GaMRes function

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.

GaMRes(
  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
)

Arguments

• times: Numeric positive vector. Failure times.

• delta: Logical vector. Status indicator. TRUE (1) indicates exact lifetime is known, FALSE (0) indicates that the corresponding failure time is right censored.

• type.t: Integer. 1=computes uniformly-dense intervals; 2= partition arbitrarily defined by the user with parameter utao and 3=same length intervals.

• K: Integer. Partition length for the hazard function if type.t=1 or type.t=3.

• 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.

• 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.

• a.eps: Numeric. Shape parameter for the prior gamma distribution of epsilon when type.c = 4.

• b.eps: Numeric. Scale parameter for the prior gamma distribution of epsilon when type.c = 4.

• type.c: 1=assigns c.r a zero-entry vector; 2=lets the user define c.r freely; 3=assigns c.r 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 is to reducec autocorrelation.

• printtime: Logical. If TRUE, prints out the execution time.

Details

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

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)