mcgml / QUAIL

A unified framework to estimate genetic effects on the variance of quantitative traits

QUAIL: a unified framework to estimate genetic effects on the variance of quantitative traits

Introduction

QUAIL (quantile integral linear model) is a quantile regression-based framework to estimate genetic effects on the variance of quantitative traits. QUAIL can be used in

• Genome-wide vQTL analysis - QUAIL constructs a quantile integral phenotype which aggregates information from all quantile levels, and only requires fitting two linear regressions per SNP in genome-wide analysis.
• Evaluating the vPGS performance - QUAIL can be extended to continuous predictors such as vPGS and quantify the performance of vPGS in predicting the phenotypic variability.

Updates

• Feb 25, 2022: Add the dispersion effects.
• Jan 13, 2022: Add the test data part.
• Apr 13, 2021: Initial release. Release the codes for Genome-wide vQTL analysis and evaluating the vPGS performance.

Prerequisites

The software is developed using R and tested in Linux environments. The statistical computing software R (>=3.5.1) and the following R packages are required:

• data.table (>=1.11.8)
• optparse (>=1.6.6)
• quantreg (>=5.85)
• parallel (>=3.5.1)
• BEDMatrix (>=2.0.3)

Download QUAIL

You can download QUAIL by:

$ git clone https://github.com/qlu-lab/QUAIL
$ cd ./QUAIL

Input Data Format

Phenotype file

The input phenotype file need to be an n x 3 table, where n is the sample size. The columns in order are the FID, IID, and the phenotype. Here is an example of the phenotype file pheno.txt:

FID	IID	bmi
1	1	31.0920070855422
2	2	34.9722947258896
3	3	26.651358296193
4	4	11.3265202767703
5	5	28.1784063613473
...
...

Covariate file

The input Covariate file needs to be an n x (m+2) table, where m is the number of covariates to include. The columns in order are the FID, IID, and the covariates. Here is an example of the covariate file covar.txt:

FID	IID	sex	age	pc1
1	1	0	40	0.0496566810517587
2	2	1	41	-0.30689382604118
3	3	1	42	0.0662231532694345
4	4	0	43	0.653681021333332
5	5	1	44	0.50856163868585
...
...

Genotype file

The input genotype file needs to be in the plink bed/bim/fam format. The path only includes the prefix, not the suffix. For example, the path to the input genotype file is geno where the genotype files are geno.bed, geno.bim, geno.fam.

vPGS file

The input vPGS file needs to be an n x 3 table, where n is the sample size. The columns in order are the FID, IID, and the vPGS. Here is an example of the vPGS file vpgs.txt:

FID	IID	vpgs
1000	1000	-0.166044638683817
1001	1001	0.325459663014065
1002	1002	-0.0589986740920006
1003	1003	0.176636938025438
1004	1004	0.266151552296392
1005	1005	0.376450240002708
...
...

Genome-wide vQTL analysis

There are two steps to conduct the Genome-wide vQTL analysis:

Step1: Obtain the quantile integrated rank score

Example:

The following script transform the phenotype in pheno.txt into the quantile integrated rank score using 2000 quantile levels. It adjusted the covaraites in covar.txt and 5 cores are used for parallel computing. The output phenotypic rank score file will be written to pheno_rank_score.txt.

Rscript Obtain_Rank_Score.R \
  --pheno pheno.txt \
  --covar covar.txt \
  --output pheno_rank_score.txt \
  --num_levels 2000 \
  --num_cores 5

where the inputs are

Flag	Description
pheno	The path to the phenotype file
covar	The path to the covariate file
output	The path to the output phenotypic rank score file
num_levels	Number of quantile levels to fit
num_cores	Number of cores for parallel computing

Step2: Perform genome-wide vQTL analysis

Example:

The following script perform genome-wide vQTL analysis from the 1-1000 SNPs in plink genotype file geno using output of quantile integrated rank score in step1 pheno_rank_score.txt. This analysis adjusted the covaraites in covar.txt and 5 cores are used for parallel computing.

Rscript QUAIL_vQTL.R \
  --pheno_rs pheno_rank_score.txt \
  --geno geno \
  --covar covar.txt \
  --output output_1-100.txt \
  --num_cores 5 \
  --start 1 \
  --end 1000

where the inputs are

Flag	Description
pheno_rs	The path to output phenotypic rank score file from step1
geno	The path of the genotype file following the PLINK format.
covar	The path to the covariate file
output	The path to the output summary statistics file
num_cores	Number of cores for parallel computing
start	(Optional) Index of SNP that starts computing
end	(Optional) Index of SNP that ends computing

Note that

• For both genotype vQTL analysis and vPGS analysis(described following), the --num_levels depends on the sample size in the analytic sample. We recommend using 500 levels when the sample size is around 10000 and 2000 levels when the sample size > 10000. However, you can check the robustness of your results by using more levels.

• The script is designed to run on chromosome segments to facilitate parallel computation on the cluster. If --start or --end is not specified, the script will perform the analysis on all SNPs in the plink test file.

Explanation of Output

The final result has the following fields:

Column	Description
CHR	Chromosome
SNP	rs ID
BP	Base pair position
A1	Allele 1 (effect allele)
A2	Allele 2 (non-effect allele)
FREQ	allele frequency of allele 1
BETA	The estimated effect size
SE	The estimated standard error of BETA
P	The P-value for testing variance effects
N	Sample size

Note that the BETA in the output of QUAIL is the standardized effect size. You can calculate the allele effect size by BETA_allele = BETA/sqrt(2 * FREQ * (1-FREQ)), where BETA and FREQ come from the output of QUAIL.

Evaluate the predictive performance of vPGS

Example:

The following script evaluate the performance of vPGS from the test.all.score in predicting the variability of phenotype from pheno.txt using 500 quantile levels. The analysis adjusted the covaraites in covar.txt and 5 cores are used for parallel computing. The performance is written out to output_vpgs.txt.

Rscript QUAIL_vPGS.R \
  --pheno pheno.txt \
  --vpgs  vpgs.txt \
  --covar covar.txt \
  --output output_vpgs.txt \
  --num_levels 500 \
  --num_cores 5

Note that

• The choice of --num_levels can be found in the Genome-wide vQTL analysis part.

The final result has the following fields:

Column	Description
BETA	The estimated effect size of vPGS to phenotypic variability
SE	The estimated standard error of BETA
P	The P-value for testing variance effects for vPGS
N	Sample size

Test data

The test data is randomly generated. Here is an example to use the test data:

cd ./QUAIL
Rscript Obtain_Rank_Score.R \
  --pheno ./test_data/pheno_test.txt \
  --covar ./test_data/covar_test.txt \
  --output pheno_rank_score.txt \
  --num_levels 2000 \
  --num_cores 5

Citation

If you use QUAIL, please cite

Miao, J., Lin, Y., Wu, Y., Zheng, B., Schmitz, L. L., Fletcher, J. M., & Lu, Q. (2021). A quantile integral linear model to quantify genetic effects on phenotypic variability. bioRxiv, 2021.2004.2014.439847

License

All rights reserved for Lu-Laboratory