Contents

1 Introduction

RaMWAS provides a complete toolset for methylome-wide association studies (MWAS). It is primarily designed for data from enrichment-based methylation assays, but can be applied to other methylomic data (e.g. Illumina methylation array) as well as other data types like gene expression and genotype data (see vignette).

RaMWAS includes the following major components (steps):

  1. Scanning aligned reads from BAM files.
  2. Calculation of quality control (QC) measures, aggregate QC plots, fragment size distribution estimation.
  3. Creation of CpG score (coverage) matrix, sample normalization.
  4. Principal component analysis.
  5. Methylome-wide association study (MWAS).
  6. Annotation of top findings using the BioMart database.
  7. Multi-marker analysis (methylation risk score) using elastic net.
  8. MWAS with correction for effect of SNPs.

Most steps of RaMWAS are internally parallelized. This is made possible, in part, by the use of the filematrix package for storing the data and accessing it in parallel jobs.

2 Getting started

2.1 Installation

To install the most recent version of RaMWAS please follow instructions at GitHub.com (R 3.3 or newer required).
To install the Bioconductor version of RaMWAS (R 3.4 or newer requred) use the following commands:

## try http:// if https:// URLs are not supported
if (!requireNamespace("BiocManager", quietly=TRUE))
    install.packages("BiocManager")
BiocManager::install("ramwas")

2.2 Loading package and viewing documentation

The package vignettes and reference manual can be viewed online and with the following commands.

library(ramwas) # Loads the package
browseVignettes("ramwas") # Opens vignettes
help(package = "ramwas") # Lists package functions

3 RaMWAS steps

Pipeline Workflow
Pipeline Workflow

To illustrate the main steps of RaMWAS we first create an artificial data set.

library(ramwas)
dr = paste0(tempdir(), "/simulated_project")
ramwas0createArtificialData(
            dir = dr,
            nsamples = 20,
            nreads = 100e3,
            ncpgs = 25e3,
            threads = 2)
cat("Project directory:", dr)
## Project directory: /tmp/Rtmpvc8i5f/simulated_project

Note. The project directory dr can be set to a more convenient location when running the code.

The function ramwas0createArtificialData created the following files and subdirectories in the project directory.

Each RaMWAS step accepts parameters in the form of a list. Here is the parameter set we will use for all steps below.

param = ramwasParameters(
    dirproject = dr,
    dirbam = "bams",
    filebamlist = "bam_list.txt",
    filecpgset = "Simulated_chromosome.rds",
    cputhreads = 2,
    scoretag = "MAPQ",
    minscore = 4,
    minfragmentsize = 50,
    maxfragmentsize = 250,
    minavgcpgcoverage = 0.3,
    minnonzerosamples = 0.3,
    filecovariates = "covariates.txt",
    modelcovariates = NULL,
    modeloutcome = "age",
    modelPCs = 0,
    toppvthreshold = 1e-5,
    bihost = "grch37.ensembl.org",
    bimart = "ENSEMBL_MART_ENSEMBL",
    bidataset = "hsapiens_gene_ensembl",
    biattributes = c("hgnc_symbol","entrezgene","strand"),
    bifilters = list(with_hgnc_trans_name = TRUE),
    biflank = 0,
    cvnfolds = 5,
    mmalpha = 0,
    mmncpgs = c(5, 10, 50, 100, 500, 1000, 2000)
)

We describe the role of each parameter as they are used below. The complete description of all RaMWAS parameters is available in the parameter vignette.

3.1 Scan BAM files and calculate QC indices

This step scans all BAM files listed in the filebamlist file, it records read start locations, and calculates a number of quality control metrics. The BAMs must be located in dirbam directory.

Reads are filtered by the scoretag parameter, which is usually either the “MAPQ” field or “AS” tag in the BAM file (see BAM file format). Reads with scores below minscore are excluded.

The minfragmentsize and maxfragmentsize parameters define the minimum and maximum size of DNA fragments that were sequenced. Please note, these parameters are not equal to the read length but instead reflect the length of the DNA fragments that were extracted and sequenced.

The set of CpGs is loaded from the filecpgset file. For more information see the CpG set vignette.

RaMWAS uses cputhreads CPU cores (parallel jobs) to scan BAMs. Hard disk speed can be a bottleneck for this step. If BAMs are stored on a single rotational hard drive, using more than 4 parallel jobs may not provide further speed improvements.

ramwas1scanBams(param)

This creates the following subdirectories in the project directory:

  • qc – directory with a number of quality control (QC) plots, one plot per QC metrix per BAM.
    For more information see BAM QC vignette.
    • edit_distance – plots showing distribution of edit distance, i.e. number of mismatches between the aligned read and the reference genome.
    • isolated_distance – plots showing distribution of distances from read starts to isolated CpGs.
      The CpGs are called isolated if they are located at least maxfragmentsize basepairs away from any other CpG.
      The distribution of reads around these CpGs is used later for estimation of fragment size distribution.
    • matched_length – plots showing distribution of the length of the reads aligned to the reference genome.
    • score – plots showing distribution of the score (scoretag parameter).
    • coverage_by_density – plots showing average CpG score (coverage) as a function of CpG density.
      These plots illustrate the performance of the enrichment protocol. It is a sign of a stable protocol if the shape of these plots is the same across BAMs.
  • rds_rbam and rds_qc – directories with RaMWAS BAM info files (BAM read start locations) and BAM quality control metrics, one RDS file per BAM.

Here is a coverage_by_density plot for the simulated data. It shows higher average CpG score (fragment coverage) for regions with higher CpG densities, up to the saturation point.

pfull = parameterPreprocess(param)
qc = readRDS(paste0(pfull$dirrqc, "/BAM007.qc.rds"))
plot(qc$qc$avg.coverage.by.density)

Note. If a BAM file has previously been scanned, it will not be scanned again in subsequent calls of ramwas1scanBams. This way Step 1 can be rerun multiple times to efficiently include additional BAMs (samples) when they become available.
Note. The BAM files are no longer needed after this step and the RaMWAS BAM info files are 50 to 100 times smaller than the original BAMs.

3.2 Summarize QC measures

This step aggregates quality control metrics across all scanned BAM files, produces a number of summary plots and tables, and estimates fragment size distribution.

In practice, multiple BAM files may correspond to the same sample. For simplicity, in the example here each BAM corresponds to one sample with the same name. RaMWAS can be instructed about BAM to sample correspondence via filebam2sample or bam2sample parameters (See parameter vignette).

ramwas2collectqc(param)

The following files and directories are created in the project directory:

  • Fragment_size_distribution.txt – text file with estimated fragment size distribution.
  • qc/Fragment_size_distribution_estimate.pdf – plot showing both estimated fragment size distribution and the distribution of distances from read starts to isolated CpGs.
  • Four sub-directories in the “qc” directory
    • summary_bams – by BAMs.
      This information can be used to exclude BAMs that fail selected QC criteria.
    • summary_bams_in_bam2sample – by BAMs, but only those listed in filebam2sample parameter.
      This information can be used to confirm that all BAMs that did not pass QC are no longer used in further analyses.
    • summary_by_sample – by sample.
      Slightly different QC criteria can be applied on sample level. For example, samples with low number of total reads can be excluded.
    • summary_total – total across all BAMs.
      This information presents the project summary of all BAMs in filebam2sample.
  • The directories listed above contain
    • Summary_QC.txt – table with a number of numerical QC measures, in an Excel friendly format.
    • Summary_QC_R.txt – table with a number of numerical QC measures, in an R friendly format.
    • qclist.rds – an R file with list of QC objects.
    • Fig_hist_*.pdf – histograms of several QC measures across samples.
    • Fig_*.pdf – PDF files with various QC plots, one page per BAM or sample, depending on the directory.

After exclusion of BAMs and samples not passing QC, step 2 should be rerun. This ensures that fragment size distribution is estimated using selected data only.

The fragment size distribution estimation plot is presented below. The points indicate the number of reads (y-axis) observed at varying distances from isolated CpGs (x-axis). The red line is the parametic fit for these points. For more information on estimation of fragment size distribution see (Oord et al. 2013).

qc = readRDS(paste0(pfull$dirqc, "/summary_total/qclist.rds"))
frdata = qc$total$hist.isolated.dist1
estimate = as.double(readLines(
    con = paste0(pfull$dirproject,"/Fragment_size_distribution.txt")))
plotFragmentSizeDistributionEstimate(frdata, estimate)

3.3 Calculate CpG score matrix

This step creates a CpG score matrix (a.k.a. fragment coverage matrix) for all samples and all CpGs in the CpG set. The samples are defined by either filebam2sample or bam2sample parameter. The CpGs are defined by the filecpgset parameter, see CpG set vignette for more information.

RaMWAS can filter out CpGs with low scores. These CpGs are unmethylated and are unlikely to produce any findings. A CpG is preserved if

  • CpG has average equal or greater than the threshold minavgcpgcoverage (default is 0.3).
  • CpG has at least minnonzerosamples proportion of samples with nonzero coverage
    (default is 0.3, i.e. a CpG is preserved if at least 30% of samples have non-zero coverage).

For each sample, the CpG scores are affected by the number of sequenced DNA fragments, which varies from sample to sample. To remove this variation, the CpG score matrix is normalized to have the same average score for each sample.

ramwas3normalizedCoverage(param)

This step a new creates directory named coverage_norm_X in the project directory (X is the number of samples, see Directory names) with the following files:

  • Coverage.* – filematrix with the CpG scores for all samples and all CpGs that passed the filtering.
    Each row has coverage for a single sample.
    Each column has coverage for a single CpG.
    See filematrix package for format details.
  • CpG_locations.* – filematrix with the location of the CpGs that passed the threshold.
    It has two columns – chr and position.
  • CpG_chromosome_names.txt – file with chromosome names (factor levels) for the integer column chr in CpG_locations.* filematrix.
  • raw_sample_sums.* – filematrix with total coverage for each sample before normalization.

Note. This step created temporary files in the dirtemp directory.

3.4 Principal component analysis

This step performs principal component analysis (PCA) on the CpG score matrix.

PCA is capturing the main directions of unmeasured sources of variation in the data. The main goal of PCA is estimation of laboratory technical variations which can be used as covariates in the association analyses. PCA can be performed after regressing out known covariates as they represent measured sources of variation, which we need not estimate.

Additionally, large sample loadings of the top PCs can indicate multidimensional outlying samples. Such sample may be excluded from the analysis.

If measured covariates are regressed out prior to conducting the PCA, these covariates are loaded from the file filecovariates. The file can be comma or tab-separated, with sample names in the first column. The artificial data set includes a covariate file covariates.txt.

The parameter modelcovariates names the covariates regressed out before PCA (NULL for none).

ramwas4PCA(param)

This step creates sub-directory PCA_X_cvrts_Y in the directory with score matrix, where X is the number of covariates regressed out and Y is a code distinguishing different sets with the same number of covariates (see Directory names). The sub-directory includes:

  • covmat.*, eigenvalues.*, and eigenvectors.* – filematrices with the sample covariance matrix and its eigenvalue decomposition.
  • PC_values.txt – principal components scores.
  • PC_loadings.txt – sample loadings for the top 20 PCs.
  • PC_plot_covariates_removed.pdf – plots of principal components scores (i.e. % variance explained on page 1) and sample loadings for the top 40 PCs (pages 2+).
  • PC_vs_covariates_corr.txt – correlations of principal components with phenotypes/covariates (from filecovariates file).
  • PC_vs_covariates_pvalue.txt – p-values for these correlations.

The PC plot for artificial data shows one strong component and no outliers in the sample loadings, with first PC clearly capturing sample sex.

eigenvalues = fm.load(paste0(pfull$dirpca, "/eigenvalues"));
eigenvectors = fm.open(
                filenamebase = paste0(pfull$dirpca, "/eigenvectors"),
                readonly = TRUE);
plotPCvalues(eigenvalues)

plotPCvectors(eigenvectors[,1], 1)

plotPCvectors(eigenvectors[,2], 2)

close(eigenvectors)

The file with correlations shows strong correlation of the top PCs with age and sex.

tblcr = read.table(
            file = paste0(pfull$dirpca, "/PC_vs_covs_corr.txt"),
            header = TRUE,
            sep = "\t")
pander(head(tblcr, 3))
name age sex
PC1 -0.28 0.997
PC2 0.723 0.0335
PC3 -0.184 0.0281

The file with p-values indicate statistical significance of these correlations.

Table: Correlations in PC_vs_covariates_corr.txt file.

tblpv = read.table(
            file = paste0(pfull$dirpca, "/PC_vs_covs_pvalue.txt"),
            header = TRUE,
            sep = "\t")
pander(head(tblpv, 3))
P-values in PC_vs_covariates_pvalue.txt file.
name age sex
PC1 0.231 1.62e-21
PC2 0.000319 0.889
PC3 0.437 0.906

3.5 Methylome-wide association study (MWAS)

This step performs tests for association between normalized CpG scores and the outcome variable named by modeloutcome parameter. The analysis corrects for covariates listed in modelcovariates parameter and a number of top principal components (modelPCs). Tests are performed using the linear regression model if the outcome variable is numeric, ANOVA if categorical.

All results are saved in a filematrix. Findings passing the toppvthreshold p-value threshold are recorded in a text file.

ramwas5MWAS(param)

This step creates a sub-directory in the PCA directory named Testing_X_Y_PCs, where X is the name of the outcome variable and Y is the number of top PCs included as covariates (see Directory names). The sub-directory includes:

  • QQ_plot.pdf – QQ-plot with a confidence band and inflation factor lambda (median of the chi-squared test statistics divided by the expected median of the chi-squared distribution under null).
  • Top_tests.txt – text file with the top findings.
  • Stats_and_pvalues.* – filematrix with MWAS results. The columns include test statistic, p-value, and q-value (calculated using Benjamini-Hochberg Procedure (Benjamini and Hochberg 1995)). The rows match the CpGs of the coverage matrix.
  • DegreesOfFreedom.txt – file with the numbers of degrees of freedom for the t- or F test used for testing.

For the simulated data the QQ-plot for age shows moderate deviation from the diagonal for many CpGs, suggesting many markers with small effects. This is consistent with how the data was generated – there is weak signal in 1% of CpGs.

RaMWAS also creates a Manhattan plot with matching Y axis.

mwas = getMWASandLocations(param)
layout(matrix(c(1,2), 1, 2, byrow = TRUE), widths=c(1,2.2))
qqPlotFast(mwas$`p-value`)
man = manPlotPrepare(
        pvalues = mwas$`p-value`,
        chr = mwas$chr,
        pos = mwas$start,
        chrmargins = 0)
manPlotFast(man)

3.6 Annotation of top results

RaMWAS can annotate top findings using data from biomaRt.

The parameters include:

  • bihost – biomart host site.
  • bimart – BioMart database name.
  • bidataset – data set.
  • biattributes – are attributes of interest.
  • bifilters – list of filters (if any).
  • biflank – indicates the maximum allowed distance from the CpG to the annotation element.

For detailed description of these parameters and R script for listing allowed values see parameter vignette

Here we annotate top findings with human gene symbols, gene ids, and strand information.

ramwas6annotateTopFindings(param)

The function updates the Top_tests.txt file in the MWAS directory.

Example of the Top_tests.txt file.
chr position tstat pvalue qvalue hgnc_symbol entrezgene strand
chr1 15,975,530 8.771 6.446x10-8 0.022 DDI2/DDI2 84301/6248 1/1
chr1 15,975,533 8.568 9.097x10-8 0.022 DDI2/DDI2 84301/6248 1/1
chr1 15,418,248 -7.654 4.571x10-7 0.071 KAZN 23254 1

3.7 Methylation risk score

While it is important to find individual CpGs associated with a phenotype, we can often achieve better predictive power by combining information from multiple CpGs.

We take an approach similar to the one proposed by (Horvath 2013) for predicting biological age from methylation data. In particular, we combine signal across multiple CpGs using the elastic net model (Tibshirani et al. 2012). To avoid overfitting and correctly estimate the predictive power of the model we use k-fold cross-validation. Within the cross-validation procedure, for each training set of samples we perform MWAS, select top MWAS sites, train the elastic net, and make predictions for the test samples. The set of predictions is recorded as the MRS.

RaMWAS predicts the outcome variable (modeloutcomes parameter) using top mmncpgs CpGs from the MWAS on the training set of samples. If mmncpgs is a vector of several values, each number of CpGs is tested separately.

The elastic net parameter alpha can be set via mmalpha parameter. The number of folds cvnfolds in the K-fold cross validation is 10 by default.

ramwas7riskScoreCV(param)

This step creates CV_X_folds sub-directory in MWAS directory, where X is the number of folds in k-fold cross validation (see Directory names). It contains:

  • fold_* – directories with MWAS on 90% of the data, each with different 10% of the samples excluded from the analysis.
    Samples with missing (NA) outcome variable are not included in these MWAS.
  • MMCVN_prediction_folds=10_CpGs=*.txt – table with true outcome and cross-validation prediction.
  • MMCVN_prediction_folds=10_CpGs=*.pdf – scatter-plot of true outcome vs. cross-validation prediction.
  • Prediction_alpha=0.000000.pdf – scatter plot of outcome-prediction correlations as a function of the number of CpGs used for prediction.

For the simulated data we get moderately good prediction using just 50 top CpGs.

cv = readRDS(paste0(pfull$dircv, "/rds/CpGs=000050_alpha=0.000000.rds"))
plotPrediction(
        param = pfull,
        outcome = cv$outcome,
        forecast = cv$forecast,
        cpgs2use = 50,
        main = "Prediction success (EN on coverage)")

The correlation of prediction with actual age is maximal when we use 100 top CpGs in elastic net.

cl = readRDS(sprintf("%s/rds/cor_data_alpha=%f.rds",
                    pfull$dircv,
                    pfull$mmalpha))
plotCVcors(cl, pfull)

3.8 CpG-SNP analysis

Point mutated CpG sites, called CpG-SNPs (Shoemaker et al. 2010), are interesting sites for human diseases because in addition to the sequence variation they may show individual differences in DNA methylation. RaMWAS can perform CpG-SNP analyses if SNP data from the same subjects/samples is also available. These tests are performed using a regression model that assesses whether the case-control differences are proportional to the number of CpG sites (Oord et al. 2015).

This type of analysis is explained in the CpG-SNP vignette.

4 Directory names

The names of CpG score/PCA/MWAS/MRS directories can be recovered by first calling parameterPreprocess function.

pfull = parameterPreprocess(param)
cat("CpG score directory:", "\n", pfull$dircoveragenorm,"\n")
## CpG score directory: 
##  /tmp/Rtmpvc8i5f/simulated_project/coverage_norm_20
cat("PCA directory:", "\n", pfull$dirpca, "\n")
## PCA directory: 
##  /tmp/Rtmpvc8i5f/simulated_project/coverage_norm_20/PCA_00_cvrts
cat("MWAS directory:", "\n", pfull$dirmwas, "\n")
## MWAS directory: 
##  /tmp/Rtmpvc8i5f/simulated_project/coverage_norm_20/PCA_00_cvrts/Testing_age_0_PCs
cat("MRS directory:", "\n", pfull$dircv, "\n")
## MRS directory: 
##  /tmp/Rtmpvc8i5f/simulated_project/coverage_norm_20/PCA_00_cvrts/Testing_age_0_PCs/CV_05_folds
cat("CpG-SNP directory:", "\n", pfull$dirSNPs, "\n")
## CpG-SNP directory: 
##  /tmp/Rtmpvc8i5f/simulated_project/coverage_norm_20/Testing_wSNPs_age_0cvrts_0PCs

5 Version information

sessionInfo()
## R Under development (unstable) (2024-10-21 r87258)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so 
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] ramwas_1.31.0    filematrix_1.3   pander_0.6.5     knitr_1.48      
## [5] BiocStyle_2.35.0
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.1            dplyr_1.1.4                
##  [3] blob_1.2.4                  filelock_1.0.3             
##  [5] Biostrings_2.75.0           bitops_1.0-9               
##  [7] fastmap_1.2.0               BiocFileCache_2.15.0       
##  [9] GenomicAlignments_1.43.0    digest_0.6.37              
## [11] lifecycle_1.0.4             survival_3.7-0             
## [13] KEGGREST_1.47.0             RSQLite_2.3.7              
## [15] magrittr_2.0.3              compiler_4.5.0             
## [17] rlang_1.1.4                 sass_0.4.9                 
## [19] progress_1.2.3              tools_4.5.0                
## [21] utf8_1.2.4                  yaml_2.3.10                
## [23] prettyunits_1.2.0           S4Arrays_1.7.0             
## [25] curl_5.2.3                  bit_4.5.0                  
## [27] DelayedArray_0.33.0         xml2_1.3.6                 
## [29] abind_1.4-8                 BiocParallel_1.41.0        
## [31] KernSmooth_2.23-24          BiocGenerics_0.53.0        
## [33] grid_4.5.0                  stats4_4.5.0               
## [35] fansi_1.0.6                 iterators_1.0.14           
## [37] tinytex_0.53                biomaRt_2.63.0             
## [39] SummarizedExperiment_1.37.0 cli_3.6.3                  
## [41] rmarkdown_2.28              crayon_1.5.3               
## [43] generics_0.1.3              httr_1.4.7                 
## [45] DBI_1.2.3                   cachem_1.1.0               
## [47] stringr_1.5.1               zlibbioc_1.53.0            
## [49] splines_4.5.0               parallel_4.5.0             
## [51] AnnotationDbi_1.69.0        BiocManager_1.30.25        
## [53] XVector_0.47.0              matrixStats_1.4.1          
## [55] vctrs_0.6.5                 glmnet_4.1-8               
## [57] Matrix_1.7-1                jsonlite_1.8.9             
## [59] bookdown_0.41               IRanges_2.41.0             
## [61] hms_1.1.3                   S4Vectors_0.45.0           
## [63] bit64_4.5.2                 magick_2.8.5               
## [65] foreach_1.5.2               jquerylib_0.1.4            
## [67] glue_1.8.0                  codetools_0.2-20           
## [69] stringi_1.8.4               shape_1.4.6.1              
## [71] GenomeInfoDb_1.43.0         GenomicRanges_1.59.0       
## [73] UCSC.utils_1.3.0            tibble_3.2.1               
## [75] pillar_1.9.0                rappdirs_0.3.3             
## [77] htmltools_0.5.8.1           GenomeInfoDbData_1.2.13    
## [79] R6_2.5.1                    dbplyr_2.5.0               
## [81] httr2_1.0.5                 evaluate_1.0.1             
## [83] lattice_0.22-6              Biobase_2.67.0             
## [85] highr_0.11                  png_0.1-8                  
## [87] Rsamtools_2.23.0            memoise_2.0.1              
## [89] bslib_0.8.0                 Rcpp_1.0.13                
## [91] SparseArray_1.7.0           xfun_0.48                  
## [93] MatrixGenerics_1.19.0       pkgconfig_2.0.3

References

Benjamini, Y., and Y. Hochberg. 1995. “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” Journal of the Royal Statistical Society. Series B (Methodological), 289–300.
Horvath, Steve. 2013. “DNA Methylation Age of Human Tissues and Cell Types.” Genome Biology 14 (10): 3156.
Oord, Edwin JCG van den, Jozsef Bukszar, Gábor Rudolf, Srilaxmi Nerella, Joseph L McClay, Lin Y Xie, and Karolina A Aberg. 2013. “Estimation of CpG Coverage in Whole Methylome Next-Generation Sequencing Studies.” BMC Bioinformatics 14 (1): 50.
Oord, Edwin JCG van den, Shaunna L Clark, Lin Ying Xie, Andrey A Shabalin, Mikhail G Dozmorov, Gaurav Kumar, Vladimir I Vladimirov, et al. 2015. “A Whole Methylome CpG-SNP Association Study of Psychosis in Blood and Brain Tissue.” Schizophrenia Bulletin, sbv182.
Shoemaker, Robert, Jie Deng, Wei Wang, and Kun Zhang. 2010. “Allele-Specific Methylation Is Prevalent and Is Contributed by CpG-SNPs in the Human Genome.” Genome Research 20 (7): 883–89.
Tibshirani, Robert, Jacob Bien, Jerome Friedman, Trevor Hastie, Noah Simon, Jonathan Taylor, and Ryan J Tibshirani. 2012. “Strong Rules for Discarding Predictors in Lasso-Type Problems.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74 (2): 245–66.