prevalence.msm | R Documentation |
This provides a rough indication of the goodness of fit of a multi-state model, by estimating the observed numbers of individuals occupying each state at a series of times, and comparing these with forecasts from the fitted model.
prevalence.msm(
x,
times = NULL,
timezero = NULL,
initstates = NULL,
covariates = "population",
misccovariates = "mean",
piecewise.times = NULL,
piecewise.covariates = NULL,
ci = c("none", "normal", "bootstrap"),
cl = 0.95,
B = 1000,
cores = NULL,
interp = c("start", "midpoint"),
censtime = Inf,
subset = NULL,
plot = FALSE,
...
)
x |
A fitted multi-state model produced by |
times |
Series of times at which to compute the observed and expected prevalences of states. |
timezero |
Initial time of the Markov process. Expected values are forecasted from here. Defaults to the minimum of the observation times given in the data. |
initstates |
Optional vector of the same length as the number of states. Gives the numbers of individuals occupying each state at the initial time, to be used for forecasting expected prevalences. The default is those observed in the data. These should add up to the actual number of people in the study at the start. |
covariates |
Covariate values for which to forecast expected state
occupancy. With the default Predictions for fixed covariates can be obtained by supplying covariate
values in the standard way, as in This argument is ignored if |
misccovariates |
(Misclassification models only) Values of covariates
on the misclassification probability matrix for converting expected true to
expected misclassified states. Ignored if |
piecewise.times |
Times at which piecewise-constant intensities change.
See |
piecewise.covariates |
Covariates on which the piecewise-constant
intensities depend. See |
ci |
If If If |
cl |
Width of the symmetric confidence interval, relative to 1 |
B |
Number of bootstrap replicates |
cores |
Number of cores to use for bootstrapping using parallel
processing. See |
interp |
Suppose an individual was observed in states If If |
censtime |
Adjustment to the observed prevalences to account for limited follow-up in the data. If the time is greater than This can be supplied as a single value, or as a vector with one element per
subject (after any This is ignored if it is less than the subject's maximum observation time. |
subset |
Subset of subjects to calculate observed prevalences for. |
plot |
Generate a plot of observed against expected prevalences. See
|
... |
Further arguments to pass to |
The fitted transition probability matrix is used to forecast expected
prevalences from the state occupancy at the initial time. To produce the
expected number in state j
at time t
after the start, the number
of individuals under observation at time t
(including those who have
died, but not those lost to follow-up) is multiplied by the product of the
proportion of individuals in each state at the initial time and the
transition probability matrix in the time interval t
. The proportion
of individuals in each state at the "initial" time is estimated, if
necessary, in the same way as the observed prevalences.
For misclassification models (fitted using an ematrix
), this aims to
assess the fit of the full model for the observed states. That is,
the combined Markov progression model for the true states and the
misclassification model. Thus, expected prevalences of true states
are estimated from the assumed proportion occupying each state at the
initial time using the fitted transition probabiliy matrix. The vector of
expected prevalences of true states is then multiplied by the fitted
misclassification probability matrix to obtain the expected prevalences of
observed states.
For general hidden Markov models, the observed state is taken to be the
predicted underlying state from the Viterbi algorithm
(viterbi.msm
). The goodness of fit of these states to the
underlying Markov model is tested.
In any model, if there are censored states, then these are replaced by imputed values of highest probability from the Viterbi algorithm in order to calculate the observed state prevalences.
For an example of this approach, see Gentleman et al. (1994).
A list of matrices, with components:
Observed |
Table of observed numbers of individuals in each state at each time |
Observed percentages |
Corresponding percentage of the individuals at risk at each time. |
Expected |
Table of corresponding expected numbers. |
Expected percentages |
Corresponding percentage of the individuals at risk at each time. |
Or if ci.boot = TRUE
, the component Expected
is a list with
components estimates
and ci
.
estimates
is a matrix
of the expected prevalences, and ci
is a list of two matrices,
containing the confidence limits. The component Expected percentages
has a similar format.
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
Gentleman, R.C., Lawless, J.F., Lindsey, J.C. and Yan, P. Multi-state Markov models for analysing incomplete disease history data with illustrations for HIV disease. Statistics in Medicine (1994) 13(3): 805–821.
Titman, A.C., Sharples, L. D. Model diagnostics for multi-state models. Statistical Methods in Medical Research (2010) 19(6):621-651.
msm
, summary.msm
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