R: Bootstrap resampling for multi-state models

boot.msm {msm} | R Documentation

## Bootstrap resampling for multi-state models

### Description

Draw a number of bootstrap resamples, refit a `msm` model to the resamples, and calculate statistics on the refitted models.

### Usage

    boot.msm(x, stat=pmatrix.msm, B=1000, file=NULL, cores=NULL)

### Arguments

`x` | A fitted msm model, as output by `msm`.
`stat` | A function to call on each refitted msm model. By default this is `pmatrix.msm`, returning the transition probability matrix in one time unit. If `NULL` then no function is computed.
`B` | Number of bootstrap resamples.
`file` | Name of a file in which to save partial results after each replicate. This is saved using `save` and can be restored using `load`, producing an object called `boot.list` containing the partial results. Not supported when using parallel processing.
`cores` | Number of processor cores to use for parallel processing. Requires the doParallel package to be installed. If not specified, parallel processing is not used. If `cores` is set to the string `"default"`, the default methods of `makeCluster` (on Windows) or `registerDoParallel` (on Unix-like) are used.

### Details

The bootstrap datasets are computed by resampling independent transitions between pairs of states (for non-hidden models without censoring), or independent individual series (for hidden models or models with censoring). Therefore this approach doesn't work if, for example, the data for a HMM consist of a series of observations from just one individual, and is inaccurate for small numbers of independent transitions or individuals.

Confidence intervals or standard errors for the corresponding statistic can be calculated by summarising the returned list of `B` replicated outputs. This is currently implemented for most the output functions `qmatrix.msm`, `ematrix.msm`, `qratio.msm`, `pmatrix.msm`, `pmatrix.piecewise.msm`, `totlos.msm` and `prevalence.msm`. For other outputs, users will have to write their own code to summarise the output of `boot.msm`.

Most of msm's output functions present confidence intervals based on asymptotic standard errors calculated from the Hessian. These are expected to be underestimates of the true standard errors (Cramer-Rao lower bound). Some of these functions use a further approximation, the delta method (see `deltamethod`) to obtain standard errors of transformed parameters. Bootstrapping should give a more accurate estimate of the uncertainty.

An alternative method which is less accurate though faster than bootstrapping, but more accurate than the delta method, is to draw a sample from the asymptotic multivariate normal distribution implied by the maximum likelihood estimates (and covariance matrix), and summarise the transformed estimates. See `pmatrix.msm`.

All objects used in the original call to `msm` which produced `x`, such as the `qmatrix`, should be in the working environment, or else `boot.msm` will produce an “object not found” error. This enables `boot.msm` to refit the original model to the replicate datasets. However there is currently a limitation. In the original call to `msm`, the `"formula"` argument should be specified directly, as, for example,

`msm(state ~ time, data = ...)`

and not, for example,

`form = data$state ~ data$time`

`msm(formula=form, data = ...)`

otherwise `boot.msm` will be unable to draw the replicate datasets.

`boot.msm` will also fail with an incomprehensible error if the original call to msm used a used-defined object whose name is the same as a built-in R object, or an object in any other loaded package. For example, if you have called a Q matrix `q`, when `q()` is the built-in function for quitting R.

If `stat` is `NULL`, then `B` different `msm` model objects will be stored in memory. This is unadvisable, as `msm` objects tend to be large, since they contain the original data used for the `msm` fit, so this will be wasteful of memory.

To specify more than one statistic, write a function consisting of a list of different function calls, for example,

`stat = function(x) list (pmatrix.msm(x, t=1), pmatrix.msm(x, t=2))`

### Value

A list with `B` components, containing the result of calling function `stat` on each of the refitted models. If `stat` is `NULL`, then each component just contains the refitted model. If one of the `B` model fits was unsuccessful and resulted in an error, then the corresponding list component will contain the error message.

### Author(s)

C.H.Jackson <chris.jackson@mrc-bsu.cam.ac.uk>

### References

Efron, B. and Tibshirani, R.J. (1993) An Introduction to the Bootstrap, Chapman and Hall.

### See Also

`qmatrix.msm`, `qratio.msm`, `sojourn.msm`, `ematrix.msm`, `pmatrix.msm`, `pmatrix.piecewise.msm`, `totlos.msm`, `prevalence.msm`.

### Examples

    ## Not run:
      ## Psoriatic arthritis example
      data(psor)
      psor.q <- rbind(c(0,0.1,0,0),c(0,0,0.1,0),c(0,0,0,0.1),c(0,0,0,0))
      psor.msm <- msm(state ~ months, subject=ptnum, data=psor, qmatrix =
        psor.q, covariates = ~ollwsdrt+hieffusn,
        constraint = list(hieffusn=c(1,1,1),ollwsdrt=c(1,1,2)),
        control = list(REPORT=1,trace=2), method="BFGS")
      ## Bootstrap the baseline transition intensity matrix.  This will take a long time.
      q.list <- boot.msm(psor.msm, function(x)x$Qmatrices$baseline)
      ## Manipulate the resulting list of matrices to calculate bootstrap standard errors.
      apply(array(unlist(q.list), dim=c(4,4,5)), c(1,2), sd)
      ## Similarly calculate a bootstrap 95% confidence interval
      apply(array(unlist(q.list), dim=c(4,4,5)), c(1,2),
            function(x)quantile(x, c(0.025, 0.975)))
      ## Bootstrap standard errors are larger than the asymptotic standard
      ## errors calculated from the Hessian
      psor.msm$QmatricesSE$baseline

    ## End(Not run)

[Package msm version 1.6.9 Index]