CGaMRes {BGPhazard}  R Documentation 
Markov Gamma Model with Covariates
Description
Posterior inference for the Bayesian nonparametric 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 uniformlydense 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 noninformative prior distribution. 
beta 
Nonnegative entry vector. Small entries are recommended in order to specify a noninformative 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 MetropolisHastings 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 burnin period for the Markov chain. 
thinning 
Integer. Factor by which the chain will be thinned. Thinning the Markov chain reduces autocorrelation. 
printtime 
Logical. If 
Details
Computes the Gibbs sampler with the full conditional distributions of
Lambda and Theta (NietoBarajas, 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
 NietoBarajas, L. E. (2003). Discrete time Markov gamma processes and time dependent covariates in survival analysis. Bulletin of the International Statistical Institute 54th Session. Berlin. (CDROM).
 NietoBarajas, L. E. & Walker, S. G. (2002). Markov beta and gamma processes for modelling hazard rates. Scandinavian Journal of Statistics 29: 413424.
See Also
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 "Coxgamma 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)