89 percent replicating OneK1K signals. Similarly, in an induced pluripotent stem cell dataset derived from primary open-angle glaucoma patients across six ocular lineages, SAIGE-QTL identified 46 to 99 percent more eGenes than TensorQTL. The authors noted that future developments must address Poisson model limitations in highly overdispersed genes.

Subject of Research: Single-cell expression quantitative trait locus mapping using Poisson mixed models

Article Title: Efficient and accurate mixed model association tool for single-cell eQTL analysis

Article References: Zhou, W., Cuomo, A. S. E., Hu, L., Xue, A., Kanai, M., Liu, Y. C., Kang, T., Kim, Y., Rodriguez, A., Madduri, R. K., Gorissen, B. L., Chau, G., Senabouth, A., Gordon, M. G., Perez, R., Kathail, P., Kim, M. C., Ye, C. J., Krishna, C., … Neale, B. M. (2026). Efficient and accurate mixed model association tool for single-cell eQTL analysis. Nature Genetics. https://doi.org/10.1038/s41588-026-02798-2

Image Credits: AI Generated

DOI: 10.1038/s41588-026-02798-2

Keywords: statistical genetics, single-cell RNA sequencing, eQTL mapping, Poisson mixed models, SAIGE-QTL, computational biology, genomics, gene expression, Efficient, accurate, mixed, model