R: Cox Model Markov Chain Monte Carlo

sam_Cox {bamlss} | R Documentation

## 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)

### See Also

`opt_Cox`, `cox_bamlss`, `surv_transform`, `simSurv`, `bamlss`

### 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)

[Package bamlss version 1.1-7 Index]