Unveiling Population Stratification in eQTL Studies

SV eQTL based on Linear Mixed model (preliminary) June 26th, 2014 3/17/2025 1

The main blame in GWAS : population stratification A simple example for spurious association Population B Population A Ref Allele Alt Allele High expression Low expression Then all the variations that is population specific would be under significant association! (up to 10000+) 3/17/2025 2

Stratification Correction Options Matched case and control association Not possible in eQTL studies Remove samples? hidden relatedness, sub-population structures, reduced statistical power PCA based association studies (after 2007) Not enough for complicated population structures Linear Mixed Models (pioneer paper on 2007, simplified but still under extensive computation) 3/17/2025 3

A Simple Linear Mixed Model y Log(gene expression) Parameters for eQTL studies x Genotype info z Indicator function for population y = bx +b1z1+b2z2+e Fixed coefficient to be estimated Random variables Assumptions: o Genotype effect is fixed across all populations o b1 and b2 are multivariable normally distributed, basically we are assuming different intercept for different population groups to control population difference o is the i.i.d. random variables for the error items o To test whether =0 or not e 3/17/2025 4

Challenges at first glance How many populations could we assume? Dimension of z equal to # of samples (Different from the Lobster eQTLs where just 2 groups are used) Computational Burden Large Matrix inversion during Newton-Raphson Method SVD decomposition for the matrix inversion steps with predefined relatedness matrix estimation Relatedness Matrix Computation use the common SNPs to calculate the matrix (tentative, suggested) 3/17/2025 5

The non SNV variants overview - length 0.5 0.4 count percent 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 20 70 120 170 500 1500 3500 5500 7500 9500 variant length region 2000 1500 count 1000 500 0 70 120 170 500 1500 2500 3500 4500 5500 6500 7500 8500 9500 variant length region 3/17/2025 6

The non SNV variants overview - missingness Histogram of impute[len <= 10] 4e+05 impute percent 2e+05 0e+00 0.0 0.2 0.4 0.6 0.8 1.0 impute[len <= 10] High Missingness != rare, since missingness = uncertein due to coverage or other issue Around half of the variants have imputation rate > 0.15, which are not believable for further association test (although can be used anyway) Somehow: the length>500 variants all with imputation rate = 0.128 (need to be checked up later) Longer variants are supposed to have larger number of missingness 3/17/2025 7

The non SNV variants overview rare alleles Larger SVs are usually rare (even after ignoring of missingness), how to do the association study? (collapsed tests?) 3/17/2025 8

Current Scheme Relatedness matrix Search all SNVs Require imputation rate < 0.7 (probably too high , would decrease) Require MAF >= 0.05, common SNP definition Centralized covariant matrix used SVs used Search all non-SNV variants Just use genotype for association Imputation rate filter: <0.70 MAF filter: >=0.05 Cis-element association: for each gene search the region within up and downstream 100kbp (and inside gene body and introns) BH correction for P values 3/17/2025 9

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Next Step Reliable SV calls (other than phase 1 data?) Missingness: no way to avoid, just remove some or directly use anything from imputation Rare variants: pooled regression within a whole region Repressor used? SV length as x? not a good option for longer SVs Functional impact score? Max/average/impact score, such as single base resolution Funseq scores? Model comparison: before and after the stratification correction 3/17/2025 11