For a general Markov chain multi-state model with interval censored transitions calculate the NPMLE using an EM algorithm with multinomial approach
EM_multinomial(
gd,
tmat,
tmat2,
inits,
beta_params,
support_manual,
exact,
maxit,
tol,
conv_crit,
manual,
verbose,
newmet,
include_inf,
checkMLE,
checkMLE_tol,
prob_tol,
remove_bins,
init_int = init_int,
...
)A data.frame with the following named columns
id:Subject idenitifier;
state:State at which the subject is observed at time;
time:Time at which the subject is observed;
The true transition time between states is then interval censored between the times.
A transition matrix as created by transMat
Which distribution should be used to generate the initial estimates
of the intensities in the EM algorithm. One of c("equalprob", "unif", "beta"),
with "equalprob" assigning 1/K to each intensity, with K the number of distinct
observation times (length(unique(gd[, "time"]))). For "unif", each
intensity is sampled from the Unif[0,1]
distribution and for "beta" each intensity is sampled from the Beta(a, b) distribution.
If "beta" is chosen, the argument beta_params must be specified as a
vector of length 2 containing the parameters of the beta distribution.
Default = "equalprob".
A vector of length 2 specifying the beta distribution parameters
for initial distribution generation. First entry will be used as shape1
and second entry as shape2. See help(rbeta). Only used if inits = "beta".
Used for specifying a manual support region for the transitions.
A list of length the number of transitions in tmat,
each list element containing a data frame with 2 named columns L and R indicating the
left and right values of the support intervals. When specified, all intensities
outside of these intervals will be set to zero for the corresponding transitions.
Intensities set to zero cannot be changed by the EM algorithm. Will use inits = "equalprob".
Numeric vector indicating to which states transitions are observed at exact times.
Must coincide with the column number in tmat.
Maximum number of iterations.
Tolerance of the procedure.
Convergence criterion. Stops procedure when the difference
in the chosen quantity between two consecutive iterations is smaller
than the tolerance level tol. One of the following:
Stop when change in maximum estimated intensities (hazards) < tol.
Stop when change in estimated probabilities < tol.
Stop when change in observed-data likelihood < tol.
Default is "haz". The options "haz" and "lik" can be compared across different
methods, but "prob" is dependent on the chosen method. Most
conservative (requiring most iterations) is "prob", followed by "haz" and finally "lik".
Manually specify starting transition intensities?
Should iteration messages be printed? Default is FALSE
Should contributions after last observation time also be used in the likelihood? Default is FALSE.
Should an additional bin from the largest observed time to infinity be included in the algorithm? Default is FALSE.
Should a check be performed whether the estimate has converged towards a true Maximum Likelihood Estimate? Default is TRUE.
Tolerance for checking whether the estimate has converged to MLE. Whenever an estimated transition intensity is smaller than the tolerance, it is assumed to be zero.
If an estimated probability is smaller than prob_tol,
it will be set to zero during estimation. Default value is tol/10.
Should a bin be removed during the algorithm if all
estimated intensities are zero for a single bin? Can improve
computation speed for large data sets. Note that zero means the estimated intensities
are smaller than prob_tol. Default is FALSE.
A vector of length 2, with the first entry indicating what percentage of mass should be distributed over (second entry) what percentage of all first bins. Default is c(0, 0), in which case the argument is ignored. This argument has no practical uses and only exists for demonstration purposes in the related article.
Not used yet
Michael G. Hudgens, On Nonparametric Maximum Likelihood Estimation with Interval Censoring and Left Truncation, Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 67, Issue 4, September 2005, Pages 573-587, tools:::Rd_expr_doi("10.1111/j.1467-9868.2005.00516.x")