R/GaMRes.R

In BGPhazard: Markov Beta and Gamma Processes for Modeling Hazard Rates

#' Markov Gamma Model
#' 
#' Computes the Gibbs sampler given by the full conditional distributions of U,
#' Lambda, C and Epsilon (Nieto-Barajas & Walker, 2002) and arranges the
#' resulting Markov chain into a tibble which can be used to obtain posterior
#' summaries.
#'  
#'  
#' @details  Posterior inference for the Bayesian non-parametric Markov gamma model in
#' survival analysis.
#' 
#' 
#' @param times Numeric positive vector. Failure times.
#' @param delta Logical vector. Status indicator. \code{TRUE} (1) indicates
#' exact lifetime is known, \code{FALSE} (0) indicates that the corresponding
#' failure time is right censored.
#' @param type.t Integer. 1=computes uniformly-dense intervals; 2=
#' partition arbitrarily defined by the user with parameter utao and 3=same length intervals.
#' @param K Integer. Partition length for the hazard function if
#' \code{type.t}=1 or \code{type.t}=3.
#' @param utao vector. Partition specified by the user when type.t = 2. The first value of 
#' the vector has to be 0 and the last one the maximum observed time, either censored or uncensored.
#' @param alpha Nonnegative entry vector. Small entries are recommended in
#' order to specify a non-informative prior distribution.
#' @param beta Nonnegative entry vector. Small entries are recommended in order
#' to specify a non-informative prior distribution.
#' @param c.r Nonnegative vector. The higher the entries, the higher the correlation 
#' of two consecutive intervals.
#' @param c.nu Tuning parameter for the proposal distribution for c.
#' @param a.eps Numeric. Shape parameter for the prior gamma distribution of
#' epsilon when \code{type.c = 4}.
#' @param b.eps Numeric. Scale parameter for the prior gamma distribution of
#' epsilon when \code{type.c = 4}.
#' @param type.c 1=assigns \code{c.r} a zero-entry vector; 2=lets the user
#' define \code{c.r} freely; 3=assigns \code{c.r} an exponential prior
#' distribution with mean 1; 4=assigns \code{c.r} an exponential hierarchical
#' distribution with mean \code{epsilon} which in turn has a Ga(a.eps, b.eps)
#' distribution.
#' @param epsilon Double. Mean of the exponential distribution assigned to
#' \code{c.r} when \code{type.c = 3}
#' @param iterations Integer. Number of iterations including the \code{burn.in}
#' to be computed for the Markov chain.
#' @param burn.in Integer. Length of the burn-in period for the Markov chain.
#' @param thinning Integer. Factor by which the chain will be thinned. Thinning
#' the Markov chain is to reducec autocorrelation.
#' @param printtime Logical. If \code{TRUE}, prints out the execution time.
#' @examples
#' 
#' 
#' ## Simulations may be time intensive. Be patient.
#' 
#' ## Example 1 
#' data(gehan) 
#' timesG <- gehan$time[gehan$treat == "6-MP"] 
#' deltaG <- gehan$cens[gehan$treat == "6-MP"] 
#'  GEX1 <- GaMRes(timesG, deltaG, K = 8, iterations = 3000)
#' 
#' ## Example 2 
#' data(leukemiaFZ) 
#' timesFZ <- leukemiaFZ$time 
#' deltaFZ <- leukemiaFZ$delta 
#' GEX2 <- GaMRes(timesFZ, deltaFZ, type.c = 4)
#' 
#' 
#' 
#' @export GaMRes
GaMRes<-
  function(times, delta = rep(1, length(times)), type.t = 3, K = 5, utao = NULL,
           alpha = rep(0.01, K), beta = rep(0.01, K), 
           c.r = rep(1, (K - 1)), c.nu = 1, a.eps = 0.1, b.eps = 0.1,
           type.c = 4, epsilon = 1, 
           iterations = 1000, burn.in = floor(iterations * 0.2), 
           thinning = 5, printtime = TRUE) {
    tInit <- proc.time()
    if (min(times) < 0) {
      stop ("Invalid argument: 'times' must be a nonnegative vector.")
    }
    if (min((delta  ==  0) + (delta  ==  1 )) == 0) {
      stop ("Invalid argument: 'delta' must have 0 - 1 entries.")
    }
    if (length(times) != length(delta)) {
      stop ("Invalid argument: 'times' and 'delta' must have same length.")
    }
    if (type.t == 2) {
      if(is.null(utao)) stop("If type.t = 2 you need to specify utao.")
      utao <- sort(utao)
      if(utao[1]!=0){
        warning("The first value of the partition needs to be 0, utao fixed and now starting with 0.")
        utao <- c(0, utao)
      } 
      if(max(times) > max(utao)){
        utao <- c(utao,max(times))
        warning("The last value of the partition needs to be", max(times),", utao fixed and set to ",max(times),".")
      }
      K <- length(utao) - 1
    }
    if (type.t == 1 || type.t == 3) {
      if (inherits(try(K != 0, TRUE), "try-error")) {
        K.aux <- 5
        warning ("'K' value not specified. 'K' fixed at ", K.aux, ".")
      } else {K.aux <- K}
      K <- K.aux
    }
    tol <- .Machine$double.eps ^ 0.5
    if (abs(type.t - round(type.t)) > tol || type.t < 1 || type.t > 3) {
      stop ("Invalid argument: 'type.t' must be an integer between 1 and 3.")
    }
    if (K <= 2 || abs(K - round(K)) > tol) {
      stop ("Invalid argument: 'K' must be an integer greater than 2.")
    }
    if (length(alpha) != K || length(beta) != K) {
      stop (c("Invalid argument: 'alpha', 'beta', must have length "), K)
    }
    if (min(c(alpha, beta)) < 0) {
      stop ("Invalid argument: 'alpha' and 'beta' must have nonnegative entries.")
    } 
    if (abs(type.c - round(type.c)) > tol || type.c < 1 || type.c > 4) {
      stop ("Invalid argument: 'type.c' must be an integer between 1 and 4.")
    }
    if (type.c == 1 || type.c == 2) {
      if (length(c.r) != (K - 1)) {
        stop (c("Invalid argument: 'c.r' must have length, "), K - 1)
      }
      if (sum(abs(c.r - round(c.r)) > tol) != 0 || min(c.r) < 0) {
        stop ("Invalid argument: 'c.r' entries must be nonnegative integers.")
      }
    }
    if (type.c == 1 && sum(abs(c.r)) != 0 ) {
      c.r <- rep(0, K - 1)
      warning (c("'c.r' redefined as rep(0,", K - 1, ") because type.c = 1."))
    }
    if ((type.c == 3 || type.c == 4) && epsilon < 0) {
      stop ("Invalid argument: 'epsilon' must be nonnegative.")
    }
    if (iterations <= 0 || abs(iterations - round(iterations)) > tol 
        || iterations < 50) {
      stop ("Invalid argument: 'iterations' must be an integer greater than 50.")
    }
    if (burn.in < 0 || abs(burn.in - round(burn.in)) > tol 
        || burn.in > iterations*0.9) {
      stop ("Invalid argument: 'burn.in' must be a postitive integer smaller than 
            iterations = ", iterations * 0.9, ".")
    }
    if (!inherits(thinning, "numeric")) {
      stop ("Invalid argument: 'thinning' must be a numeric value.")
    }
    if (thinning <= 0 || abs(thinning - round(thinning)) > tol 
        || thinning > 0.1 * iterations) {
      stop ("Invalid argument: 'thinning' must be a postitive integer smaller than 
            iterations * 0.10 = ", iterations * 0.1, ".")
    }
    if (printtime != TRUE && printtime != FALSE) {
      stop ("Invalid argument: 'printtime' must be a logical value.")
    }
    nm <- NM(times, delta, type.t, K, utao)
    n <- nm$n
    m <- nm$m
    tao <- nm$tao
    t.unc <- nm$t.unc
    acceptance.c <- 0
    if (type.c == 3) {
      c.r <- rep(5, (K - 1))
    }
    if (type.c == 4) {
      Epsilon <- rep(NA, iterations)
    }
    cat(c("Iterating...", "\n"), sep = "")
    Lambda <- matrix(NA, nrow = iterations, ncol = K)
    U <- matrix(NA, nrow = iterations, ncol = K - 1)
    C <- matrix(NA, nrow = iterations, ncol = K - 1)
    lambda.r <- rep(0.1, K)
    pb <- dplyr::progress_estimated(iterations)
    for(j in 1:iterations) {
      pb$tick()$print()
      u.r <- UpdU(alpha, beta, c.r, lambda.r)
      lambda.r <- UpdLambda(alpha, beta, c.r, u.r, n, m)
      if (type.c == 3 || type.c == 4) {
        if (type.c == 4) {
          epsilon <- rgamma(1, shape = a.eps + K, scale = 1 / (b.eps + sum(c.r)))
        }
        auxc.r <- GaUpdC(alpha, beta, c.r, lambda.r, u.r, epsilon, c.nu, acceptance.c)
        c.r <- auxc.r[[1]]
        acceptance.c <- auxc.r[[2]]
      }
      Lambda[j, ] <- lambda.r
      U[j, ] <- u.r
      C[j, ] <- c.r
      if (type.c == 4) Epsilon[j] <- epsilon
    }
    Lambda <- Lambda[seq(burn.in + 1, iterations, thinning), ]
    U <- U[seq(burn.in + 1, iterations, thinning), ]
    C <- C[seq(burn.in + 1, iterations, thinning), ]
    if (type.c == 4) Epsilon <- Epsilon[seq(burn.in + 1, iterations, thinning)]
    writeLines(c("Done.", "\n", "Generating survival function estimates.", "\n"), 
        sep = "")
    rows <- nrow(Lambda)
    s <- max(tao) * seq.int(0,100) / 100
    X <- as.matrix(unname(Lambda))
    pb <- dplyr::progress_estimated(length(s))
    S <-purrr::map(s,function(s = .x){
      pb$tick()$print()
      do.call(base::c,purrr::map(seq_len(rows) ,.f= ~exp(-sum((s > tao[-1]) * tao[-1] * X[.x,] + 
                                                (s > tao[-length(tao)] & s <= tao[-1]) * s * X[.x,] -
                                                (s > tao[-length(tao)]) * tao[-(length(tao))] * X[.x,])
      )))
    })
    cat(c("Done.", "\n"), sep = "")
    if (printtime) {
      cat(">>> Total processing time (sec.):\n")
      print(procTime <- proc.time() - tInit)
    }
    if(type.c == 4) {
      X = tibble::enframe(list(Lambda = Lambda, 
                       U = U, C = C, Epsilon = Epsilon))} else { 
                         X = tibble::enframe(list(Lambda = Lambda, U = U, C = C))
                       }
    out <- tibble::enframe(list(times = times, delta = delta, type.t = type.t, tao = tao, K = K, 
                        t.unc = t.unc, iterations = rows, simulations = X, s = s,
                        acceptance = acceptance.c/((K-1)*iterations), S = S))
    out
  }