Omics data integration with o2plsda
In o2plsda: Multiomics Data Integration

knitr::opts_chunk$set(echo = TRUE)

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 $Y$: $TW^\top$ and $UC^\top$,
a part contained inside $X/Y$ that is uncorrelated (orthogonal) to $X$ and $Y$: $T_{yosc} W_{yosc} ^\top$ and $U_{xosc} C_{xosc}^\top$,
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 $||Y - \hat{Y}||$, where $\hat{Y}$ 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: $||X - \hat{X}||+||Y - \hat{Y}||$.

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 [$TW^\top$, $UC^\top$] 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)
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)

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)


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

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)