Expected total length of stay in specific states, from a fully-parametric, semi-Markov multi-state model

The expected total time spent in each state for semi-Markov multi-state models fitted to time-to-event data with flexsurvreg. This is defined by the integral of the transition probability matrix, though this is not analytically possible and is computed by simulation.

Usage

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

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

Maximum time to predict to.

start

Starting state.

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.

group

Optional grouping for the states. For example, if there are four states, and group=c(1,1,2,2), then totlos.simfs returns the expected total time in states 1 and 2 combined, and states 3 and 4 combined.

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.

Value

The expected total time spent in each state (or group of states given by group) up to time t, and corresponding confidence intervals if requested.

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 M will be very slow.

The equivalent function for time-inhomogeneous Markov models is totlos.fs. Note neither of these functions give errors or warnings if used with the wrong type of model, but the results will be 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))

# predict 4 years spent without BOS, 3 years with BOS, before death
# As t increases, this should converge
totlos.simfs(bexp, t=10, trans=tmat)
#>        1        2        3 
#> 3.744539 2.125464 4.129996 
totlos.simfs(bexp, t=1000, trans=tmat)
#>          1          2          3 
#>   4.127571   2.957678 992.914751