Cox Model Markov Chain Monte Carlo

This sampler function implements a derivative based MCMC algorithm for flexible Cox models with structured additive predictors.

sam_Cox(x, y, family, start, weights, offset,
  n.iter = 1200, burnin = 200, thin = 1,
  verbose = TRUE, digits = 4, step = 20, ...)

cox_mcmc(x, y, family, start, weights, offset,
  n.iter = 1200, burnin = 200, thin = 1,
  verbose = TRUE, digits = 4, step = 20, ...)

Arguments

x

The x list, as returned from function bamlss.frame and transformed by function surv_transform, holding all model matrices and other information that is used for fitting the model.

y

The model response, as returned from function bamlss.frame.

family

A bamlss family object, see family.bamlss. In this case this is the cox_bamlss family object.

start

A named numeric vector containing possible starting values, the names are based on function parameters.

weights

Prior weights on the data, as returned from function bamlss.frame.

offset

Can be used to supply model offsets for use in fitting, returned from function bamlss.frame.

n.iter

Sets the number of MCMC iterations.

burnin

Sets the burn-in phase of the sampler, i.e., the number of starting samples that should be removed.

thin

Defines the thinning parameter for MCMC simulation. E.g., thin = 10 means, that only every 10th sampled parameter will be stored.

verbose

Print information during runtime of the algorithm.

digits

Set the digits for printing when verbose = TRUE.

step

How many times should algorithm runtime information be printed, divides n.iter.

...

Currently not used.

Details

The sampler uses derivative based proposal functions to create samples of parameters. For time-dependent functions the proposals are based on one Newton-Raphson iteration centered at the last state, while for the time-constant functions proposals can be based on iteratively reweighted least squares (IWLS), see also function GMCMC. The integrals that are part of the time-dependent function updates are solved numerically. In addition, smoothing variances are sampled using slice sampling.

Value

The function returns samples of parameters. The samples are provided as a

mcmc matrix.

References

Umlauf N, Klein N, Zeileis A (2016). Bayesian Additive Models for Location Scale and Shape (and Beyond). (to appear)

See also

opt_Cox, cox_bamlss, surv_transform, simSurv, bamlss

Examples

if (FALSE) library("survival")
set.seed(123)

## Simulate survival data.
d <- simSurv(n = 500)

## Formula of the survival model, note
## that the baseline is given in the first formula by s(time).
f <- list(
  Surv(time, event) ~ s(time) + s(time, by = x3),
  gamma ~ s(x1) + s(x2)
)

## Cox model with continuous time.
## Note the the family object cox_bamlss() sets
## the default optimizer and sampler function!
## First, posterior mode estimates are computed
## using function opt_Cox(), afterwards the
## sampler sam_Cox() is started.
b <- bamlss(f, family = "cox", data = d)
#> Error in Surv(time, event): could not find function "Surv"

## Plot estimated effects.
plot(b)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'b' not found