Markov Gamma Model with Covariates
Posterior inference for the Bayesian non-parametric Markov gamma model with covariates in survival analysis.
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 )
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 |
b.eps |
Double. Scale parameter for the prior gamma distribution of
epsilon when |
type.c |
1=defines |
epsilon |
Double. Mean of the exponential distribution assigned to
|
iterations |
Integer. Number of iterations including the |
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 |
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.
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.
- 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.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.