CGaMRes {BGPhazard}

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.

Note

It is recommended to verify chain's stationarity. This can be done by checking each element individually. See CGaPlotDiag To obtain posterior summaries of the coefficients use function CGaPloth.

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.

See Also

CGaPlotDiag, CGaPloth

Examples

## 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)