Extract the estimated transition intensity matrix, and the corresponding standard errors, from a fitted multi-state model at a given set of covariate values.

## Usage

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

## Arguments

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

`msm`

.- covariates
The covariate values at which to estimate the intensity matrix. 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,or 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 more clearly, a named list,

`list (age = 60, sex = 1)`

If some covariates are specified but not others, the missing ones default to zero.

With

`covariates="mean"`

, for factor / categorical variables, the mean of the 0/1 dummy variable for each factor level is used, representing an average over all values in the data, rather than a specific factor level.- sojourn
Set to TRUE if the estimated sojourn times and their standard errors should also be returned.

- 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. Normality on the log scale is assumed.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.

- cores
Number of cores to use for bootstrapping using parallel processing. See

`boot.msm`

for more details.

## Value

A list with components:

- estimate
Estimated transition intensity matrix.

- SE
Corresponding approximate standard errors.

- L
Lower confidence limits

- U
Upper confidence limits

Or if `ci="none"`

, then `qmatrix.msm`

just returns the estimated
transition intensity matrix.

If `sojourn`

is `TRUE`

, extra components called `sojourn`

,
`sojournSE`

, `sojournL`

and `sojournU`

are included,
containing the estimates, standard errors and confidence limits,
respectively, of the mean sojourn times in each transient state.

The default print method for objects returned by `qmatrix.msm`

presents estimates and confidence limits. To present estimates and standard errors, do something like

`qmatrix.msm(x)[c("estimates","SE")]`

## Details

Transition intensities and covariate effects are estimated on the log scale
by `msm`

. A covariance matrix is estimated from the Hessian of
the maximised log-likelihood.

A more practically meaningful parameterisation of a continuous-time Markov model with transition intensities \(q_{rs}\) is in terms of the mean sojourn times \(-1 / q_{rr}\) in each state \(r\) and the probabilities that the next move of the process when in state \(r\) is to state \(s\), \(-q_{rs} / q_{rr}\).

## Author

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