Mean sojourn times from a multi-state model

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