Estimate the mean sojourn times in the transient states of a multi-state model and their confidence limits.

## Usage

```
sojourn.msm(
x,
covariates = "mean",
ci = c("delta", "normal", "bootstrap", "none"),
cl = 0.95,
B = 1000
)
```

## Arguments

- x
A fitted multi-state model, as returned by

`msm`

.- covariates
The covariate values at which to estimate the mean sojourn times. This can either be:

the string

`"mean"`

, denoting the means of the covariates in the data (this is the default),the number

`0`

, indicating that all the covariates should be set to zero,a list of values, with optional names. For example,

`list(60, 1)`

, where the order of the list follows the order of the covariates originally given in the model formula, or a named list, e.g.`list (age = 60, sex = 1)`

- ci
If

`"delta"`

(the default) then confidence intervals are calculated by the delta method, or by simple transformation of the Hessian in the very simplest cases.If

`"normal"`

, then calculate a confidence interval by simulating`B`

random vectors from the asymptotic multivariate normal distribution implied by the maximum likelihood estimates (and covariance matrix) of the log transition intensities and covariate effects, then transforming.If

`"bootstrap"`

then calculate a confidence interval by non-parametric bootstrap refitting. This is 1-2 orders of magnitude slower than the`"normal"`

method, but is expected to be more accurate. See`boot.msm`

for more details of bootstrapping in msm.- cl
Width of the symmetric confidence interval to present. Defaults to 0.95.

- B
Number of bootstrap replicates, or number of normal simulations from the distribution of the MLEs

## Value

A data frame with components:

- estimates
Estimated mean sojourn times in the transient states.

- SE
Corresponding standard errors.

- L
Lower confidence limits.

- U
Upper confidence limits.

## Details

The mean sojourn time in a transient state \(r\) is estimated by \(- 1 / q_{rr}\), where \(q_{rr}\) is the \(r\)th entry on the diagonal of the estimated transition intensity matrix.

A continuous-time Markov model is fully specified by the mean sojourn times
and the probability that each state is next (`pnext.msm`

). This
is a more intuitively meaningful description of a model than the transition
intensity matrix (`qmatrix.msm`

).

Time dependent covariates, or time-inhomogeneous models, are not supported. This would require the mean of a piecewise exponential distribution, and the package author is not aware of any general analytic form for that.

## Author

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