msm (version 0.5.2)

totlos.msm: Total length of stay

Description

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.

Usage

totlos.msm(x, start=1, fromt=0, tot=Inf, covariates="mean", ...)

Arguments

x

A fitted multi-state model, as returned 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,

...

Further arguments to be passed to the integrate function to control the numerical integration.

Value

• A vector of expected total lengths of stay for each transient state.

Details

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 the individual entries of $P(t) = \exp(tQ)$ are 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 getting the disease.

See Also

sojourn.msm, integrate.