We used a DGLM (3335) to simulate the phenotype based on two models with simulated SNP data in a sample of 10,000 individuals, i.e., a single-SNP model and multiple-SNP model with two covariates (i.e., age and sex). The single-SNP model can be written asy=wβg+e with log(σe2)=wϕg+log(σ2)and the multiple-SNP model can be expressed asy=Σj=1lcjβcj+Σk=1mwkβgk+e with log(σe2)=Σj=1lcjϕcj+Σk=1mwkϕgk+log(σ2)where y is a simulated phenotype; w or wk is a standardized SNP genotype, i.e., w=(x2f)/2f(1f), with x being the genotype indicator variable coded as 0, 1, or 2, generated from binomial(2, f) and f being the MAF generated from uniform(0.01, 0.5); cj is a standardized covariate with c1 (sex) generated from binomial(1, 0.5) and c2 (age) generated from uniform(20, 60); e is an error term with mean 0 and variance σe2. To simulate the error term with different levels of skewness and kurtosis, we generated e from five different distributions, including normal distribution, t-distribution with df = 10 or 3, and χ2 distribution with df = 15 or 1. β (ϕ) is the effect on mean (variance) generated from N(0,1) if exists, 0 otherwise. Log(σ2) is the intercept of the second linear model, which was set to 0. We rescaled the different components to control the variance explained, i.e., 0.1 and 0.9 for the genotype component and error term, respectively, in the single-SNP model, and 0.2, 0.4, and 0.4 for the covariate component, genotype component, and error term, respectively, in the multiple-SNP model. We simulated the SNP effects in four different scenarios: (i) effect on neither mean nor variance (nei), (ii) effect on mean only (mean), (iii) effect on variance only (var), or (iv) effect on both mean and variance (both). We simulated only one causal SNP in the single-SNP model and 4, 40, or 80 causal SNPs in the multiple-SNP model.

We performed vQTL analyses using the simulated phenotype and SNP data to compare four vQTL methods, including the Bartlett’s test (29), the Levene’s test (31), the FK test (32), and the DGLM (note S2). We also performed the Levene’s test with six phenotype process strategies, including raw phenotype (raw), raw phenotype adjusted for covariates (adj), RINT after adj (rint) (note S3), logarithm transformation after adj (log), square transformation after adj (sq), and cube transformation after adj (cub). We repeated the simulation 1000 times and calculated the FPR and power at P < 0.05 at a single-SNP level.

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