CGaMRes: Markov Gamma Model with Covariates

Description

Posterior inference for the Bayesian non-parametric Markov gamma model with covariates in survival analysis.

Usage

CGaMRes(
  data,
  type.t = 2,
  length = 1,
  K = 5,
  alpha = rep(0.01, K),
  beta = rep(0.01, K),
  c.r = rep(1, K - 1),
  c.nu = 1,
  var.theta.str = 25,
  var.theta.ini = 100,
  a.eps = 0.1,
  b.eps = 0.1,
  type.c = 4,
  epsilon = 1,
  iterations = 1000,
  burn.in = floor(iterations * 0.2),
  thinning = 3,
  printtime = TRUE
)

Arguments

data: Double tibble. Contains failure times in the first column, status indicator in the second, and, from the third to the last column, the covariate(s).
type.t: Integer. 1=computes uniformly-dense intervals; 2=length intervals defined by user and 3=same length intervals.
length: Integer. Interval length of the partition.
K: Integer. Partition length for the hazard function.
alpha: Nonnegative entry vector. Small entries are recommended in order to specify a non-informative prior distribution.
beta: Nonnegative entry vector. Small entries are recommended in order to specify a non-informative prior distribution.
c.r: Nonnegative vector. The higher the entries, the higher the correlation of two consecutive intervals.
c.nu: Tuning parameter for the proposal distribution for c.
var.theta.str: Double. Variance of the proposal normal distribution for theta in the Metropolis-Hastings step.
var.theta.ini: Double. Variance of the prior normal distribution for theta.
a.eps: Double. Shape parameter for the prior gamma distribution of epsilon when type.c = 4.
b.eps: Double. Scale parameter for the prior gamma distribution of epsilon when type.c = 4.
type.c: 1=defines c.r as a zero-entry vector; 2=lets the user define c.r freely; 3=assigns c.r by computing an exponential prior distribution with mean 1; 4=assigns c.r an exponential hierarchical distribution with mean epsilon which in turn has a Ga(a.eps, b.eps) distribution.
epsilon: Double. Mean of the exponential distribution assigned to c.r when type.c = 3.
iterations: Integer. Number of iterations including the burn.in to be computed for the Markov chain.
burn.in: Integer. Length of the burn-in period for the Markov chain.
thinning: Integer. Factor by which the chain will be thinned. Thinning the Markov chain reduces autocorrelation.
printtime: Logical. If TRUE, prints out the execution time.

Details

Computes the Gibbs sampler with the full conditional distributions of Lambda and Theta (Nieto-Barajas, 2003) and arranges the resulting Markov chain into a matrix which can be used to obtain posterior summaries. Prior distributions for the re gression coefficients (Theta) are assumed independent normals with zero mean and variance var.theta.ini.

References

- Nieto-Barajas, L. E. (2003). Discrete time Markov gamma processes and time dependent covariates in survival analysis. Bulletin of the International Statistical Institute 54th Session. Berlin. (CD-ROM).

- Nieto-Barajas, L. E. & Walker, S. G. (2002). Markov beta and gamma processes for modelling hazard rates. Scandinavian Journal of Statistics 29: 413-424.

Examples

Run this code




## Simulations may be time intensive. Be patient.

## Example 1
#  data(leukemiaFZ)
#  leukemia1 <- leukemiaFZ
#  leukemia1$wbc <- log(leukemiaFZ$wbc)
#  CGEX1 <- CGaMRes(data = leukemia1, K = 10, iterations = 100, thinning = 1)

## Example 2. Refer to "Cox-gamma model example" section in package vignette for details.
# SampWeibull <- function(n, a = 10, b = 1, beta = c(1, 1)) {
#   M <- tibble(i = seq(n), x_i1 = runif(n), x_i2 = runif(n), 
#               t_i = rweibull(n, shape = b, 
#                                 scale = 1 / (a * exp(x_i1*beta[1] + x_i2*beta[2]))),
#               c_i = rexp(n), delta = t_i > c_i,
#               `min{c_i, d_i}` = min(t_i, c_i))
#   return(M)
# }
#  dat <- SampWeibull(100, 0.1, 1, c(1, 1))
#  dat <- dat %>% select(4,6,2,3) 
#  CG <- CGaMRes(data = leukemia1, K = 10, iterations = 100, thinning = 1)
#  CGaPloth(CG)