SpaCE: Spatial Cellular Estimator for Tumors

Documented in SpaCET.deconvolution

#' @title Deconvolve tumor ST data set
#' @description Estimate the cell fraction of cell lineages and sub lineages.
#' @param SpaCET_obj An SpaCET object.
#' @param cancerType Cancer type of the current tumor ST dataset.
#' @param coreNo Core number in parallel computation.
#' @return An SpaCET object.
#' @examples
#' SpaCET_obj <- SpaCET.deconvolution(SpaCET_obj, cancerType="BRCA", coreNo=8)
#'
#' @rdname SpaCET.deconvolution
#' @export
#'
SpaCET.deconvolution <- function(SpaCET_obj, cancerType, coreNo=8)
{
  coreNoDect <- parallel::detectCores()
  if(coreNoDect<coreNo) coreNo <- coreNoDect
  if(Sys.info()[['sysname']] == "Windows")
  {
    print("Since Windows does not support > 1 core, coreNo=1 is used automatically.")
    coreNo <- 1
  }

  st.matrix.data <- SpaCET_obj@input$counts
  st.matrix.data <- st.matrix.data[Matrix::rowSums(st.matrix.data)>0,]

  # filter the matrix with ref genes in case the matrix is too big
  load( system.file("extdata",'combRef_0.5.rda',package = 'SpaCET') )
  if(ncol(st.matrix.data) > 20000)
  {
    st.matrix.data <- st.matrix.data[rownames(st.matrix.data)%in%rownames(Ref$refProfiles),]
  }

  print("Stage 1. Infer malignant cell fraction.")
  malRes <- inferMal_cor(st.matrix.data,cancerType)

  print("Stage 2. Hierarchically deconvolve non-malignant cell fraction.")

  if(ncol(st.matrix.data) <= 20000)
  {
    propMat <- SpatialDeconv(
      ST=st.matrix.data,
      Ref=Ref,
      malProp=malRes$malProp,
      malRef=malRes$malRef,
      mode="standard",
      coreNo=coreNo
    )
  }else{
    subNo <- ceiling(ncol(st.matrix.data)/5000)
    for(x in 1:subNo)
    {
      print(paste0("Processing ",x,"/",subNo))

      if(x!=subNo)
      {
        spotSub <- (5000*(x-1)+1):(5000*x)
      }else{
        spotSub <- (5000*(x-1)+1):ncol(st.matrix.data)
      }

      propMatSub <- SpatialDeconv(
        ST=st.matrix.data[,spotSub],
        Ref=Ref,
        malProp=malRes$malProp[spotSub],
        malRef=malRes$malRef,
        mode="standard",
        coreNo=coreNo
      )

      if(x==1)
      {
        propMat <- propMatSub
      }else{
        propMat <- cbind(propMat, propMatSub)
      }
    }
  }

  SpaCET_obj@results$deconvolution$Ref <- Ref
  SpaCET_obj@results$deconvolution$propMat <- propMat
  SpaCET_obj
}


inferMal_cor <- function(st.matrix.data, cancerType)
{
  load( system.file("extdata", 'cancerDictionary.rda', package = 'SpaCET') )
  cancerTypes <- unique(c(names(cancerDictionary$CNA),names(cancerDictionary$expr)))
  cancerTypes <- sapply(strsplit(cancerTypes,"_",fixed=T),function(x) return(x[2]))
  if(!cancerType%in%cancerTypes)
  {
    stop("The input cancer type does not match anyone in the build-in dictionary of SpaCET.
         Please make sure you have input the correct cancer type name.
         If yes, it means the dictionary of SpaCET does not include the signature for input cancer type.
         User can set cancerType='PANCAN' to use the pan-cancer expression signature.")
  }

  st.matrix.data.diff <- Matrix::t(Matrix::t(st.matrix.data)*1e6/Matrix::colSums(st.matrix.data))
  st.matrix.data.diff[is.na(st.matrix.data.diff)] <- 0
  st.matrix.data.diff@x <- log2(st.matrix.data.diff@x+1)
  st.matrix.data.diff <- st.matrix.data.diff-Matrix::rowMeans(st.matrix.data.diff)

  if(ncol(st.matrix.data.diff) < 20000)
  {
    print("Stage 1 - Step 1. Clustering.")

    # clustering
    set.seed(123)
    suppressPackageStartupMessages(
      library(MUDAN)
    )

    matnorm.info <- normalizeVariance(methods::as(st.matrix.data, "dgCMatrix"),details=TRUE,verbose=FALSE)
    matnorm <- log10(matnorm.info$mat+1)
    pcs <- getPcs(matnorm[matnorm.info$ods,],nGenes=length(matnorm.info$ods),nPcs=30,verbose=FALSE)

    d <- as.dist(1-cor(t(pcs)))
    hc <- hclust(d, method='ward.D')

    cluster_numbers <- 2:9
    clustering <- cutree(hc,k=cluster_numbers)
    clustering <- t(clustering)
    rownames(clustering) <- paste0("c",rownames(clustering))

    # silhouette
    suppressPackageStartupMessages({
      library(factoextra)
      library(NbClust)
      library(cluster)
    })

    v <- c()
    for(i in cluster_numbers)
    {
      clustering0 <- cutree(hc,k=i)
      sil <- silhouette(clustering0, d, Fun=mean)
      v <- c(v, mean(sil[,3]))
    }

    v_diff <- v[1:(length(v)-1)]-v[2:length(v)]
    maxN <- which( v_diff == max(v_diff) ) +1  # find one that has the biggest decrease

    silMat <- cbind(cluster=cluster_numbers,silhouette=v)
    silMat <- cbind(silMat,maxN=cluster_numbers%in%maxN)

    clustering <- clustering[paste0("c",maxN),] # find optimal k


    print("Stage 1 - Step 2. Find tumor clusters.")

    for(CNA_expr in c("CNA","expr"))
    {
      cancerTypeExists <- grepl(cancerType,names(cancerDictionary[[CNA_expr]]))

      if(sum(cancerTypeExists) > 0)
      {
        sig <- as.matrix(cancerDictionary[[CNA_expr]][cancerTypeExists][[1]],ncol=1)
      }else{
        if(CNA_expr=="CNA") next
      }

      cor_sig <- corMat(as.matrix(st.matrix.data.diff),sig)

      stat.df <- data.frame()
      for(i in sort(unique(clustering)))
      {
        cor_sig_clustering <- cor_sig[clustering==i,]

        stat.df[i,"cluster"] <- i
        stat.df[i,"spotNum"] <- nrow(cor_sig_clustering)
        stat.df[i,"mean"] <- mean(cor_sig_clustering[,1])
        stat.df[i,"fraction_spot_padj"] <- sum(cor_sig_clustering[,"cor_r"]>0&cor_sig_clustering[,"cor_padj"]<0.25)/nrow(cor_sig_clustering)
        stat.df[i,"wilcoxTestG0"] <- suppressWarnings(wilcox.test(cor_sig_clustering[,1],mu=0,alternative="greater")$ p.value)
      }

      clusterMal <- which(
        stat.df[1:i,"mean"]>0&stat.df[1:i,"wilcoxTestG0"]<0.05 &
        stat.df[1:i,"fraction_spot_padj"]>=sum(cor_sig[,"cor_r"]>0&cor_sig[,"cor_padj"]<0.25)/nrow(cor_sig)
      )

      if(length(clusterMal)!=0) # find malignant spots.
      {
        print(paste0("                  > Use ",CNA_expr," signature: ",cancerType))
        malFlag <- TRUE
        break
      }else{
        if(CNA_expr=="expr")
        {
          print(paste0("                  > No malignant cells detected in this tumor ST data set."))
          malFlag <- FALSE
        }
      }

    }

    print("Stage 1 - Step 3. Infer malignant cells.")
    if(malFlag)
    {
      spotMal <- names(clustering)[clustering%in%clusterMal & cor_sig[,"cor_r"]>0]
      malRef <- Matrix::rowMeans( Matrix::t( Matrix::t(st.matrix.data[,spotMal])*1e6/Matrix::colSums(st.matrix.data[,spotMal]) ) )

      sig <- apply(st.matrix.data.diff[,spotMal,drop=F],1,mean)
      sig <- matrix(sig)
      rownames(sig) <- rownames(st.matrix.data.diff)

      cor_sig <- corMat(as.matrix(st.matrix.data.diff),sig)

      malProp <- cor_sig[,"cor_r"]
      names(malProp) <- rownames(cor_sig)

      malPropSorted <- sort(malProp)
      top5p <- round(length(malPropSorted)*0.05)
      p5 <- malPropSorted[top5p]
      p95 <- malPropSorted[length(malPropSorted)-top5p+1]

      malProp[malProp<=p5] <- p5
      malProp[malProp>=p95] <- p95

      malProp <- ( malProp-min(malProp) ) / ( max(malProp)-min(malProp) )

      list("malRef"=malRef,"malProp"=malProp)
    }else{
      malProp <- rep(0,dim(st.matrix.data.diff)[2])
      names(malProp) <- colnames(st.matrix.data.diff)

      list("malRef"=NULL,"malProp"=malProp)
    }

  }else{ # spot > 20000
    CNA_expr <- "CNA"

    cancerTypeExists <- grepl(cancerType,names(cancerDictionary[[CNA_expr]]))
    sig <- as.matrix(cancerDictionary[[CNA_expr]][cancerTypeExists][[1]],ncol=1)

    subNo <- ceiling(ncol(st.matrix.data.diff)/5000)
    malProp <- c()
    for(x in 1:subNo)
    {
      if(x!=subNo)
      {
        cor_sig <- corMat(as.matrix(st.matrix.data.diff[,(5000*(x-1)+1):(5000*x)]),sig)
      }else{
        cor_sig <- corMat(as.matrix(st.matrix.data.diff[,(5000*(x-1)+1):ncol(st.matrix.data.diff)]),sig)
      }

      malPropSub <- cor_sig[,"cor_r"]
      names(malPropSub) <- rownames(cor_sig)

      malProp <- c(malProp, malPropSub)
    }

    malPropSorted <- sort(malProp)
    top5p <- round(length(malPropSorted)*0.02)
    p5 <- malPropSorted[top5p]
    p95 <- malPropSorted[length(malPropSorted)-top5p+1]

    malProp[malProp<=p5] <- p5
    malProp[malProp>=p95] <- p95

    malProp <- ( malProp-min(malProp) ) / ( max(malProp)-min(malProp) )


    malRef <- Matrix::rowMeans( Matrix::t( Matrix::t(st.matrix.data[,malProp>=1])*1e6/Matrix::colSums(st.matrix.data[,malProp>=1]) ) )

    list("malRef"=malRef,"malProp"=malProp)
  }

}


SpatialDeconv <- function(
    ST,
    Ref,
    malProp,
    malRef,
    mode=c("standard","deconvMal","deconvWithSC","deconvWithSC_alt"),
    Unidentifiable=TRUE,
    MacrophageOther=TRUE,
    coreNo
)
{
  Reference <- Ref$refProfiles
  Signature <- Ref$sigGenes
  Tree <- Ref$lineageTree

  olpGenes <- intersect(rownames(ST), rownames(Reference))

  ST <- ST[olpGenes,]
  Reference <- Reference[olpGenes,]

  ST <- Matrix::t( Matrix::t(ST)*1e6/Matrix::colSums(ST) )
  Reference <- t( t(Reference)*1e6/colSums(Reference) )

  ST <- ST[,!is.nan(ST[1,])]

  if(sum(malProp)>0)
  {
    if(is.matrix(malRef))
    {
      olpGenes <- intersect(rownames(ST), rownames(malRef))

      ST <- ST[olpGenes,]
      malRef <- malRef[olpGenes,]

      ST <- Matrix::t( Matrix::t(ST)*1e6/Matrix::colSums(ST) )
      malRef <- t( t(malRef)*1e6/colSums(malRef) )

      ST <- ST[,!is.nan(ST[1,])]

      mixtureMal <- malRef%*%malProp[colnames(malRef),] # -1 for minus unidentifiable
    }else{
      malRef <- malRef[rownames(ST)]
      malRef <- malRef*1e6/sum(malRef)
      mixtureMal <- matrix(malRef,ncol=1)%*%matrix(malProp,nrow=1)
      colnames(mixtureMal) <- names(malProp)
    }

    olpSpots <- intersect(colnames(ST), colnames(mixtureMal))
    ST <- ST[,olpSpots]
    mixtureMal <- mixtureMal[,olpSpots]

    mixtureMinusMal <- ST - mixtureMal
  }else{
    mixtureMinusMal <- ST
  }

  tempReference <- Reference
  tempSignature <- Signature


  ###### level 1 deconv ######
  Level1 <- names(Tree)[names(Tree)%in%colnames(tempReference)]

  if(mode!="deconvMal")
  {
    print("Stage 2 - Level 1. Estimate the major lineage.")

    mixture <- mixtureMinusMal
    Reference <- tempReference[,Level1]
    Signature <- tempSignature[c(Level1,"T cell")]

    nSpot <- dim(mixture)[2]
    nCell <- dim(Reference)[2]
    thetaSum <- (1-malProp)-1e-5

    Signature <- unique(unlist(Signature))
    Signature <- Signature[Signature%in%olpGenes]

    mixture <- mixture[Signature,]
    Reference <- Reference[Signature,]

    propList <- parallel::mclapply(
      1:nSpot,
      FUN=function(i){
        theta <- rep(thetaSum[i]/nCell, nCell)

        if(thetaSum[i]>0.01)
        {
          if(Unidentifiable==TRUE)
          {
            ppmin <- 0
          }else{
            ppmin <- 1-malProp[i]-2e-5
          }
          ppmax <- 1-malProp[i]

          ui <- rbind(diag(nCell), rep(1, nCell), rep(-1, nCell))
          ci <- c(rep(0,nCell), ppmin, -ppmax) #ppmin, ppmax


          f0 <- function(A, x, b){
            sum( (A %*% x - b)^2 )
          }
          res <- stats::constrOptim(theta=theta, f=f0, grad=NULL, ui=ui, ci=ci, A=Reference, b=mixture[,i])
          prop <- res$par
          names(prop) <- colnames(Reference)


          bhat <- Reference %*% prop
          f <- function(A, x, b){
            sum( (A %*% x - b)^2 * ( 1 / ( (bhat +1) ) ) )
          }

          res <- stats::constrOptim(theta=theta, f=f, grad=NULL, ui=ui, ci=ci, A=Reference, b=mixture[,i])
          prop <- res$par
          names(prop) <- colnames(Reference)
        }else{
          prop <- theta
        }

        return(prop)
      },
      mc.cores=coreNo
    )

    propMat <- as.matrix(as.data.frame(propList))
    colnames(propMat) <- colnames(mixture)
    rownames(propMat) <- colnames(Reference)

    if(mode%in%c("standard","deconvWithSC_alt"))
    {
      propMat <- rbind(Malignant=malProp[colnames(propMat)], propMat)
    }

    if(Unidentifiable==TRUE)
    {
      if(mode=="standard")
      {
        propMat <- rbind(propMat, Unidentifiable=1-colSums(propMat))
      }else if(mode=="deconvWithSC_alt"){
        propMat_nonMal <- propMat[-1,]
        propMat_nonMal <- t( t(propMat_nonMal)/colSums(propMat_nonMal) )
        propMat_nonMal <- t( t(propMat_nonMal)*(1-propMat[1,]) )
        propMat[-1,] <- propMat_nonMal
      }else{ # deconvWithSC
        propMat <- t( t(propMat)/colSums(propMat) )
      }
    }

    propMatLevel1 <- propMat

  }else{
    propMatLevel1 <- matrix(1-colSums(malProp),nrow=1)
    rownames(propMatLevel1) <- "Malignant"
    colnames(propMatLevel1) <- colnames(malProp)
  }

  if(mode!="deconvMal")
  {
    print("Stage 2 - Level 2. Estimate the sub lineage.")
  }

  ###### level 2 deconv ######
  for(cellSpe in names(Tree)[unlist(lapply(Tree,function(x) length(x)>=2))])
  {
      if(!cellSpe%in%rownames(propMatLevel1)) next

      cellsub <- Tree[[cellSpe]]
      cellsub <- setdiff(cellsub,"Macrophage other")

      if( length(setdiff(Level1,cellSpe)) > 0)
      {
        mixture <- mixtureMinusMal - tempReference[,setdiff(Level1,cellSpe),drop=F] %*% propMatLevel1[setdiff(Level1,cellSpe),,drop=F]
      }else{
        mixture <- mixtureMinusMal
      }
      Reference <- tempReference[,colnames(tempReference)%in%cellsub,drop=F]
      Signature <- tempSignature[names(tempSignature)%in%cellsub] ######

      nSpot <- dim(mixture)[2]
      nCell <- dim(Reference)[2]
      thetaSum <- propMatLevel1[cellSpe,]-1e-5

      Signature <- unique(unlist(Signature))
      Signature <- Signature[Signature%in%olpGenes]

      mixture <- mixture[Signature,]
      Reference <- Reference[Signature,,drop=F]

      ui <- rbind(diag(nCell), rep(1, nCell), rep(-1, nCell))

      propList <- parallel::mclapply(
        1:nSpot,
        FUN=function(i){
          theta <- rep(thetaSum[i]/nCell, nCell)

          if(thetaSum[i]>0.01)
          {
            if(cellSpe=="Macrophage")
            {
              if(MacrophageOther)
              {
                ppmin <- 0
              }else{
                ppmin <- propMatLevel1[cellSpe,i]-2e-5
              }
              ppmax <- propMatLevel1[cellSpe,i]
            }else{
              ppmin <- propMatLevel1[cellSpe,i]-2e-5
              ppmax <- propMatLevel1[cellSpe,i]
            }

            ci <- c(rep(0,nCell), ppmin, -ppmax)

            f0 <- function(A, x, b){
              sum( (A %*% x - b)^2 )
            }
            res <- stats::constrOptim(theta=theta, f=f0, grad=NULL, ui=ui, ci=ci, A=Reference, b=mixture[,i])
            prop <- res$par
            names(prop) <- colnames(Reference)

            bhat <- Reference %*% prop
            f <- function(A, x, b){
              sum( (A %*% x - b)^2 * ( 1 / ( (bhat +1) ) ) )
            }

            res <- stats::constrOptim(theta=theta, f=f, grad=NULL, ui=ui, ci=ci, A=Reference, b=mixture[,i])
            prop <- res$par
            names(prop) <- colnames(Reference)

          }else{
            prop <- theta
          }

          return(prop)
        },
        mc.cores=coreNo
      )

      propMat <- as.matrix(as.data.frame(propList))
      colnames(propMat) <- colnames(mixture)
      rownames(propMat) <- colnames(Reference)

      if(mode=="standard"&MacrophageOther&cellSpe=="Macrophage")
      {
        propMat <- rbind(propMat, "Macrophage other"=propMatLevel1[cellSpe,]-colSums(propMat))
      }

      propMatLevel1 <- rbind(propMatLevel1, propMat)
  }

  propMat <- propMatLevel1

  propMat[propMat<0] <- 0
  propMat[propMat>1] <- 1

  propMat
}


corMat <- function(X,Y,method="pearson")
{
  olp <- intersect(rownames(X),rownames(Y))

  cc_corr <- psych::corr.test(
    X[olp,,drop=F],
    Y[olp,,drop=F],
    method=method,adjust="none",ci=FALSE)

  cc_corr_r <- round(cc_corr$r[,1],3)
  cc_corr_p <- signif(cc_corr$p[,1],3)

  cc_corr_rp <- data.frame(
    cor_r=cc_corr_r,
    cor_p=cc_corr_p,
    cor_padj=p.adjust(cc_corr_p, method = "BH")
  )

  cc_corr_rp
}