# sojourn.msm: Mean sojourn times from a multi-state model In msm: Multi-State Markov and Hidden Markov Models in Continuous Time

## Description

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

## Usage

 ```1 2``` ```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

## Details

The mean sojourn time in a transient state r is estimated by - 1 / q_{rr}, where q_{rr} is the rth 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.

## 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.

## Author(s)

C. H. Jackson [email protected]

`msm`, `qmatrix.msm`, `deltamethod`