# cox_mcmc

##### Cox Model Markov Chain Monte Carlo

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

- Keywords
- regression, survival

##### Usage

```
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

##### 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 cox_mode(), afterwards the
## sampler cox_mcmc() is started.
b <- bamlss(f, family = "cox", data = d)
## Plot estimated effects.
plot(b)
# }
```

*Documentation reproduced from package bamlss, version 1.1-2, License: GPL-2 | GPL-3*