o2plsda: Omics data integration with o2plsda

Description

o2plsda provides functions to do O2PLS-DA analysis for multiple omics integration.The algorithm came from “O2-PLS, a two-block (X±Y) latent variable regression (LVR) method with an integral OSC filter” which published by Johan Trygg and Svante Wold at 2003. O2PLS is a bidirectional multivariate regression method that aims to separate the covariance between two data sets (it was recently extended to multiple data sets) (Löfstedt and Trygg, 2011; Löfstedt et al., 2012) from the systematic sources of variance being specific for each data set separately. It decomposes the variation of two datasets in three parts:

a joint part that is correlated (predictive) to X and Y (i.e. variation related to both X and Y), denoted as X/Y joint variation in X and Y: TW^⊤ and UC^⊤,
a part contained inside X/Y that is uncorrelated (orthogonal) to X and Y: T_yoscW_yosc^⊤ and U_xoscC_xosc^⊤,
A noise part for X and Y: E_xy and F_yx.

The number of columns in T, U, W and C are denoted by as nc and are referred to as the number of joint components. The number of columns in T_yosc and W_yosc are denoted by as nx and are referred to as the number of X-specific components. Analoguous for Y, where we use ny to denote the number of Y-specific components. The relation between T and U makes the joint part the joint part: U = TB_U + H or U = TB_T′ + H′. The number of components (nc, nx, ny) are chosen beforehand (e.g. with Cross-Validation).

Cross-Validation

In order to avoid overfitting of the model, the optimal number of latent variables for each model structure was estimated using group-balanced Monte Carlo cross-validation (MCCV). The package could use the group information when we select the best parameters with cross-validation. In cross-validation (CV) one minimizes a certain measure of error over some parameters that should be determined a priori. Here, we have three parameters: (nc, nx, ny). A popular measure is the prediction error ||Y − Ŷ||, where Ŷ is a prediction of Y. In our case the O2PLS method is symmetric in X and Y, so we minimize the sum of the prediction errors: ||X − X̂|| + ||Y − Ŷ||.

Here nc should be a positive integer, and nx and ny should be non-negative. The ‘best’ integers are then the minimizers of the prediction error.

The O2PLS-DA analysis was performed as described by Bylesjö et al. (2007); briefly, the O2PLS predictive variation [TW^⊤, UC^⊤] was used for a subsequent O2PLS-DA analysis. The Variable Importance in the Projection (VIP) value was calculated as a weighted sum of the squared correlations between the OPLS-DA components and the original variable.

Installation

install.package("o2plsda")

Examples

library(o2plsda)

## 
## Attaching package: 'o2plsda'

## The following object is masked from 'package:stats':
## 
##     loadings

set.seed(123)
# sample * values
X = matrix(rnorm(5000),50,100)
# sample * values
Y = matrix(rnorm(5000),50,100)
##add sample names
rownames(X) <- paste("S",1:50,sep="")
rownames(Y) <- paste("S",1:50,sep="")
## gene names
colnames(X) <- paste("Gene",1:100,sep="")
colnames(Y) <- paste("Lipid",1:100,sep="")
##scaled
X = scale(X, scale = TRUE)
Y = scale(Y, scale = TRUE)
## group factor could be omitted if you don't have any group 
group <- rep(c("Ctrl","Treat"), each = 25)

Do cross validation with group information

set.seed(123)
## nr_folds : cross validation k-fold (suggest 10)
## ncores : parallel paramaters for large datasets
cv <- o2cv(X,Y,1:5,1:3,1:3, group = group, nr_folds = 10)

## #####################################

## The best parameters are nc = 1, nx = 3, ny = 2

## #####################################

## The the RMSE is: 1.98008867052826

## #####################################

Then we can do the O2PLS analysis with nc = 1, nx = 2, ny =1. You can also select the best parameters by looking at the cross validation results.

fit <- o2pls(X,Y,1,2,1)
summary(fit)

## 
## ######### Summary of the O2PLS results #########
## ### Call o2pls(X, Y, nc= 1 , nx= 2 , ny= 1 ) ###
## ### Total variation 
## ### X: 4900 ; Y: 4900  ###
## ### Total modeled variation ### X: 0.108 ; Y: 0.098  ###
## ### Joint, Orthogonal, Noise (proportions) ###
##                X     Y
## Joint      0.039 0.052
## Orthogonal 0.070 0.046
## Noise      0.892 0.902
## ### Variation in X joint part predicted by Y Joint part: 0.882 
## ### Variation in Y joint part predicted by X Joint part: 0.882 
## ### Variation in each Latent Variable (LV) in Joint part: 
##     LV1
## X 0.039
## Y 0.052
## ### Variation in each Latent Variable (LV) in X Orthogonal part: 
##     LV1   LV2
## X 0.036 0.034
## ### Variation in each Latent Variable (LV) in Y Orthogonal part: 
##     LV1
## Y 0.046
## 
## ############################################

############################################

Extract the loadings and scores from the fit results and generated figures

Xl <- loadings(fit,loading="Xjoint")
Xs <- scores(fit,score="Xjoint")
plot(fit,type="score",var="Xjoint", group=group)

plot(fit,type="loading",var="Xjoint", group=group,repel=F,rotation=TRUE)

Do the OPLSDA based on the O2PLS results and calculate the VIP values

res <- oplsda(fit,group, nc=1)
plot(res,type="score", group=group,repel=TRUE)

vip <- vip(res)
plot(res,type="vip", group = group, repel = FALSE,order=TRUE)

Citation

If you like this package, please contact me for the citation.

Contact information

For any questions please contact [email protected] or https://github.com/guokai8/o2plsda/issues

- o2plsda: Omics data integration with o2plsda