Probability of each state being next

Compute a matrix of the probability of each state \(s\) being the next state of the process after each state \(r\). Together with the mean sojourn times in each state (sojourn.msm), these fully define a continuous-time Markov model.

Usage

pnext.msm(
  x,
  covariates = "mean",
  ci = c("normal", "bootstrap", "delta", "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 intensities. 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 a named list,

list (age = 60, sex = 1)

ci

If "normal" (the default) 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.

If "delta" then confidence intervals are calculated based on the delta method SEs of the log rates, but this is not recommended since it may not respect the constraint that probabilities are less than one.

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

The matrix of probabilities that the next move of a process in state \(r\) (rows) is to state \(s\) (columns).

Details

For a continuous-time Markov process in state \(r\), the probability that the next state is \(s\) is \(-q_{rs} / q_{rr}\), where \(q_{rs}\) is the transition intensity (qmatrix.msm).

A continuous-time Markov model is fully specified by these probabilities together with the mean sojourn times \(-1/q_{rr}\) in each state \(r\). This gives a more intuitively meaningful description of a model than the intensity matrix.

Remember that msm deals with continuous-time, not discrete-time models, so these are not the same as the probability of observing state \(s\) at a fixed time in the future. Those probabilities are given by pmatrix.msm.

Author

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