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Analysis code

Armin Rauschenberger

2025-03-26

Source: vignettes/analysis.Rmd
analysis.Rmd

We obtained our results on 2025-01-03 using R version 4.4.0 (2024-04-24, “Puppy Cup”) running on a Dell Latitude 5440 laptop with a 13th Gen Intel(R) Core(TM) i7-1365U processor (1800 Mhz) and the operating system Microsoft Windows 10 Enterprise. The total computation time was around 2 hours (excluding data download, without parallel computing).

Working environment

This vignette includes code chunks with a long computation time (e.g., analysing simulated and experimental data) and code chunks with a short computation time (e.g., generating figures and tables). The logical options sim.app and fig.tab determine whether the chunks for (i) running the simulation and application or (ii) generating figures and tables are evaluated, respectively. Running this vignette with sim.app=FALSE and fig.tab=TRUE means that figures and tables will be generated from previously obtained results. Running this vignette with sim.app=TRUE and fig.tab=TRUEand means that all results will be reproduced (including data download and data processing). It is also possible to execute individual chunks (e.g., for reproducing a specific figure or table), but then it is important to provide the required inputs (e.g., “Requires: file X in folder Y, execution of chunk Z”).

knitr::opts_chunk$set(echo=TRUE,eval=FALSE)
sim.app <- FALSE # reproduce simulation and application?
fig.tab <- FALSE # reproduce figures and tables?

This chunk verifies the working environment. The working directory, specified by the object path, must contain the R functions in “package/R/functions.R” as well as the folders “results” and “manuscript”. Alternatively, the R functions can be loaded from the R package sparselink. This chunk also installs missing R packages from CRAN or Bioconductor.

path <- "C:/Users/arauschenberger/Desktop/sparselink" # LIH (Windows)
#path <- "/Users/armin.rauschenberger/Desktop/LIH/sparselink" # LCSB (Mac)

dir <- c("results","manuscript","package/R/functions.R")
for(i in seq_along(dir)){
  if(!dir.exists(file.path(path,dir[i]))&!file.exists(file.path(path,dir[i]))){
    stop(paste0("Require folder/file'",dir[i],"'."))
  } 
}
source(file.path(path,"package/R/functions.R")) # Or load 'sparselink' package.

inst <- rownames(utils::installed.packages())
pkgs <- c("knitr","rmarkdown","glmnet","BiocManager")
for(i in seq_along(pkgs)){
  if(!pkgs[i]%in%inst){
    utils::install.packages(pkgs[i])
  }
}
pkgs <- c("recount3","edgeR")
for(i in seq_along(pkgs)){
  if(!pkgs[i]%in%inst){
    BiocManager::install(pkgs[i])
  }
}

blue <- "blue"; red <- "red"

if(exists("sim.app")&exists("fig.tab")){
  if(!sim.app&fig.tab){
    files <- c("simulation_multiple.RData","simulation_transfer.RData","recount3_data.RData","explore_data.RData","application.RData")
    for(i in seq_along(files)){
      if(!file.exists(file.path(path,"results",files[i]))){
        stop("File",files[i],"is missing.")
      }
    }
  }
}

Methods

This chunk generates the figure for the methods section.

  • Requires: execution of chunk setup

  • Execution time: 11 second

  • Ensures: file fig_flow.eps in folder manuscript

#<<setup>>

grDevices::postscript(file=file.path(path,"manuscript","fig_flow.eps"),width=6,height=2.5)
graphics::par(mfrow=c(1,1),mar=c(0,0,0,0))
graphics::plot.new()
graphics::plot.window(xlim=c(-0.2,1.0),ylim=c(0.0,1.0))
cex <- 0.8

pos <- data.frame(left=0.2,right=0.8,top=0.8,centre=0.45,bottom=0.1)
mar <- data.frame(vertical=0.08,horizontal=0.08,dist=0.04)

graphics::text(labels=paste("problem",1:2),x=c(pos$left,pos$right),y=pos$top+2*mar$vertical,font=2,col=c(blue,red),cex=cex)
graphics::text(labels=expression(hat(beta)["j,1"]^{init}),x=pos$left,y=pos$top,col=blue)
graphics::text(labels=expression(hat(beta)["j,2"]^{init}),x=pos$right,y=pos$top,col=red)

graphics::arrows(x0=rep(c(pos$left,pos$right),each=2),x1=rep(c(pos$left,pos$right),times=2)+c(-mar$horizontal,-mar$horizontal,mar$horizontal,mar$horizontal),y0=pos$top-mar$vertical,y1=pos$centre+mar$vertical,length=0.1,col=rep(c(blue,red),each=2),lwd=2)

graphics::text(labels=expression(w["j,1"]^{int}),x=pos$left-mar$horizontal-mar$dist,y=pos$centre,col=blue)
graphics::text(labels=expression(w["p+j,1"]^{int}),x=pos$left-mar$horizontal+mar$dist,y=pos$centre,col=blue)
graphics::text(labels=expression(w["j,1"]^{ext}),x=pos$left+mar$horizontal-mar$dist,y=pos$centre,col=red)
graphics::text(labels=expression(w["p+j,1"]^{ext}),x=pos$left+mar$horizontal+mar$dist,y=pos$centre,col=red)

graphics::text(labels=expression(w["j,2"]^{ext}),x=pos$right-mar$horizontal-mar$dist,y=pos$centre,col=blue)
graphics::text(labels=expression(w["p+j,2"]^{ext}),x=pos$right-mar$horizontal+mar$dist,y=pos$centre,col=blue)
graphics::text(labels=expression(w["j,2"]^{int}),x=pos$right+mar$horizontal-mar$dist,y=pos$centre,col=red)
graphics::text(labels=expression(w["p+j,2"]^{int}),x=pos$right+mar$horizontal+mar$dist,y=pos$centre,col=red)

graphics::arrows(x0=c(pos$left,pos$right),y0=pos$centre-mar$vertical,y1=pos$bottom+mar$vertical,col=c(blue,red),length=0.1,lwd=2)
graphics::text(labels=expression(hat(beta)["j,1"]^{final}==hat(gamma)["j,1"]-hat(gamma)["p+j,1"]),x=pos$left,y=pos$bottom,col=blue)
graphics::text(labels=expression(hat(beta)["j,2"]^{final}==hat(gamma)["j,2"]-hat(gamma)["p+j,2"]),x=pos$right,y=pos$bottom,col=red)

graphics::text(x=-0.1,y=c(pos$top,pos$bottom),labels=paste("stage",1:2),font=2,cex=cex)
grDevices::dev.off()

Simulation

This chunk performs the simulation.

  • Requires: execution of chunk setup

  • Execution time: 0.5 hours

  • Ensures: files simulation_transfer.RData (transfer learning), simulation_multiple.RData (multi-task learning) and info_sim.txt (session information) in folder results

#<<setup>>

alpha.init <- 0.95; type <- "exp";  repetitions <- 10

for(mode in c("transfer","multiple")){
  
  grid <- expand.grid(prob.separate=c(0.0,0.025,0.05),prob.common=c(0.0,0.025,0.05),family="gaussian")
  grid <- grid[rep(seq_len(nrow(grid)),each=repetitions),] #
  grid$seed <- seq_len(nrow(grid))
  grid$family <- as.character(grid$family)
  deviance <- auc <- time <- mse.coef <- mse.zero <- mse.nzero <- sel.num <- sel.coef <- sel.count <- hyperpar <- list()
  for(i in seq(from=1,to=nrow(grid))){
    set.seed(seed=grid$seed[i])
    cat("i=",i,"\n")
    if(mode=="transfer"){
      data <- sim.data.transfer(prob.common=grid$prob.common[i],prob.separate=grid$prob.separate[i],family=grid$family[i])
      method <- c("glm.separate","glm.transfer","sparselink")
    } else if(mode=="multiple"){
      #--- multi-task learning ---
      data <- sim.data.multiple(prob.common=grid$prob.common[i],prob.separate=grid$prob.separate[i],family=grid$family[i])
      method <- c("glm.separate","glm.mgaussian","sparselink") # add glmnet "mgaussian" (only for linear case) or "MTPS" (not sparse)?
    }
    
    result <- traintest(y_train=data$y_train,X_train=data$X_train,y_test=data$y_test,X_test=data$X_test,family=grid$family[i],method=method,alpha.init=alpha.init,type=type,alpha=1)
    hyperpar[[i]] <- result$hyperpar
    time[[i]] <- result$time
    auc[[i]] <- result$auc
    deviance[[i]] <- result$deviance
    sel.num[[i]] <- t(sapply(result$coef,function(x) colSums(x!=0)))
    sel.count[[i]] <- t(sapply(result$coef,function(x) rowMeans(count_matrix(truth=sign(data$beta),estim=sign(x))))) # Add na.rm=TRUE?
    
    sel.coef[[i]] <- t(sapply(result$coef,function(x) colMeans(sign(x)!=sign(data$beta))))
    # CONTINUE HERE: consider sparsity, true positives, false negatives, signs
    
    mse.coef[[i]] <- t(sapply(result$coef,function(x) colMeans((data$beta-x)^2)))
    mse.zero[[i]] <- t(sapply(result$coef,function(x) colMeans(((data$beta==0)*(data$beta-x))^2)))
    mse.nzero[[i]] <- t(sapply(result$coef,function(x) colMeans(((data$beta!=0)*(data$beta-x))^2)))
  }
  save(grid,deviance,auc,sel.num,sel.count,sel.coef,mse.coef,mse.zero,mse.nzero,time,file=file.path(path,"results",paste0("simulation_",mode,".RData")))
}

writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),      sessioninfo::session_info()),con=paste0(path,"/results/info_sim.txt"))

The following chunk generate the figures for the simulation study.

  • Requires: execution of chunk setup, files simulation_transfer.RData and simulation_multiple.RData in folder results (generated by chunk simulation)

  • execution time: 11 second

  • Ensures: files fig_sim_multiple.eps and fig_sim_transfer.eps in folder manuscript

#<<setup>>

caption <- paste(c("\\textbf{Multi-task learning.}","\\textbf{Transfer learning.}"),"Comparison of different measures (rows) between an available method (red) and the proposed method (blue) in different simulation settings (columns), based on the average of three problems",c("(tasks)","(datasets)"),"for each repetition out of ten. Measures: performance metric (mean squared error on hold-out data, as a fraction of the one from standard lasso regression; a point below the dashed line means that",c("multi-task","transfer"),"learning improves predictions), sparsity (number of non-zero coefficients), precision (number of coefficients with correct signs divided by number of non-zero coefficients). The arrows point in the direction of improvement. Settings: percentage of features with a common effect for all problems ($\\pi_\\theta$), percentage of features with a specific effect for each problem ($\\pi_\\delta$).",c("\\label{fig_sim_multiple}","\\label{fig_sim_transfer}"))

figure_change <- function(){
  
  mode <- paste0(100*grid$prob.common,"%\n",100*grid$prob.separate,"%")
  
  graphics::par(mfrow=c(3,1),mar=c(3,3,1,1))
  
  label <- function(){
    cex <- 0.5
    at <- 0.3
    graphics::mtext(text=expression(pi[theta]==phantom(.)),side=1,line=0.2,at=at,cex=cex)
    graphics::mtext(text=expression(pi[delta]==phantom(.)),side=1,line=1.2,at=at,cex=cex)
  }
  
  #--- predictive performance ---
  means <- t(sapply(X=deviance,FUN=rowMeans))
  means <- means/means[,"glm.separate"]
  change(x=mode,y0=means[,model.ref],y1=means[,model.own],main="metric",increase=FALSE)
  graphics::abline(h=1,lty=2,col="grey")
  label()
  
  #--- sparsity ---
  nzero <- sapply(X=sel.num,FUN=rowMeans)
  change(x=mode,y0=nzero[model.ref,],y1=nzero[model.own,],main="sparsity",increase=FALSE)
  graphics::abline(h=0,lty=2,col="grey")
  label()
  
  #--- precision ---
  precision <- sapply(X=sel.count,FUN=function(x) x[,"precision"])
  precision[is.na(precision)] <- 0
  change(x=mode,y0=precision[model.ref,],y1=precision[model.own,],main="precision",increase=TRUE)
  graphics::abline(h=0,lty=2,col="grey")
  label()
  
}

grDevices::postscript(file=file.path(path,"manuscript","fig_sim_multiple.eps"),width=6.5,height=6)
load(file.path(path,paste0("results/simulation_multiple.RData")))
model.ref <- "glm.mgaussian"
model.own <- "sparselink"
figure_change()
grDevices::dev.off()

grDevices::postscript(file=file.path(path,"manuscript","fig_sim_transfer.eps"),width=6.5,height=6)
load(file.path(path,paste0("results/simulation_transfer.RData")))
model.ref <- "glm.transfer"
model.own <- "sparselink"
figure_change()
grDevices::dev.off()

Application

Data preparation

This chunk defines the references and the project identifiers for the application.

  • Requires: nothing

  • Execution time: 11 second

  • Ensures: list project in working environment

project <- list()
project$IBD <- c("Tew (2016)"="SRP063496",
                 "Haberman (2019)"="SRP129004",
                 "Verstockt (2019)"="ERP113396",
                 "Verstockt (2020)"="ERP114636",
                 "Boyd (2018)"="SRP100787")
project$RA <- c("Baker (2019)"="SRP169062",
                "Moncrieffe (2017)"="SRP074736",
                "Goldberg (2018)"="SRP155483")
extra <- c("Lewis (2019)"="ERP104864") # https://doi.org/10.1016/j.celrep.2019.07.091

This chunk downloads the data for the application.

  • Requires: execution of chunks setup and define_projects

  • Execution time: depends on internet speed and cached files

  • Ensures: files recount3_data.RData (data sets) and info_data.txt (system information) in folder results

#<<setup>>
#<<define_projects>>

data <- list()
for(i in c(unlist(project),extra)){
  data[[i]] <- recount3::create_rse_manual(
    project=i,
    project_home="data_sources/sra",
    organism="human",
    annotation = "gencode_v26",
    type="gene")
}
save(data,file=file.path(path,"results/recount3_data.RData"))

writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),
      sessioninfo::session_info()),con=paste0(path,"/results/info_data.txt"))

This chunk preprocesses the data.

  • Requires: execution of chunks setup and define_projects, file recount3_data.RData (generated by chunk download_data)

  • Execution time: 55 seconds

  • Ensures: lists y (targets) and x (features) in working environment

#<<setup>>
#<<define_projects>>

load(file.path(path,"results/recount3_data.RData"))

#- - - - - - - - - - - - - - -
#- - - extract features  - - - 
#- - - - - - - - - - - - - - -

# extract features
x <- list()
for(i in c(unlist(project),extra)){
  counts <- t(SummarizedExperiment::assays(data[[i]])$raw_counts)
  colnames(counts) <- SummarizedExperiment::rowRanges(data[[i]])$gene_name
  x[[i]] <- counts
}

# select most expressed protein-coding genes (for all TL projects together)
select <- list()
total <- numeric()
for(i in unlist(project)){
  total <- rbind(total,Matrix::colSums(x[[i]])) # original: mean filtering
  #total <- rbind(total,apply(X=x[[i]],MARGIN=2,FUN=stats::var)) # alternative: variance filtering
}
type <- SummarizedExperiment::rowData(data[[i]])$gene_type
cond <- type=="protein_coding"
total[,!cond] <- 0
rank <- apply(X=total,MARGIN=1,FUN=rank)
mean_rank <- rowMeans(rank)
temp <- cond & apply(total,2,function(x) all(x>0)) & (mean_rank >= sort(mean_rank[cond],decreasing=TRUE)[2000]) # double-check (remove?) second condition
for(i in unlist(project)){
  select[[i]] <- temp
}

# select most expressed protein-coding genes (for MTL project)
mean <- apply(X=x[[extra]],MARGIN=2,FUN=mean)
temp <- cond & mean >= sort(mean[cond],decreasing=TRUE)[250] # change number
select[[extra]] <- temp

# pre-processing
for(i in c(unlist(project),extra)){
  lib.size <- Matrix::rowSums(x[[i]])
  x[[i]] <- x[[i]][,select[[i]],drop=FALSE]
  norm.factors <- edgeR::calcNormFactors(object=t(x[[i]]),lib.size=lib.size)
  gamma <- norm.factors*lib.size/mean(lib.size)
  gamma <- matrix(data=gamma,nrow=nrow(x[[i]]),ncol=ncol(x[[i]]))
  x[[i]] <- x[[i]]/gamma
  x[[i]] <- 2*sqrt(x[[i]] + 3/8) # Anscombe transform
  x[[i]] <- scale(x[[i]]) # scale because of different datasets!?
}

#- - - - - - - - - - - - - -
#- - - extract targets - - -
#- - - - - - - - - - - - - -

# extract information on samples
frame <- list()
for(i in c(unlist(project),extra)){
  list <- strsplit(data[[i]]$sra.sample_attributes,split="\\|")
  data[[i]]$sra.experiment_attributes
  # What about sra.experiment_attributes?
  n <- length(list)
  cols <- unique(sapply(strsplit(unlist(list),split=";;"),function(x) x[1]))
  ncol <- length(cols)
  frame[[i]] <- matrix(data=NA,nrow=n,ncol=ncol,dimnames=list(rownames(x[[i]]),cols))
  for(j in seq_len(n)){
    for(k in seq_len(ncol)){
      vector <- list[[j]]
      which <- which(substring(text=vector,first=1,last=nchar(cols[k]))==cols[k])
      string <- vector[which]
      if(length(string)==0){next}
      frame[[i]][j,k] <- strsplit(string,split=";;")[[1]][2]
    }
  }
  frame[[i]] <- as.data.frame(frame[[i]])
}

# extract binary outcome
y <- z <- list()
for(i in unlist(project)){
  # CONTINUE HERE!!!
  if(i=="ERP113396"){
    y[[i]] <- sapply(X=frame[[i]]$`clinical history`,FUN=function(x) switch(EXPR=x,"responder"=1,"non-responder"=0,stop("invalid")))
  } else if(i=="ERP114636"){
    y[[i]] <- sapply(X=frame[[i]]$`clinical information`,FUN=function(x) switch(EXPR=x,"response to vedolizumab therapy"=1-1,"no response to vedolizumab therapy"=0+1,stop("invalid")))
    warning("Inverting response and non-response!")
  } else if(i=="SRP100787"){
    y[[i]] <- sapply(X=frame[[i]]$condition,FUN=function(x) switch(EXPR=x,"CD inactive"=1,"UC inactive"=1,"CD active"=0,"UC active"=0,control=NA,"NA"=NA,stop("invalid")))
  } else if(i=="SRP129004"){
    y[[i]] <- sapply(X=frame[[i]]$`week 4 remission`,FUN=function(x) switch(EXP=x,"Yes"=1,"No"=0,"NA"=NA,stop("invalid")))
    suppressWarnings(z[[i]] <- data.frame(pucai=as.numeric(frame[[i]]$pucai),mayo=as.numeric(frame[[i]]$`total mayo score`),histology=as.numeric(frame[[i]]$`histology severity score`)))
  } else if(i=="SRP063496"){
    y[[i]] <- sapply(X=frame[[i]]$`remission at week 10`,FUN=function(x) switch(x, "Remitter"=1,"Non-remitter"=0,"N/A"=NA,stop("invalid")))
  } else if(i=="SRP169062"){
    y[[i]] <- sapply(X=frame[[i]]$`flare event`,FUN=function(x) switch(x,"no flare"=1,"flare"=0,stop("invalid")))
  } else if(i=="SRP155483"){
    y[[i]] <- sapply(X=frame[[i]]$`disease activity`,FUN=function(x) switch(x,"remission"=1,"Low"=0,"Moderate"=0,"High"=0,"--"=NA,stop("invalid")))
    z[[i]] <- sapply(X=frame[[i]]$`disease activity`,FUN=function(x) switch(x,"remission"=0,"Low"=1,"Moderate"=2,"High"=3,"--"=NA,stop("invalid")))
  } else if(i=="SRP074736"){
    y[[i]] <- sapply(X=frame[[i]]$`mtx response status`,FUN=function(x) switch(x,"responder"=1,"non-responder"=0,"control"=NA,stop("invalid")))
  }
}

# overlap
for(j in unlist(project)){
  is.na <- is.na(y[[j]])
  if(length(is.na)!=nrow(x[[j]])){stop()}
  y[[j]] <- y[[j]][!is.na]
  if(!is.null(z[[j]])){
    if(is.vector(z[[j]])){
      z[[j]] <- z[[j]][!is.na]
    } else {
      z[[j]] <- z[[j]][!is.na,]
    }
  }
  x[[j]] <- x[[j]][!is.na,]
}

Data exploration

This chunk performs the exploratory data analysis.

  • Requires: execution of chunks setup, define_projects and preprocess_data

  • Execution time: 0.50.5 minutes

  • Ensures: files explore_data.RData (results) and info_explore.txt (session information) in folder results

#<<setup>>
#<<define_projects>>
#<<preprocess_data>>

set.seed(1)
alpha.holdout <- 0
alpha.crossval <- 1
family <- "binomial"
nfolds <- 10
codes <- unlist(project)
coef <- matrix(data=NA,nrow=ncol(x[[1]]),ncol=length(codes),dimnames=list(NULL,codes))
auc <- auc.pvalue <- matrix(data=NA,nrow=length(codes),ncol=length(codes),dimnames=list(codes,codes))
foldid <- make.folds.trans(y=y,family="binomial",nfolds=nfolds)

ridge <- lasso <- list()
for(i in seq_along(codes)){
  ridge[[i]] <- glmnet::cv.glmnet(x=x[[codes[i]]],y=y[[codes[i]]],family=family,alpha=alpha.holdout,foldid=foldid[[i]])
  coef[,i] <- stats::coef(ridge[[i]],s="lambda.min")[-1]
  for(j in seq_along(codes)){
    if(i==j){
      y_hat <- rep(x=NA,times=length(y[[i]]))
      for(k in seq_len(nfolds)){
        holdout <- foldid[[i]]==k
        temp <- glmnet::cv.glmnet(x=x[[codes[i]]][!holdout,],y=y[[codes[i]]][!holdout],family=family,alpha=alpha.crossval)
        y_hat[holdout] <- predict(object=temp,newx=x[[codes[i]]][holdout,],s="lambda.min",type="response")
      }
    } else {
      y_hat <- as.numeric(predict(object=ridge[[i]],newx=x[[j]],s="lambda.min",type="response"))
    }
    auc[i,j] <- pROC::auc(response=y[[codes[j]]],predictor=y_hat,direction="<",levels=c(0,1))
    auc.pvalue[i,j] <- stats::wilcox.test(rank(y_hat)~y[[codes[[j]]]],alternative="less",exact=FALSE)$p.value
  }
}

save(coef,auc,auc.pvalue,codes,file=file.path(path,"results","explore_data.RData"))

writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),
      sessioninfo::session_info()),con=paste0(path,"/results/info_explore.txt"))

This chunk generates the tables for the exploratory data analysis.

  • Requires: execution of chunk setup, file explore_data.RData in folder results (generated by chunk explore_apply)

  • execution time: 11 second

  • Ensures: files tab_cor.tex and tab_auc.tex in folder manuscript

#<<setup>>
#if(any(unlist(project)!=names(refs))){stop("not compatible")}

load(file.path(path,"results/explore_data.RData"))
names <- gsub(pattern="IBD.|RA.",replacement="",x=names(unlist(project)))
codes <- colnames(coef)
cor.pvalue <- matrix(data=NA,nrow=length(codes),ncol=length(codes),dimnames=list(codes,codes))
for(i in seq_along(codes)){
  for(j in seq_along(codes)){
    cor.pvalue[i,j] <- stats::cor.test(x=coef[,i],y=coef[,j],method="spearman",exact=FALSE)$p.value
  }
}
diag(cor.pvalue) <- NA

insert.space <- function(table,cut){
  index.left <- index.top <- seq_len(cut)
  index.right <- index.bottom <- seq(from=cut+1,to=ncol(table))
  top <- cbind(table[index.top,index.left],"",table[index.top,index.right])
  bottom <- cbind(table[index.bottom,index.left],"",table[index.bottom,index.right])
  out <- rbind(top,"",bottom)
  colnames(out)[colnames(out)==""] <- " "
  return(out)
}

table <- stats::cor(coef,method="spearman")
rownames(table) <- colnames(table) <- names
black <- (!is.na(cor.pvalue)) & (cor.pvalue<=0.05)
star <- (!is.na(cor.pvalue)) & (cor.pvalue<=0.05/choose(n=length(codes),k=2))
nonnegative <- table>=0
table <- format(round(table,digits=2),digits=2,trim=TRUE)
table[nonnegative] <- paste0("\\phantom{-}",table[nonnegative])
table[!black] <- paste0("\\textcolor{gray}{",table[!black],"}")
table[star] <- paste0(table[star],"$^\\star$")
table[!star] <- paste0(table[!star],"\\phantom{$^\\star$}")
#table[nonnegative] <- paste0("-",table[nonnegative])
diag(table) <- "-"
table <- insert.space(table=table,cut=5)
xtable <- xtable::xtable(x=table,align="rccccccccc",caption="Spearman correlation coefficients between the ridge regression coefficients from different datasets. Pairwise combinations of datasets with significantly correlated regression coefficients are highlighted, with black colour for nominal significance ($p$-value $\\leq 0.05$) and stars for adjusted significance ($p$-value $\\leq 0.05/28$). We expect a correlation coefficient close to $0$ for unrelated problems and close to $1$ for identical problems.",label="tab_cor")
xtable::print.xtable(x=xtable,sanitize.text.function=identity,rotate.colnames=TRUE,caption.placement="top",hline.after=c(0,nrow(table)),comment=FALSE,file=file.path(path,"manuscript","tab_cor.tex")) #add.to.row=list(pos=list(5),command="\\hdashline \n")

table <- auc
rownames(table) <- colnames(table) <- names
table <- format(round(table,digits=2),digits=2)
black <- auc.pvalue<=0.05
star <- auc.pvalue<=0.05/(length(codes)*length(codes))
diag(table) <- paste0("(",diag(table),")")
table[!black] <- paste0("\\textcolor{gray}{",table[!black],"}")
table[star] <- paste0(table[star],"$^\\star$")
table[!star] <- paste0(table[!star],"\\phantom{$^\\star$}")
table <- insert.space(table=table,cut=5)
xtable <- xtable::xtable(x=table,align="rccccccccc",caption="Out-of-sample area under the receiver operating characteristic curve (\\textsc{roc-auc}) from logistic ridge regression trained on the dataset in the row and tested on the dataset in the column (off-diagonal entries), or cross-validated \\textsc{roc-auc} from logistic lasso regression trained and tested on the same dataset by $10$-fold external cross-validation (diagonal entries, between brackets). The \\textsc{roc-auc} of a random classifier is $0.5$, while that of a perfect classifier is $1.0$. Entries on and off the diagonal are not comparable. Predictions that are significantly better than random predictions (according to the one-sided Mann-Whitney $U$ test for testing whether the ranks of the predicted probabilities are significantly higher for the cases than for the controls) are highlighted, with black colour for nominal significance ($p$-value $\\leq 0.05$) and stars for adjusted significance ($p$-value $\\leq 0.05/64$).",label="tab_auc")
xtable::print.xtable(x=xtable,sanitize.text.function=identity,rotate.colnames=TRUE,caption.placement="top",hline.after=c(0,nrow(table)),comment=FALSE,file=file.path(path,"manuscript","tab_auc.tex"))

Transfer learning

This chunk performs the transfer learning analysis.

  • Requires: execution of chunks setup and define_projects, file recount3_data.RData in folder results (generated by chunk download_data), execution of chunk preprocess_data

  • Execution time: 1.5 hours

  • Ensures: application.RData (results) and info_app.txt (session information) in folder results

#<<setup>>
#<<define_projects>>
#<<preprocess_data>>

alpha.init <- 0.95; type <- "exp"

result <- list()
for(i in names(project)){
  cat("project:",i,"\n")
  result[[i]] <- list()
  for(j in seq_len(5)){ # 5 repetitions of 10-fold CV
    set.seed(j)
    codes <- project[[i]]
    result[[i]][[j]] <- crossval(y=y[codes],X=x[codes],family="binomial",method=c("glm.separate","glm.transfer","sparselink","glm.common"),nfolds=10,alpha=1,alpha.init=alpha.init,type=type)
  }
}
save(result,project,file=file.path(path,"results","application.RData"))

writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),
      sessioninfo::session_info()),con=paste0(path,"/results/info_app.txt"))

This chunk generates the figure on the predictive performance.

  • Requires: execution of chunk setup, file application.RData in folder results (generated by chunk transfer_apply)

  • Execution time: 11 second

  • Ensures: file fig_app.eps in folder manuscript

#<<setup>>

grDevices::postscript(file=file.path(path,"manuscript","fig_app.eps"),width=6.5,height=4)
graphics::par(mfrow=c(2,1),mar=c(4,2,1,1),oma=c(0,0,0,0))
load(file.path(path,paste0("results/application.RData")))

reference <- "glm.transfer"
experimental <- "sparselink"

# predictivity
metric <- lapply(result,function(x) do.call(what="rbind",args=lapply(x,function(x) x$auc))) # DEV and AUC need different directions (increase=FALSE/TRUE)!
metric <- do.call(what="rbind",args=metric)
metric <- metric/metric[,"glm.separate"]
#xlab <- refs[rownames(metric)]
#names <- gsub(pattern="",replacement="\n",x=unlist(project))

label <- gsub(pattern="IBD.|RA.",replacement="",x=gsub(pattern=" ",replacement="\n",x=names(unlist(project))))
index <- match(x=rownames(metric),table=unlist(project))

xlab <- label[index]
change(x=xlab,y0=metric[,reference],y1=metric[,experimental],main="metric",increase=TRUE,cex.main=0.8)
graphics::axis(side=1,at=length(project$IBD)+0.5,labels="|",tick=FALSE,line=-0.25,font=2)
graphics::abline(h=0.5,lty=2,col="grey")
graphics::abline(h=1,lty=2,col="grey")

# sparsity
nzero <- lapply(result,function(x) lapply(x,function(x) sapply(x$refit$coef,function(x) colSums(x!=0))))
nzero <- do.call(what="rbind",args=do.call(what="c",args=nzero))
change(x=xlab,y0=nzero[,reference],y1=nzero[,experimental],main="sparsity",increase=FALSE,cex.main=0.8)
graphics::axis(side=1,at=length(project$IBD)+0.5,labels="|",tick=FALSE,line=-0.25,font=2)
graphics::abline(h=0,lty=2,col="grey")
grDevices::dev.off()

# percentage change
# (reported in section 4 "application" subsection 4.3 "transfer learning")

disease <- ifelse(rownames(metric) %in% project$IBD,"IBD",ifelse(rownames(metric) %in% project$RA,"RA",NA))

#round(100*colMeans(metric)-100,digits=2)
round(100*colMeans(metric[disease=="IBD",])-100,digits=2)
round(100*colMeans(metric[disease=="RA",])-100,digits=2)

colMeans(nzero)
colMeans(nzero[disease=="IBD",])
colMeans(nzero[disease=="RA",])

This chunk generates the figure on feature selection.

  • Requires: execution of chunk setup, file application.RData in folder results (generated by chunk transfer_apply)

  • Execution time: 11 second

  • Ensures: file fig_coef.eps in folder manuscript

#<<setup>>

load(file.path(path,"results","application.RData"))

coefs <- list()
for(i in seq_along(result$IBD)){
  coefs[[i]] <- result$IBD[[i]]$refit$coef$sparselink
  colnames(coefs[[i]]) <- names(project$IBD)
  rownames(coefs[[i]]) <- rownames(result$IBD[[1]]$refit$coef$glm.transfer) # try to avoid this
}

any <- rowSums(sapply(coefs,function(x) apply(x,1,function(x) any(x!=0))))!=0
for(i in seq_along(result$IBD)){
  coefs[[i]] <- coefs[[i]][any,]
}
table <- Reduce(f="+",x=coefs)/5

cex <- 0.7

grDevices::postscript(file=file.path(path,"manuscript","fig_coef.eps"),width=7,height=4)
graphics::par(mfrow=c(1,1),mar=c(2.5,4.5,0.5,1.5),oma=c(0,0,0,0))
graphics::plot.new()
graphics::plot.window(xlim=c(0.6,ncol(table)+0.4),ylim=c(0.5,nrow(table)+0.5))
col <- apply(table,1,function(x) ifelse(all(x<=0),"blue",ifelse(all(x>=0),"red","black")))
colnames <- gsub(x=colnames(table),pattern=" ",replacement="\n")
graphics::mtext(text=colnames,side=1,at=seq_len(ncol(table)),cex=cex,line=1)
rownames <- rownames(table)
graphics::mtext(text=rownames,side=2,at=seq_len(nrow(table)),las=2,cex=cex,line=0.7,col=col)
star <- rowSums(table!=0)>1
graphics::mtext(text="*",side=2,at=which(star),line=-0.3)
graphics::mtext(text=ifelse(col=="blue","-",ifelse(col=="red","+",".")),side=4,at=seq_len(nrow(table)),las=2,cex=cex,line=0.5,col=col)
for(i in seq_len(nrow(table))){
  for(j in seq_len(ncol(table))){
    for(k in 1:5){
      col <- ifelse(coefs[[k]][i,j]<0,"blue",ifelse(coefs[[k]][i,j]>0,"red","white"))
      cex <- pmax(sqrt(5*abs(coefs[[k]][i,j])),0.2)
      graphics::points(x=j-(-3+k)*0.17,y=i,col=col,cex=cex,pch=16)
    }
  }
}
graphics::abline(v=seq(from=0.5,to=5.5,by=1))
grDevices::dev.off()

Multi-task learning (under development) 

rm(list=ls())
path <- "C:/Users/arauschenberger/Desktop/sparselink" # LIH (Windows)
#path <- "/Users/armin.rauschenberger/Desktop/LIH/sparselink" # LCSB (Mac)

dir <- c("results","manuscript","package/R/functions.R")
for(i in seq_along(dir)){
  if(!dir.exists(file.path(path,dir[i]))&!file.exists(file.path(path,dir[i]))){
    stop(paste0("Require folder/file'",dir[i],"'."))
  } 
}
source(file.path(path,"package/R/functions.R")) # Or load 'sparselink' package.

inst <- rownames(utils::installed.packages())
pkgs <- c("knitr","rmarkdown","glmnet","BiocManager")
for(i in seq_along(pkgs)){
  if(!pkgs[i]%in%inst){
    utils::install.packages(pkgs[i])
  }
}
pkgs <- c("recount3","edgeR")
for(i in seq_along(pkgs)){
  if(!pkgs[i]%in%inst){
    BiocManager::install(pkgs[i])
  }
}

blue <- "blue"; red <- "red"

if(exists("sim.app")&exists("fig.tab")){
  if(!sim.app&fig.tab){
    files <- c("simulation_multiple.RData","simulation_transfer.RData","recount3_data.RData","explore_data.RData","application.RData")
    for(i in seq_along(files)){
      if(!file.exists(file.path(path,"results",files[i]))){
        stop("File",files[i],"is missing.")
      }
    }
  }
}
project <- list()
project$IBD <- c("Tew (2016)"="SRP063496",
                 "Haberman (2019)"="SRP129004",
                 "Verstockt (2019)"="ERP113396",
                 "Verstockt (2020)"="ERP114636",
                 "Boyd (2018)"="SRP100787")
project$RA <- c("Baker (2019)"="SRP169062",
                "Moncrieffe (2017)"="SRP074736",
                "Goldberg (2018)"="SRP155483")
extra <- c("Lewis (2019)"="ERP104864") # https://doi.org/10.1016/j.celrep.2019.07.091
#<<setup>>
#<<define_projects>>

load(file.path(path,"results/recount3_data.RData"))

#- - - - - - - - - - - - - - -
#- - - extract features  - - - 
#- - - - - - - - - - - - - - -

# extract features
x <- list()
for(i in c(unlist(project),extra)){
  counts <- t(SummarizedExperiment::assays(data[[i]])$raw_counts)
  colnames(counts) <- SummarizedExperiment::rowRanges(data[[i]])$gene_name
  x[[i]] <- counts
}

# select most expressed protein-coding genes (for all TL projects together)
select <- list()
total <- numeric()
for(i in unlist(project)){
  total <- rbind(total,Matrix::colSums(x[[i]])) # original: mean filtering
  #total <- rbind(total,apply(X=x[[i]],MARGIN=2,FUN=stats::var)) # alternative: variance filtering
}
type <- SummarizedExperiment::rowData(data[[i]])$gene_type
cond <- type=="protein_coding"
total[,!cond] <- 0
rank <- apply(X=total,MARGIN=1,FUN=rank)
mean_rank <- rowMeans(rank)
temp <- cond & apply(total,2,function(x) all(x>0)) & (mean_rank >= sort(mean_rank[cond],decreasing=TRUE)[2000]) # double-check (remove?) second condition
for(i in unlist(project)){
  select[[i]] <- temp
}

# select most expressed protein-coding genes (for MTL project)
mean <- apply(X=x[[extra]],MARGIN=2,FUN=mean)
temp <- cond & mean >= sort(mean[cond],decreasing=TRUE)[250] # change number
select[[extra]] <- temp

# pre-processing
for(i in c(unlist(project),extra)){
  lib.size <- Matrix::rowSums(x[[i]])
  x[[i]] <- x[[i]][,select[[i]],drop=FALSE]
  norm.factors <- edgeR::calcNormFactors(object=t(x[[i]]),lib.size=lib.size)
  gamma <- norm.factors*lib.size/mean(lib.size)
  gamma <- matrix(data=gamma,nrow=nrow(x[[i]]),ncol=ncol(x[[i]]))
  x[[i]] <- x[[i]]/gamma
  x[[i]] <- 2*sqrt(x[[i]] + 3/8) # Anscombe transform
  x[[i]] <- scale(x[[i]]) # scale because of different datasets!?
}

#- - - - - - - - - - - - - -
#- - - extract targets - - -
#- - - - - - - - - - - - - -

# extract information on samples
frame <- list()
for(i in c(unlist(project),extra)){
  list <- strsplit(data[[i]]$sra.sample_attributes,split="\\|")
  data[[i]]$sra.experiment_attributes
  # What about sra.experiment_attributes?
  n <- length(list)
  cols <- unique(sapply(strsplit(unlist(list),split=";;"),function(x) x[1]))
  ncol <- length(cols)
  frame[[i]] <- matrix(data=NA,nrow=n,ncol=ncol,dimnames=list(rownames(x[[i]]),cols))
  for(j in seq_len(n)){
    for(k in seq_len(ncol)){
      vector <- list[[j]]
      which <- which(substring(text=vector,first=1,last=nchar(cols[k]))==cols[k])
      string <- vector[which]
      if(length(string)==0){next}
      frame[[i]][j,k] <- strsplit(string,split=";;")[[1]][2]
    }
  }
  frame[[i]] <- as.data.frame(frame[[i]])
}

# extract binary outcome
y <- z <- list()
for(i in unlist(project)){
  # CONTINUE HERE!!!
  if(i=="ERP113396"){
    y[[i]] <- sapply(X=frame[[i]]$`clinical history`,FUN=function(x) switch(EXPR=x,"responder"=1,"non-responder"=0,stop("invalid")))
  } else if(i=="ERP114636"){
    y[[i]] <- sapply(X=frame[[i]]$`clinical information`,FUN=function(x) switch(EXPR=x,"response to vedolizumab therapy"=1-1,"no response to vedolizumab therapy"=0+1,stop("invalid")))
    warning("Inverting response and non-response!")
  } else if(i=="SRP100787"){
    y[[i]] <- sapply(X=frame[[i]]$condition,FUN=function(x) switch(EXPR=x,"CD inactive"=1,"UC inactive"=1,"CD active"=0,"UC active"=0,control=NA,"NA"=NA,stop("invalid")))
  } else if(i=="SRP129004"){
    y[[i]] <- sapply(X=frame[[i]]$`week 4 remission`,FUN=function(x) switch(EXP=x,"Yes"=1,"No"=0,"NA"=NA,stop("invalid")))
    suppressWarnings(z[[i]] <- data.frame(pucai=as.numeric(frame[[i]]$pucai),mayo=as.numeric(frame[[i]]$`total mayo score`),histology=as.numeric(frame[[i]]$`histology severity score`)))
  } else if(i=="SRP063496"){
    y[[i]] <- sapply(X=frame[[i]]$`remission at week 10`,FUN=function(x) switch(x, "Remitter"=1,"Non-remitter"=0,"N/A"=NA,stop("invalid")))
  } else if(i=="SRP169062"){
    y[[i]] <- sapply(X=frame[[i]]$`flare event`,FUN=function(x) switch(x,"no flare"=1,"flare"=0,stop("invalid")))
  } else if(i=="SRP155483"){
    y[[i]] <- sapply(X=frame[[i]]$`disease activity`,FUN=function(x) switch(x,"remission"=1,"Low"=0,"Moderate"=0,"High"=0,"--"=NA,stop("invalid")))
    z[[i]] <- sapply(X=frame[[i]]$`disease activity`,FUN=function(x) switch(x,"remission"=0,"Low"=1,"Moderate"=2,"High"=3,"--"=NA,stop("invalid")))
  } else if(i=="SRP074736"){
    y[[i]] <- sapply(X=frame[[i]]$`mtx response status`,FUN=function(x) switch(x,"responder"=1,"non-responder"=0,"control"=NA,stop("invalid")))
  }
}

# overlap
for(j in unlist(project)){
  is.na <- is.na(y[[j]])
  if(length(is.na)!=nrow(x[[j]])){stop()}
  y[[j]] <- y[[j]][!is.na]
  if(!is.null(z[[j]])){
    if(is.vector(z[[j]])){
      z[[j]] <- z[[j]][!is.na]
    } else {
      z[[j]] <- z[[j]][!is.na,]
    }
  }
  x[[j]] <- x[[j]][!is.na,]
}

#--- prepare data ---
vars <- c("CCP","CRP","crp","DAS28","ESR","esr","HAQ","VAS","SWOLLEN","TENDER") # "inflammatory score" dropped due to NA # "RF" dropped because binary
#vars <- c("DAS28","SWOLLEN","TENDER")
Y <- frame$ERP104864[,vars]
if(any(!is.na(Y$CRP)&!is.na(Y$crp))){
  stop("Invalid.")
} else {
  Y$CRP[is.na(Y$CRP)] <- Y$crp[is.na(Y$CRP)]
  Y$crp <- NULL
}
if(any(!is.na(Y$ESR)&!is.na(Y$esr))){
  stop("Invalid.")
} else {
  Y$ESR[is.na(Y$ESR)] <- Y$esr[is.na(Y$ESR)]
  Y$esr <- NULL
}
for(i in seq_len(ncol(Y))){
  class(Y[[i]]) <- "numeric"
}

#--- explore similarity ---
cor <- cor(Y,use="pairwise.complete.obs",method="spearman")
image(t(cor)[,ncol(cor):1])

stats::heatmap(x=as.matrix(Y),Rowv=NA)

d <- stats::dist(x=t(Y))
hclust <- stats::hclust(d=d)
plot(hclust)

X <- x$ERP104864

cond <- apply(X=Y,MARGIN=1,FUN=function(x) all(!is.na(x)))
y <- as.matrix(Y)[cond,]
x <- X[cond,]

problem <- list()
problem$joint <- c("SWOLLEN","TENDER")
problem$proms <- c("VAS","HAQ")
problem$labor <- c("CRP","ESR") # CCP might be too different (check cor)

#cor(rowSums(scale(Y)),Y,method="spearman")

alpha.init <- 0.95; alpha <- 1; type <- "exp"

results <- list()
for(k in seq_along(problem)){
  results[[k]] <- list()
  for(i in seq_len(3)){ # 5 repetitions of 10-fold CV
    set.seed(i)
    method <- c("glm.separate","glm.mgaussian","sparselink","devel")
    #method <- c("glm.separate","devel")
    #method <- c("glm.separate","devel","sparselink")
    results[[k]][[i]] <-  cv.multiple(y=y[,colnames(y) %in% problem[[k]]],X=x,family="gaussian",method=method,nfolds=10,alpha=alpha,alpha.init=alpha.init,type=type)
  }
}

cm <- numeric()
for(k in seq_along(problem)){
  for(i in seq_len(3)){
    dev <- results[[k]][[i]]$deviance
    temp <- colMeans(dev/dev[,"glm.separate"])
    cm <- rbind(cm,temp)
    #cat(cm,"\n")
  }
}
colMeans(cm)
# separate, mgaussian, sparselink and devel have similar performance (i.e., MTL has no benefit with any of these three approaches), examine whether other approaches are better

# examine whether group lasso for TL/MTL performs better



# unit interval
#glm.separate        devel   sparselink 
#   1.0000000    0.9742187    0.9598362 

# flexible
#glm.separate        devel   sparselink 
#   1.0000000    0.9745329    0.9475552 

# Consider using different candidate values, e.g., 0.01,0.5,1,1.5,2,10 also for sparselink. Removing 0 might be a good choice. (If 0 is not included, however, initial ridge regression might be better.)

test <- list()
for(k in seq_along(problem)){
  test[[k]] <- list()
  for(i in 1){
    test[[k]][[i]] <- joinet:::cv.joinet(Y=y[,colnames(y) %in% problem[[k]]],X=x,family="gaussian")
  }
}

rowMeans(sapply(test,function(x) rowMeans(apply(x,2,rank))))

This chunk saves the session information for generating figures and tables.