bamlss: cox.mcmc – R documentation

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cox.mcmc

Cox Model Markov Chain Monte Carlo

Description

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

Usage

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)

Examples

## Not run: 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)

## Plot estimated effects.
plot(b)

## End(Not run)

bamlss

Bayesian Additive Models for Location, Scale, and Shape (and Beyond)

v1.1-3

GPL-2 | GPL-3

Authors

Nikolaus Umlauf [aut, cre] (<https://orcid.org/0000-0003-2160-9803>), Nadja Klein [aut] (<https://orcid.org/0000-0002-5072-5347>), Achim Zeileis [aut] (<https://orcid.org/0000-0003-0918-3766>), Meike Koehler [ctb], Thorsten Simon [aut] (<https://orcid.org/0000-0002-3778-7738>), Stanislaus Stadlmann [ctb]

Initial release

2021-01-25