R/hsaftallcorr.R

In PanCanVarSel: Pan-Cancer Variable Selection

#'

#'

#' This function extends the main function \code{\link{hsaft}} to create correlation among covariates.

#'

#'

#'

#' @references Stephanie van der Pas, James Scott, Antik Chakraborty and Anirban Bhattacharya (2016). horseshoe:

#' Implementation of the Horseshoe Prior. R package version 0.1.0.

#' https://CRAN.R-project.org/package=horseshoe

#'

#' Arnab Kumar Maity, Anirban Bhattacharya, Bani K. Mallick, and Veerabhadran Baladandayuthapani (2017).

#' Joint Bayesian Estimation and Variable Selection for TCPA Protein Expression Data

#'

#'

#'

#'@param ct Response, a \eqn{n*2} matrix with first column as response and second column as right censored indicator,

#'1 is event time and 0 is right censored.

#'@param X Matrix of covariates, dimension \eqn{n*p}.

#'@param method.tau Method for handling \eqn{\tau}. Select "truncatedCauchy" for full

#' Bayes with the Cauchy prior truncated to [1/p, 1], "halfCauchy" for full Bayes with

#' the half-Cauchy prior, or "fixed" to use a fixed value (an empirical Bayes estimate,

#' for example).

#'@param tau  Use this argument to pass the (estimated) value of \eqn{\tau} in case "fixed"

#' is selected for method.tau. Not necessary when method.tau is equal to"halfCauchy" or

#' "truncatedCauchy". The default (tau = 1) is not suitable for most purposes and should be replaced.

#'@param method.sigma Select "Jeffreys" for full Bayes with Jeffrey's prior on the error

#'variance \eqn{\sigma^2}, or "fixed" to use a fixed value (an empirical Bayes

#'estimate, for example).

#'@param Sigma2 A fixed value for the error variance \eqn{\sigma^2}. Not necessary

#'when method.sigma is equal to "Jeffreys". Use this argument to pass the (estimated)

#'value of Sigma2 in case "fixed" is selected for method.sigma. The default (Sigma2 = 1)

#'is not suitable for most purposes and should be replaced.

#'@param burn Number of burn-in MCMC samples. Default is 1000.

#'@param nmc Number of posterior draws to be saved. Default is 5000.

#'@param thin Thinning parameter of the chain. Default is 1 (no thinning).

#'@param alpha Level for the credible intervals. For example, alpha = 0.05 results in

#'95\% credible intervals.

#'@param r number of groups.

#'@param n.seq a vector of sample sizes for all groups.

#'@param pk number of covariates in each group.

#'

#'

#'

#'@return \item{SurvivalHat}{Predictive survival probability.}

#'\item{LogTimeHat}{Predictive log time.}

#'\item{BetaHat}{Posterior mean of Beta, a \eqn{p} by 1 vector.}

#' \item{LeftCI}{The left bounds of the credible intervals.}

#' \item{RightCI}{The right bounds of the credible intervals.}

#' \item{BetaMedian}{Posterior median of Beta, a \eqn{p} by 1 vector.}

#' \item{Sigma2Hat}{Posterior mean of error variance \eqn{\sigma^2}. If method.sigma =

#' "fixed" is used, this value will be equal to the user-selected value of Sigma2

#' passed to the function.}

#' \item{TauHat}{Posterior mean of global scale parameter tau, a positive scalar.

#' If method.tau = "fixed" is used, this value will be equal to the user-selected value

#' of tau passed to the function.}

#' \item{BetaSamples}{Posterior samples of Beta.}

#' \item{TauSamples}{Posterior samples of tau.}

#' \item{Sigma2Samples}{Posterior samples of Sigma2.}

#' \item{BGHat}{Posterior samples of b which is a part of the mean of \eqn{\beta}.}

#' \item{BPHat}{Posterior samples of b which is the other part of the mean of \eqn{\beta}.}

#' \item{LikelihoodSamples}{Posterior Samples of likelihood.}

#'

#'

#'

#' @examples

#' # Examples for hsaftallcorr function

#' burnin <- 50   # number of burnin

#' nmc    <- 100  # number of Markov Chain samples

#' y.sd   <- 1     # standard deviation of the data

#' p      <- 80    # number of covariates

#' r      <- 5     # number of groups

#' p      <- 80    # number of covariate in each group

#' n1     <- 40    # sample size of 1st group

#' n2     <- 50    # sample size of 2nd group

#' n3     <- 70    # sample size of 3rd group

#' n4     <- 100   # sample size of 4th group

#' n5     <- 120   # sample size of 5th group

#' n      <- sum(c(n1, n2, n3, n4, n5))  # total sample size

#' n.seq  <- c(n1, n2, n3, n4, n5)

#' Beta   <- matrix(smoothmest::rdoublex(p * r), nrow = r, ncol = p, byrow = TRUE)

#' # from double exponential distribution

#' beta   <- as.vector(t(Beta))  # vectorize Beta

#' x1     <- mvtnorm::rmvnorm(n1, mean = rep(0, p))

#' x2     <- mvtnorm::rmvnorm(n2, mean = rep(0, p))

#' x3     <- mvtnorm::rmvnorm(n3, mean = rep(0, p))

#' x4     <- mvtnorm::rmvnorm(n4, mean = rep(0, p))

#' x5     <- mvtnorm::rmvnorm(n5, mean = rep(0, p))  # from multivariate normal distribution

#' y.mu1  <- x1 %*% Beta[1, ]

#' y.mu2  <- x2 %*% Beta[2, ]

#' y.mu3  <- x3 %*% Beta[3, ]

#' y.mu4  <- x4 %*% Beta[4, ]

#' y.mu5  <- x5 %*% Beta[5, ]

#' y1     <- stats::rnorm(n1, mean = y.mu1, sd = y.sd)

#' y2     <- stats::rnorm(n2, mean = y.mu2, sd = y.sd)

#' y3     <- stats::rnorm(n3, mean = y.mu3, sd = y.sd)

#' y4     <- stats::rnorm(n4, mean = y.mu4, sd = y.sd)

#' y5     <- stats::rnorm(n5, mean = y.mu5, sd = y.sd)

#' y      <- c(y1, y2, y3, y4, y5)

#' x      <- Matrix::bdiag(x1, x2, x3, x4, x5)

#' X      <- as.matrix(x)

#' y      <- as.numeric(as.matrix(y))  # from normal distribution

#' T      <- exp(y)   # AFT model

#' C      <- rgamma(n, shape = 1.75, scale = 3)  # censoring time

#' time   <- pmin(T, C)  # observed time is min of censored and true

#' status = time == T   # set to 1 if event is observed

#' ct     <- as.matrix(cbind(time = time, status = status))  # censored time

#' posterior.fit <- hsaftallcorr(ct, X, method.tau = "truncatedCauchy", method.sigma = "Jeffreys",

#'                               burn = burnin, nmc = nmc,

#'                               r = r, n.seq = n.seq, pk = p)

#' summary(posterior.fit$BetaHat)

#'

#'

#'

#' @export



# 20 November 2016

# We modify this code to update \beta for blockwise for each tumor

# Introduction of Correlation among proteins and groups all together

# calculate likelihood for lpml

# Inclusion of n_k

# Inclusion of f(n_k)

# No c

# inclusion of n_k

# compute predictive log(survival time)

# add C++ sampling for beta





hsaftallcorr <- function(ct, X, method.tau = c("fixed", "truncatedCauchy","halfCauchy"), tau = 1,
                         
                         method.sigma = c("fixed", "Jeffreys"), Sigma2 = 1,
                         
                         burn = 1000, nmc = 5000, thin = 1, alpha = 0.05,
                         
                         r, n.seq, pk)
  
{
  
  
  
  method.tau = match.arg(method.tau)
  
  
  
  method.sigma = match.arg(method.sigma)
  
  
  
  ptm=proc.time()
  
  niter <- burn+nmc
  
  effsamp=(niter -burn)/thin
  
  n=nrow(X)
  
  p=ncol(X)
  
  
  
  time        <- ct[, 1]
  
  status      <- ct[, 2]
  
  censored.id <- which(status == 0)
  
  n.censored  <- length(censored.id)  # number of censored observations
  
  X.censored   <- X[censored.id, ]
  
  y <- logtime <- log(time)   # for coding convenience, since the whole code is written with y
  
  
  
  ## parameters ##
  
  beta            <- rep(0, p)
  
  Beta            <- matrix(0, nrow = pk, ncol = r);
  
  lambda          <- rep(1,p);
  
  Lambda          <- matrix(1, nrow = pk, ncol = r)
  
  sigma_sq        <- Sigma2;
  
  bG              <- rep(0, r)
  
  sigma.bG.square <- rep(1, r)
  
  bP              <- rep(0, pk)
  
  BP              <- rep(0, p)
  
  sigma.bP.square <- rep(1, pk)
  
  B               <- rep(0, p)
  
  # f.n.seq        <- ifelse(n.seq < mean(n.seq), 1/n.seq, n.seq/sum(n.seq))
  
  f.n.seq        <- n.seq/n.seq
  
  betan           <- rep(0, p)
  
  
  
  
  
  ## output ##
  
  betaout       <- matrix(0, p, effsamp)
  
  lambdaout     <- matrix(0, p, effsamp)
  
  tauout        <- rep(0,effsamp)
  
  sigmaSqout    <- rep(1,effsamp)
  
  bGout         <- matrix(0, r, effsamp)
  
  bPout         <- matrix(0, pk, effsamp)
  
  likelihoodout <- matrix(0, n, effsamp)
  
  predsurvout   <- matrix(0, n, effsamp)
  
  logtimeout    <- matrix(0, n, effsamp)
  
  
  
  
  
  
  
  ## start Gibb's sampling ##
  
  message("Markov chain monte carlo is running")
  
  for(i in 1:niter)
    
  {
    
    
    
    
    
    mean.impute <- X.censored %*% beta
    
    sd.impute   <- sqrt(sigma_sq)
    
    ## update censored data ##
    
    time.censored <- msm::rtnorm(n.censored, mean = mean.impute, sd = sd.impute, lower = logtime[censored.id])
    
    # truncated at log(time) for censored data
    
    y[censored.id] <- time.censored
    
    
    
    mean  <- X %*% beta
    
    sd    <- sqrt(sigma_sq)
    
    predictive.survivor <- stats::pnorm(mean/sd, lower.tail = FALSE)
    
    
    
    
    
    ## update beta ##
    
    # Update beta in block for each cancer
    
    
    
    sum.nk <- 0
    
    sum.pk <- 0
    
    
    
    sum.nk1 <- sum.nk + 1
    
    sum.nk  <- sum.nk + n.seq[1]
    
    sum.pk1 <- sum.pk + 1
    
    sum.pk  <- sum.pk + pk
    
    
    
    lambdak <- lambda[sum.pk1:sum.pk]
    
    Xk <- X[sum.nk1:sum.nk, sum.pk1:sum.pk]
    
    yk <- y[sum.nk1:sum.nk]
    
    
    
    Dk     <- tau^2 * (1/f.n.seq[1]) * diag(lambdak^2)
    
    D.invk <- chol2inv(chol(Dk))
    
    D.inv  <- D.invk
    
    Ak     <- t(Xk) %*% Xk + D.invk
    
    A.invk <- chol2inv(chol(Ak))
    
    
    
    beta.mean  <- A.invk %*% (t(Xk) %*% yk + D.invk %*% B[sum.pk1:sum.pk])
    
    beta.Sigma <- sigma_sq * A.invk
    
    betak      <- t(mvtnorm::rmvnorm(1, mean = beta.mean, sigma = beta.Sigma))
    
    
    
    betan[sum.pk1:sum.pk] <- betak * sqrt(f.n.seq[1])
    
    beta[sum.pk1:sum.pk]  <- betak
    
    
    
    for(k in 2:r)
      
    {
      
      sum.nk1 <- sum.nk + 1
      
      sum.nk  <- sum.nk + n.seq[k]
      
      sum.pk1 <- sum.pk + 1
      
      sum.pk  <- sum.pk + pk
      
      
      
      lambdak <- lambda[sum.pk1:sum.pk]
      
      Xk <- X[sum.nk1:sum.nk, sum.pk1:sum.pk]
      
      yk <- y[sum.nk1:sum.nk]
      
      
      
      Dk     <- tau^2 * (1/f.n.seq[k]) * diag(lambdak^2)
      
      D.invk <- chol2inv(chol(Dk))
      
      D.inv  <- Matrix::bdiag(D.inv, D.invk)
      
      Ak     <- t(Xk) %*% Xk + D.invk
      
      A.invk <- chol2inv(chol(Ak))
      
      
      
      beta.mean  <- A.invk %*% (t(Xk) %*% yk + D.invk %*% B[sum.pk1:sum.pk])
      
      beta.Sigma <- sigma_sq * A.invk
      
      betak      <- t(mvtnorm::rmvnorm(1, mean = beta.mean, sigma = beta.Sigma))
      
      
      
      betan[sum.pk1:sum.pk] <- betak * sqrt(f.n.seq[k])
      
      beta[sum.pk1:sum.pk]  <- betak
      
    }
    
    
    
    
    
    Beta  <- matrix(beta, nrow = pk, ncol = r, byrow = FALSE)
    
    D.inv <- as.matrix(D.inv)
    
    
    
    
    
    ## update lambda_j's in a block using slice sampling ##
    
    eta = 1/(lambda^2)
    
    upsi = stats::runif(p,0,1/(1+eta))
    
    tempps = betan^2/(2*sigma_sq*tau^2)
    
    ub = (1-upsi)/upsi
    
    # now sample eta from exp(tempv) truncated between 0 & upsi/(1-upsi)
    
    Fub = 1 - exp(-tempps*ub) # exp cdf at ub
    
    Fub[Fub < (1e-4)] = 1e-4;  # for numerical stability
    
    up = stats::runif(p,0,Fub)
    
    eta = -log(1-up)/tempps
    
    lambda = 1/sqrt(eta);
    
    Lambda <- matrix(lambda, nrow = pk, ncol = r, byrow = FALSE)
    
    
    
    ## update tau ##
    
    ## Only if prior on tau is used
    
    if(method.tau == "halfCauchy"){
      
      tempt = sum((betan/lambda)^2)/(2*sigma_sq)
      
      et = 1/tau^2
      
      utau = stats::runif(1,0,1/(1+et))
      
      ubt = (1-utau)/utau
      
      Fubt = stats::pgamma(ubt,(p+1)/2,scale=1/tempt)
      
      Fubt = max(Fubt,1e-8) # for numerical stability
      
      ut = stats::runif(1,0,Fubt)
      
      et = stats::qgamma(ut,(p+1)/2,scale=1/tempt)
      
      tau = 1/sqrt(et)
      
    }#end if
    
    
    
    if(method.tau == "truncatedCauchy"){
      
      tempt = sum((betan/lambda)^2)/(2*sigma_sq)
      
      et = 1/tau^2
      
      utau = stats::runif(1,0,1/(1+et))
      
      ubt_1=1
      
      ubt_2 = min((1-utau)/utau,p^2)
      
      Fubt_1 = stats::pgamma(ubt_1,(p+1)/2,scale=1/tempt)
      
      Fubt_2 = stats::pgamma(ubt_2,(p+1)/2,scale=1/tempt)
      
      Fubt_2 = max(Fubt_2, 1e-8) # for numerical stability
      
      ut = stats::runif(1,Fubt_1,Fubt_2)
      
      et = stats::qgamma(ut,(p+1)/2,scale=1/tempt)
      
      tau = 1/sqrt(et)
      
    }
    
    
    
    ## update sigma_sq ##
    
    if(method.sigma == "Jeffreys"){
      
      
      
      E_1  <- max(t(y-X%*%beta)%*%(y-X%*%beta),(1e-10))
      
      E_21 <- max(sum((beta)^2/((tau*lambda))^2),(1e-10))
      
      E_22 <- max(t(beta - B) %*% D.inv %*% (beta - B), 1e-10)
      
      E_2  <- min(c(E_21, E_22))  # for numerical stability
      
      
      
      sigma_sq= 1/stats::rgamma(1, (n + p)/2, scale = 2/(E_1+E_2))
      
    }
    
    
    
    
    
    ## update bG  for groups ##
    
    for(k in 1:r)
      
    {
      
      denominator <- sigma_sq * tau^2 * (1/f.n.seq[k])
      
      tau.b       <- (1/denominator) * sum(1/(Lambda[, k])^2) + (1/sigma.bG.square[k])
      
      tau.b.inv   <- 1/tau.b
      
      b.mean      <- ((f.n.seq[k] * tau.b.inv)/denominator) * sum((Beta[, k] - bP)/(Lambda[, k]^2))
      
      bG[k]        <- stats::rnorm(1, mean = b.mean, sd = sqrt(tau.b.inv))
      
    }
    
    
    
    BG <- NULL
    
    for(k in 1:r)
      
    {
      
      BG <- c(BG, rep(bG[k], pk))
      
    }
    
    
    
    ## update bP for proteins ##
    
    for(j in 1:pk)
      
    {
      
      denominator <- sigma_sq * tau^2
      
      tau.b       <- (1/denominator) * sum(f.n.seq/Lambda[j, ]^2) + (1/sigma.bP.square[j])
      
      tau.b.inv   <- 1/tau.b
      
      b.mean      <- (tau.b.inv/denominator) * sum((Beta[j, ] - bG)/(Lambda[j, ]^2/f.n.seq))
      
      bP[j]       <- stats::rnorm(1, mean = b.mean, sd = sqrt(tau.b.inv))
      
    }
    
    BP <- rep(bP, k)
    
    B  <- BP + BG
    
    
    
    # likelihood
    
    likelihood <- stats::dnorm(y, mean = X %*% beta, sd = sqrt(sigma_sq))
    
    logt       <- X %*% beta
    
    
    
    
    
    if (i%%500 == 0)
      
    {
      
      message("iteration = ", i)
      
    }
    
    
    
    
    
    
    
    if(i > burn && i%%thin== 0)
      
    {
      
      betaout[, (i - burn)/thin]       <- beta
      
      lambdaout[, (i - burn)/thin]     <- lambda
      
      tauout[(i - burn)/thin]          <- tau
      
      sigmaSqout[(i-burn)/thin]        <- sigma_sq
      
      bGout[, (i - burn)/thin]         <- bG
      
      bPout[, (i - burn)/thin]         <- bP
      
      likelihoodout[ ,(i - burn)/thin] <- likelihood
      
      predsurvout[ ,(i - burn)/thin]   <- predictive.survivor
      
      logtimeout[, (i - burn)/thin]    <- logt
      
    }
    
  }
  
  
  
  
  
  pMean   <- apply(betaout, 1, mean)
  
  pMedian <- apply(betaout, 1, stats::median)
  
  pLambda <- apply(lambdaout, 1, mean)
  
  pSigma  <- mean(sigmaSqout)
  
  pTau    <- mean(tauout)
  
  pBG     <- apply(bGout, 1, mean)
  
  pBP     <- apply(bPout, 1, mean)
  
  pPS     <- apply(predsurvout, 1, mean)
  
  pLogtime<- apply(logtimeout, 1, mean)
  
  
  
  #construct credible sets
  
  left  <- floor(alpha*effsamp/2)
  
  right <- ceiling((1-alpha/2)*effsamp)
  
  
  
  BetaSort     <- apply(betaout, 1, sort, decreasing = F)
  
  left.points  <- BetaSort[left, ]
  
  right.points <- BetaSort[right, ]
  
  
  
  result=list("SurvivalHat" = pPS, "LogTimeHat" = pLogtime, "BetaHat"=pMean, "LeftCI" = left.points,
              
              "RightCI" = right.points,"BetaMedian"=pMedian, "LambdaHat" = pLambda,
              
              "Sigma2Hat"=pSigma,"TauHat"=pTau,"BetaSamples"=betaout,
              
              "TauSamples" = tauout, "Sigma2Samples" = sigmaSqout, "BGHat" = pBG, "BPHat" = pBP,
              
              "LikelihoodSamples" = likelihoodout)
  
  return(result)
  
}