R/MBImpute.R

In ProteoMM: Multi-Dataset Model-based Differential Expression Proteomics Analysis Platform

# Model-based imputaion  - last save 23/06/16
# Ref:  "A statistical framework for protein quantitation in bottom-up MS-based
#        proteomics. Karpievitch Y, Stanley J, Taverner T, Huang J, Adkins JN,
#        Ansong C, Heffron F, Metz TO, Qian WJ, Yoon H, Smith RD, Dabney AR.
#        Bioinformatics 2009
# 
# Written by Yuliya Karpievitch, Tom Taverner, and Shelley Herbrich
# for TAMU, PPNNL and community


#' Model-Based Imputation of missing values
#'
#' Impute missing values based on information
#' from multiple peptides within a protein
#' Expects the data to be filtered to contain
#' at least one observation per treatment
#' group.
#' For experiments with lower overall abundaneces such as multiplexed
#' experiments check if the imputed value is below 0, if so value is reimputed
#' untill it is above 0.
#'
#' @param mm number of peptides x number of samples matrix of intensities
#' @param treatment vector indicating the treatment group of each sample eg
#'        as.factor(c('CG','CG','CG', 'mCG','mCG','mCG')) or c(1,1,1,1,2,2,2,2)
#' @param prot.info protein metadata, 2+ columns: peptide IDs, protein IDs, etc
#' @param pr_ppos column index for protein ID in prot.info
#' @param my.pi PI value, estimate of the proportion of peptides missign
#'              completely at random, as compared to censored at lower
#'              abundance levels default values of 0.05 is usually reasoanble
#'              for missing completely at random values
#'              in proteomics data
#' @param compute_pi TRUE/FALSE (default=FALSE) estimate Pi is set to TRUE,
#'              otherwise use the provided value. We consider Pi=0.05 a
#'              reasonable estimate for onservations missing completely at
#'              random in proteomics experiments. Thus values is set to NOT
#'              estimate Pi by default. Note: spline smoothing
#'              can sometimes produce values of Pi outside the range of
#'              possible values.
#'
#' @return A structure with multiple components
#' \describe{
#'   \item{y_imputed}{number of peptides x m matrix of peptides
#'                    with no missing data}
#'   \item{imp_prot.info}{imputed protein info, 2+ columns: peptide ID,
#'                  protein IDs, etc
#'                  Dimentions should be the same as passed in}
#'}
#' @examples
#' data(mm_peptides)
#' head(mm_peptides)
#' intsCols = 8:13 # different from parameter names as R uses outer name spaces
#'                 # if variable is undefined
#' metaCols = 1:7 # reusing this variable
#' m_logInts = make_intencities(mm_peptides, intsCols)  # will reuse the name
#' m_prot.info = make_meta(mm_peptides, metaCols)
#' m_logInts = convert_log2(m_logInts)
#' grps = as.factor(c('CG','CG','CG', 'mCG','mCG','mCG'))
#' 
#' set.seed(135)
#' mm_m_ints_eig1 = eig_norm1(m=m_logInts,treatment=grps,prot.info=m_prot.info)
#' mm_m_ints_eig1$h.c # check the number of bias trends detected
#' mm_m_ints_norm = eig_norm2(rv=mm_m_ints_eig1)
#' mm_prot.info = mm_m_ints_norm$normalized[,1:7]
#' mm_norm_m =  mm_m_ints_norm$normalized[,8:13]
#' 
#' # ATTENTION: SET RANDOM NUMBER GENERATOR SEED FOR REPRODUCIBILITY !!
#' set.seed(125) # if nto set every time results will be different
#' imp_mm = MBimpute(mm_norm_m, grps, prot.info=mm_prot.info, pr_ppos=2,
#'                   my.pi=0.05, compute_pi=FALSE)
#' @export
MBimpute = function(mm, treatment, prot.info, pr_ppos=2, my.pi=0.05,
                    compute_pi=FALSE){
  warning("This function uses random number generator. For reproducibility use 
          set.seed(12345) with your choce of parameter", immediate.=TRUE)
  # calculate PI or use one passed in as parameter:
  if (compute_pi){
    message('Estimating Pi')
  	my.pi = eigen_pi(mm, toplot=TRUE)
  }

  # (From EigenMS) check if treatment is a 'factor' vs data.frame',
  # i.e. single vs multiple factors
  if(is.factor(treatment)) { # TRUE if one factor
    n.treatment = 1 # number of factors in the model
    # number of levels within the only factor
    n.u.treatment = length(unique(treatment))[1]
  } else { # data.frame
    n.treatment = dim(treatment)[2]
    # all possible treatment combinations
    n.u.treatment = dim(unique(treatment))[1]
  }

  # Match to protein
  all.proteins = unique(prot.info[,pr_ppos])
  y_imputed = NULL
  imp_prot.info = NULL
  message("Imputing...\n")

  for (kk in seq_len(length(all.proteins))) {
    prot = all.proteins[kk]
    pmid.matches = prot.info[prot.info[,pr_ppos]==prot,1]

    curr_prot.info = prot.info[prot.info[,pr_ppos]==prot,]
    idx.prot = which(prot.info[,1] %in% pmid.matches)  # do not obligate
                              # to be rownames, as those have to be Unique
    y_raw = mm[idx.prot,,drop=FALSE]
    cat(paste("Protein: ", prot, ": ", dim(y_raw)[1],
              " peptides (", kk, "/", length(all.proteins), ")", sep="" ))

    # yuliya: this should not happen here (NO observations)
    if (nrow(y_raw) == 0) next

    # peptides and proteins of poor quality are removed prior to analysis
    # "poor quality" was defined (Karpievitch et al. 2009)
    # as having little "information" abt grp differences compared to
    # other peptides estimate data parameters.
    # To speed up execution we allow EigenMS to eliminat all peptides
    # with fewer than one observation per treatment group and impte the rest.
    n.peptide = nrow(y_raw)
    yy = as.vector(t(y_raw))
    nn = length(yy)
    peptide =rep(seq_len(n.peptide), each=dim(data.frame(treatment))[1])

    # filter out min.missing
    n.present = array(NA, c(n.peptide, n.u.treatment))
    colnames(n.present) = unique(treatment)

    for(jj in seq_len( n.u.treatment) ){
       n.present[,jj] = rowSums(!is.na(y_raw[,treatment==unique(treatment)[jj],
                                             drop=FALSE]))
    }
    # remove peptides with completely missing group(s)
    # non-vectorized: present.min = apply(n.present, 1, min)
    present.min = matrixStats::rowMins(n.present)
    ii = present.min > 0
    # reassign Y_raw to a submatrix of 1+ observations in each group
    y_raw = y_raw[ii,,drop=FALSE]

    # keep track of pepIDs and prIDs here...
    if (nrow(y_raw) == 0) next
	  peptide = rep(seq_len(n.peptide), each=dim(data.frame(treatment))[1])

    # make column names for the n.present matrix
    tmp = unique(treatment)
    # this does not work if a factor
    nrow_tmp = dim(tmp)[1]
    # R does not remove the variable col_names1 from name
    # space outside of the if/else..
    if(is.factor(tmp)) {
     col_names1 = tmp
    } else {
      col_names1 = vector('character', nrow_tmp)
      bob = data.frame(lapply(tmp, as.character), stringsAsFactors=FALSE)
      for(ii in seq_len(nrow_tmp)) {
       col_names1[ii] = paste(bob[ii,1], bob[ii,2], sep='_')
      }
    }

    # calculate pooled variance for each protein
    grp = array(NA, c(1, n.u.treatment))
    for (jj in seq_len(n.u.treatment)) {
      grp[jj] = sum(n.present[, jj])
    }
    pep_var = 0 # yuliya: was not declared in impute only
    go = protein_var(y_raw, treatment) # yuliya: function, see below
    overall_var = go$overall_var

    num = 0
    den = 0
    # calculate pooled variance for each peptide
    # if only 1 onservation in a dx group assign the overall variance
    for(ii in seq_len(n.peptide))
    {
      # which treatment has more obsertations? - use one of the 2 groups
      pep = yy[peptide==ii]
      most_obs = which(max(n.present[ii,]) == n.present[ii,])
      lala = length(most_obs)
      if(lala > 1) {
        # more than 1 gorup has max # of observations, pick one at random
        most_obs = most_obs[sample(lala,1)]
      }
      tmp = data.frame(most_obs)
      treat_to_use = rownames(tmp)
      y.i = pep[treatment == treat_to_use]
      p2 = stats::var(y.i, na.rm=TRUE)
      if (is.na(p2)) { p2 = 0 }
      present = length(y.i)
      num = num + (p2 * (present-1))
      den = den + (present-1)
    }
    pep_var = num/den

    if(is.na(pep_var)) {
      pep_var = overall_var
      cat(idx.prot)
      cat('\t')
    } # only occurs if we have 1 pep per group
    if (pep_var == 0) { pep_var = overall_var }
    if (pep_var == 0) { pep_var = .0001 } # if overall var is 0...
    peptides.missing = rowSums(is.na(y_raw))

    f.treatment = factor(rep(treatment, n.peptide)) # used below
    f.peptide = factor(peptide) # used below

    # estimate rough model parameters
    # create model matrix for each protein
    # remove any missing values from consideration
    iii = (seq_len(nn))[is.na(yy)] # positions of the NA's
    if (n.peptide != 1){
      X  = stats::model.matrix(~f.peptide + f.treatment,
                        contrasts = list(f.treatment="contr.sum",
                                         f.peptide="contr.sum") )
    } else {
      X = stats::model.matrix(~f.treatment,
                              contrasts=list(f.treatment="contr.sum"))
    }
    if(length(iii) > 0){
      y.c = yy[-iii] # remove NA value
      X.c = X[-iii,] # remove rows for NA values from the model matrix
    } else {
      y.c = yy
      X.c = X
    }

    # calculate initial beta values and residuals
    beta = drop(solve(t(X.c) %*% X.c) %*% t(X.c) %*% y.c)

    # compute initial delta's
    peptides.missing[peptides.missing==0] = 0.9
    delta.y = as.numeric(1/sqrt(pep_var*peptides.missing))
    dd = delta.y[as.numeric(peptide)]

    # non-vectorized option: c_hat = apply(y_raw,1,min,na.rm=TRUE)
    c_hat = matrixStats::rowMins(as.matrix(y_raw), na.rm=TRUE)
    c_h = c_hat[as.numeric(peptide)]

    if(n.peptide==1){
      y.predict = stats::model.matrix(~f.treatment,
                               contrasts=list(f.treatment="contr.sum"))%*% beta
    } else {
      y.predict = stats::model.matrix(~f.peptide + f.treatment,
                               contrasts = list(f.treatment="contr.sum",
                                                f.peptide="contr.sum"))%*% beta
    }

    zeta = dd*(c_h - y.predict)
    PHI = stats::pnorm(zeta, 0, 1)
    prob.cen = PHI / ( (my.pi + (1-my.pi) * PHI) )

    choose.cen = stats::runif(nn) < prob.cen
    set.cen = is.na(yy) & choose.cen
    set.mar = is.na(yy) &! choose.cen

    # Imputation: Replace missing values with random numbers
    #             drawn from the estimated likelihood model
    sigma = 1/dd
    y.impute = t(y_raw)
    if(sum(set.cen) > 0) { # censored
      mus = y.predict[set.cen]
      ss = sigma[set.cen]
      cutoff = c_h[set.cen] # rep(c.guess, nn)[set.cen]
      # Apri 9, 2018 - added lo=0 cutoff, truncated normal at both ends
      # intensities below 0 are not valid
      y.impute[set.cen] = rnorm.trunc(sum(set.cen), mus, ss, lo=0, hi=cutoff)
    }
    if(sum(set.mar) > 0) { # randomly missing
      # Apri 9, 2018 - added lo=0 cutoff, truncated normal at 0
      # mainly for multiplexed experiments where abundances may be lower
      y.impute[set.mar] = rnorm.trunc(sum(set.mar), y.predict[set.mar], 
                                      sigma[set.mar], lo=0)
    }

    y.impute.return = t(y.impute)
    imp_prot.info = rbind(imp_prot.info,curr_prot.info)
    y_imputed = rbind(y_imputed, y.impute.return)
  } # end for each protein

  colnames(y_imputed) = colnames(mm)
  cat("Done imputing.\n")
  return(list(y_imputed=y_imputed,
              imp_prot.info=imp_prot.info,pi=as.matrix(my.pi)))
}
############# end imputation ###################


############## function pi #############
#' Compute PI - proportion of observations missing completely at random
#'
#' @param m matrix of abundances, numsmaples x numpeptides
#' @param toplot TRUE/FALSE plot mean vs protportion missing curve and PI
#' @return pi estimate of the proportion of
#'         observations missing completely at random
#'
#' Contributed by Shelley Herbrich & Tom Taverner for Karpievitch et al. 2009
#' @examples
#' data(mm_peptides)
#' intsCols = 8:13
#' metaCols = 1:7
#' m_logInts = make_intencities(mm_peptides, intsCols)
#' m_prot.info = make_meta(mm_peptides, metaCols)
#' m_logInts = convert_log2(m_logInts)
#' my.pi = eigen_pi(m_logInts, toplot=TRUE)
#' @export
eigen_pi = function(m, toplot=TRUE)
{
  # (1) compute 1) ave of the present values from each petide
  #             2) number of missing and present values for each peptide

  # remove completely missing rows
  m = m[rowSums(m, na.rm=TRUE)!=0,]

  pepmean = matrixStats::rowMeans2(as.matrix(m), na.rm=TRUE)
  # non-vectorized version: pepmean = apply(m, 1, mean, na.rm=TRUE)
  propmiss = rowSums(is.na(m))/ncol(m)

  smooth_span = 0.4
  fit = stats::lowess(pepmean, propmiss, f=smooth_span)
  PI = fit$y[fit$x==max(pepmean)]

  count = 1
  while (PI<=0){
    smooth_span = smooth_span-.1
    fit = stats::lowess(pepmean, propmiss, f=smooth_span)
    PI = fit$y[fit$x==max(pepmean)]
    count = count + 1
    if (count > 500) break
  }

  if (toplot){
  st = paste("PI: ", PI)
  # plot data point
  graphics::plot(pepmean, propmiss, xlab="x", ylab="y", cex=0.5) 
  graphics::lines(fit)
  graphics::title("Lowess Regression", sub = st,
      cex.main = 2,   font.main= 3, col.main= "purple",
      cex.sub = 1, font.sub = 3, col.sub = "red")
  }
  return (pi=PI)
}

######################################################
protein_var = function(Y_raw, treatment){
# estimates coefficients for all peptides from a single protein
# a portion of what get_coeffs does , without information computations
# that is nto needed in imputation
#
# Input:
#   Y_raw: m peptides by n samples arrays matrix of expression data
#          from a given protein
#   treatment: treatment groups
#
# Output:
#   overall_var:  need to check...

  n.peptide = nrow(Y_raw)
  y = as.vector(t(Y_raw))
  n = length(y)
  n.treatment = length(treatment)
  n.u.treatment = length(unique(treatment))
  peptide = rep(seq_len( n.peptide), each=n.treatment)

  n.present = array(NA, c(n.peptide, n.u.treatment))
  colnames(n.present) = unique(treatment)
  for(i in seq_len(n.peptide)) {
      for(j in seq_len(n.u.treatment)) {
          n.present[i,j] = sum(!is.na(y[peptide==i &
                                          treatment==unique(treatment)[j]]))
      }
  }

  f.treatment = factor(rep(treatment, n.peptide)) # used in model.matrix below
  f.peptide = factor(peptide) #  used in stats::model.matrix below

  # estimate rough model parameters
  # create model matrix for each protein and
  # remove any peptides with missing values
  ii = seq_len(n)[is.na(y)]
  if (n.peptide != 1){
    X  = stats::model.matrix(~f.peptide + f.treatment,
                      contrasts = list(f.treatment="contr.sum",
                                       f.peptide="contr.sum") )
  } else {
    X = stats::model.matrix(~f.treatment,
                            contrasts=list(f.treatment="contr.sum"))
  }
  if(length(ii) > 0){
    y.c = y[-ii]
    X.c = X[-ii,]
  } else {
    y.c = y
    X.c = X
  }

  # calculate initial beta values and residuals
  beta = drop(solve(t(X.c) %*% X.c) %*% t(X.c) %*% y.c)
  Y_hat = X.c %*% beta
  Y_temp = Y_raw
  Y_temp = as.vector(t(Y_temp)) # yuliya, same as in filter now
  Y_temp[!is.na(Y_temp)] = Y_hat
  Y_temp = matrix(Y_temp, nrow = n.peptide, byrow = TRUE)
  Y_hat = Y_temp

  effects = X.c %*% beta
  resid = y.c - effects
  overall_var = stats::var(resid)
  return(list(overall_var=det(overall_var)))
}

my.Psi = function(x, my.pi){
exp(log(1-my.pi)+stats::dnorm(x, 0, 1, log=TRUE) -
      log(my.pi+(1-my.pi) * stats::pnorm(x, 0, 1)))
}

my.Psi.dash = function(x, my.pi){
# calculates the derivative of Psi
-my.Psi(x, my.pi) * (x + my.Psi(x, my.pi))
}

phi = function(x){stats::dnorm(x)}

# rnorm.trunc(sum(set.cen), mus, ss, hi=cutoff)
rnorm.trunc = function (n, mu, sigma, lo=-Inf, hi=Inf){
# Calculates truncated normal
  p.lo = stats::pnorm(lo, mu, sigma)
  p.hi = stats::pnorm(hi, mu, sigma)
  u = stats::runif(n, p.lo, p.hi)
  return(stats::qnorm(u, mu, sigma))
}