totlos.msm {msm} | R Documentation |
Estimate the expected total length of stay in each transient state, for a given period of evolution of a multi-state model. This assumes that the transition rates do not change with time.
totlos.msm(x, start=1, fromt=0, tot=Inf, covariates="mean", ...)
x |
A fitted msm model, as given by
msm . |
start |
State at the beginning of the period. |
fromt |
Time from which to estimate total length of stay. Defaults to 0, the beginning of the process. |
tot |
Time up to which total length of stay is estimated. Defaults
to infinity, giving the expected time spent in the state until
absorption. For models without an absorbing state, t
must be specified. |
covariates |
The covariate values to estimate for. 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)
|
... |
Further arguments to be passed to the
integrate function to control the numerical
integration. |
The expected total length of stay in state j between times
t_1 and t_2, from the point of view of an individual in
state i at time 0,
is defined by the integral from t_1 to
t_2 of the i,j entry of the transition probability matrix P(t).
As P(t) = exp(tQ) is not available explicitly in terms of
t for a general Markov model, this integral is calculated
numerically, using the integrate
function. This may
take a long time for models with many states where P(t) is
expensive to calculate.
For a model where the individual has only one place to go from each state, and each state is visited only once, for example a progressive disease model with no recovery or death, these are equal to the mean sojourn time in each state. However, consider a three-state health-disease-death model with transitions from health to disease, health to death, and disease to death, where everybody starts healthy. In this case the mean sojourn time in the disease state will be greater than the expected length of stay in the disease state. This is because the mean sojourn time in a state is conditional on entering the state, whereas the expected total time diseased is a forecast for a healthy individual, who may die before contracting the disease.
A vector of expected total lengths of stay for each transient state.
C. H. Jackson chris.jackson@imperial.ac.uk