Integrating multiple Omics from GBM data

The following scripts illustrate how to implement the models presented in Bernal Rubio et al., G3, 2018, the scripts are also provided at: https://github.com/anainesvs/BERNAL_RUBIO_etal_G3_2018, please refer to that webpage for updates.

Contact: avazquez@msu.edu Contact: jlbernalr@gmail.com

(1) Installing BGLR

The code below illustrates how to install and load the necessary package from CRAN using install.packages().

   install.packages(pkg='BGLR')    # install BGLR
   library(BGLR); 

(2) Loading data

• XF: a matrix containing age at the moment of diagnosis (years), gender (0/1 is female, or not), race (0/1 is white, or not).
• X.ge: a matrix for gene expression.
• X.meth: a matrix for methylation values at various CpG sites.
• X.cnv: a matrix of mean CNV intensity per gene.
• y: a matrix with 4 columns. The first column 'time' is the time to last follow up or event, columns 2 and 3 are variables a and b required by BGLR to analyze censored data ( description of this analysis on BGLR can be found on https://cran.r-project.org/web/packages/BGLR/vignettes/BGLR-extdoc.pdf. Finally, the column 4 ('status 4 months') is an indicator variable (0/1) with 0 indicating whether the patient is alive at the 5th month after diagnosis.
• batch: A vector containing gene expression batch by subject.
• folds: A vector containing fold numbers (1 and 2) for cross validations. The two folds are balanced, so they have the same proportions of dead/alive individuals.

After downloading, files can be loaded into R with:

  load('GBM_DATA.rda')
  #Checking files present and dimensions
  ls()
  #[1] "X.ge"   "X.meth" "X.cnv"  "XF"     "y"   "batch" "folds"
  

(3) Pre-adjust gene expression matrix by batch

In this section we show how to pre-correct the incidence matrix corresponding to gene expression by batch effects using mixed models. The input used is the matrix "X.ge" centered and scaled, and the batch code for each sample. Using a linear mixed model, the pre-correction regresses each column of the X.ge matrix into the corresponding batch effect, assuming them as random effects.

p <- ncol(X.ge)
#Load library lme4 to fit a linear mixed model
library(lme4)
for(j in 1:p) {
  tmp <- !is.na(X.ge[, j])
  cat("Column =",j,"of",p,".\n")
  X.ge[tmp, j] <- residuals(lmer(X.ge[tmp, j] ~ 1 | batch[tmp]))
}
#Center and scaling X.ge columns.
X.ge <- scale(X.ge, scale=TRUE, center=TRUE) 

(4) Computing similarity matrices

Some of the models fitted in the study use similarity matrices of the form G=XX' computed from omics. The following code illustrates how to compute this matrix for SNP genotypes. A similar code could be used to compute a G-matrix for methylation or other omics.

   #Check https://stackoverflow.com/questions/32675820/how-to-handle-missing-values-in-crossprod-in-r
   tcrossprod.na <- function(x, val=0) tcrossprod(replace(x, is.na(x), val)) 
   #Computing a similarity matrix for SNP genotypes
   X.meth_sc<- scale(X.meth, scale=TRUE, center=TRUE) #centering and scaling
   G.meth<-tcrossprod.na(X.meth_sc)  #computing crossproductcts
   G.meth<-G.meth/mean(diag(G.meth))  #scales to an average diagonal value of 1.
   
   #The same procedure was followed for other omics.

NOTE: for larger data sets it may be more convinient to use the getG() function available in BGData R-package. This function allows computing G without loading all the data in RAM and offers methods for multi-core computing.

(5) Obtaining principal components (e.g., Methylation)

The following code shows how to obtain the PC for the methylation data. Same approach can be applied to additional omics.

   #Gmeth has been obtained as described in previous section
   EVD<-eigen(G.meth,symmetric=TRUE)
   tmp <- EVD$values >  1e-04
   pc.meth <- EVD$vectors[,tmp] %*% diag(sqrt(EVD$values[tmp]))
   rownames(pc.meth) <- rownames(G.meth)
   colnames(pc.meth) <- paste0("PC",1:ncol(pc.meth))

(6) Variance explained by omics

The following code illustrates how to use BGLR to fit mixed effects models.Predictors are given to BGLR in the form a two-level list. The argument save_at can be used to provide a path and a pre-fix to be added to the files saved by BGLR. For further details see [Perez-Rodriguez and de los Campos, Genetics, 2014] (http://www.genetics.org/content/genetics/198/2/483.full.pdf). The code also shows how to retrieve posterior quantities. In the examples below, we fit the model using the default number of iterations (1,500) and burn-in (500). In practice, longer chains are needed. The user can increase the number of iterations or the burn-in using the arguments nIter and burnIn of BGLR.

   ### Inputs: XF, pc.meth and y
   ETA.cov_meth<-list(cov = list(X = scale(XF), model = 'FIXED'),
                      meth = list(X = pc.meth, model = "BRR"))
   # Fitting the model
   fm.meth <- BGLR(y = y[,"time"], a=y[,"a"], b=y[,"b"], ETA=ETA.cov_meth, saveAt="Example_")
   # Retrieving posterior variances
   var.meth <- fm.meth$ETA$meth$varB
   var.error <- fm.meth$varE

   ### Inputs: XF, G.meth, G.ge and y
   ETA.cov_meth_ge <- ETA.cov_meth
   ETA.cov_meth_ge$ge <- list(X = pc.ge, model = "BRR")
   # Fitting the model
   fm.meth_ge <- BGLR(y = y[,"time"], a=y[,"a"], b=y[,"b"], ETA=ETA.cov_meth_ge, saveAt="Example2_")
   # Retrieving posterior variances
   var.meth <- fm.meth_ge$ETA$meth$varB
   var.ge <- fm.meth_ge$ETA$ge$varB
   var.error <- fm.meth_ge$varE

(7) Evaluating prediction accuracy.

The following code illustrates how to use BGLR to calculate prediction accuracy of omic models. Note that in Bernal-Rubio et al 2018, AUC was calculated by estimating the proportion of deaths at different time points, equivalent to every month after diagnosis (e.g. month 1 after diagnosis, month 2 after diagnosis, ...). Below is an example for month 5 after the diagnosis (vital status available in y[, 4]).

The following illustrates how to select a validation set using the model covariates+methylation as example.

#Installing and loading library pROC to compute Area Under the ROC Curve.
install.packages(pkg='pROC')    # install pROC
library(pROC)
n <- nrow(y)
status.5months <- y[, "status 5 months"]

# Cross-validation.
yNA <- y[, "time"]
aNA <- y[,"a"]
yNA[folds == 1] <- NA
aNA[folds == 1] <- -300

# Fit the model only in the training set.
fm.meth <- BGLR(y=yNA,a=aNA,b=y[,"b"],ETA=ETA.cov_meth,saveAt="Example3_")

# Storing predictions.
pred <- fm.meth$yHat[folds == 1]

# Estimate AUC
AUC <- auc(status.5months[folds == 1], pred)

# For the first individual, area under the standard normal curve (CDF) 
# of estimated y from full model:
pnorm(fm.meth$yHat[1])