# Transition probability matrix from a fully-parametric, semi-Markov multi-state model

Source:`R/mstate.R`

`pmatrix.simfs.Rd`

The transition probability matrix for semi-Markov multi-state models fitted
to time-to-event data with `flexsurvreg`

. This has \(r,s\)
entry giving the probability that an individual is in state \(s\) at time
\(t\), given they are in state \(r\) at time \(0\).

## Usage

```
pmatrix.simfs(
x,
trans,
t = 1,
newdata = NULL,
ci = FALSE,
tvar = "trans",
tcovs = NULL,
M = 1e+05,
B = 1000,
cl = 0.95,
cores = NULL,
tidy = FALSE
)
```

## Arguments

- x
A model fitted with

`flexsurvreg`

. See`msfit.flexsurvreg`

for the required form of the model and the data. Additionally this should be semi-Markov, so that the time variable represents the time since the last transition. In other words the response should be of the form`Surv(time,status)`

. See the package vignette for further explanation.`x`

can also be a list of`flexsurvreg`

models, with one component for each permitted transition, as illustrated in`msfit.flexsurvreg`

. This can be constructed by`fmsm`

.- trans
Matrix indicating allowed transitions. See

`msfit.flexsurvreg`

. This is not required if`x`

is a list constructed by`fmsm`

.- t
Time to predict state occupancy probabilities for. This can be a single number or a vector of different numbers.

- newdata
A data frame specifying the values of covariates in the fitted model, other than the transition number. See

`msfit.flexsurvreg`

.- ci
Return a confidence interval calculated by simulating from the asymptotic normal distribution of the maximum likelihood estimates. This is turned off by default, since two levels of simulation are required. If turned on, users should adjust

`B`

and/or`M`

until the results reach the desired precision. The simulation over`M`

is generally vectorised, therefore increasing`B`

is usually more expensive than increasing`M`

.- tvar
Variable in the data representing the transition type. Not required if

`x`

is a list of models.- tcovs
Predictable time-dependent covariates such as age, see

`sim.fmsm`

.- M
Number of individuals to simulate in order to approximate the transition probabilities. Users should adjust this to obtain the required precision.

- B
Number of simulations from the normal asymptotic distribution used to calculate confidence limits. Decrease for greater speed at the expense of accuracy.

- cl
Width of symmetric confidence intervals, relative to 1.

- cores
Number of processor cores used when calculating confidence limits by repeated simulation. The default uses single-core processing.

- tidy
If

`TRUE`

then the results are returned as a tidy data frame with columns for the estimate and confidence limits, and rows per state transition and time interval.

## Value

The transition probability matrix. If `ci=TRUE`

, there are
attributes `"lower"`

and `"upper"`

giving matrices of the
corresponding confidence limits. These are formatted for printing but may
be extracted using `attr()`

.

## Details

This is computed by simulating a large number of individuals `M`

using
the maximum likelihood estimates of the fitted model and the function
`sim.fmsm`

. Therefore this requires a random sampling function
for the parametric survival model to be available: see the "Details"
section of `sim.fmsm`

. This will be available for all built-in
distributions, though users may need to write this for custom models.

Note the random sampling method for `flexsurvspline`

models is
currently very inefficient, so that looping over the `M`

individuals
will be very slow.

`pmatrix.fs`

is a more efficient method based on solving the
Kolmogorov forward equation numerically, which requires the multi-state
model to be Markov. No error or warning is given if running
`pmatrix.simfs`

with a Markov model, but this is still invalid.

## Author

Christopher Jackson chris.jackson@mrc-bsu.cam.ac.uk.

## Examples

```
# BOS example in vignette, and in msfit.flexsurvreg
bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp")
tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA))
# more likely to be dead (state 3) as time moves on, or if start with
# BOS (state 2)
pmatrix.simfs(bexp, t=5, trans=tmat)
#> 1 2 3
#> 1 0.29456 0.26769 0.43775
#> 2 0.00000 0.26781 0.73219
#> 3 0.00000 0.00000 1.00000
pmatrix.simfs(bexp, t=10, trans=tmat)
#> 1 2 3
#> 1 0.08806 0.15162 0.76032
#> 2 0.00000 0.07005 0.92995
#> 3 0.00000 0.00000 1.00000
# these results should converge to those in help(pmatrix.fs), as M
# increases here and ODE solving precision increases there, since with
# an exponential distribution, the semi-Markov model is the same as the
# Markov model.
```