spRMM_SEM: Stochastic EM algorithm for semiparametric scaled mixture of censored data

Description

Stochastic EM algorithm for semiparametric scaled mixture for randomly right censored data.

Usage

spRMM_SEM(t, d = NULL, lambda = NULL, scaling = NULL, 
          centers = 2, kernelft = triang_wkde, 
          bw = rep(bw.nrd0(t),length(t)), averaged = TRUE,
          epsilon = 1e-08, maxit = 100, batchsize = 1, verb = FALSE)

Value

spRMM_SEM returns a list of class "spRMM" with the following items:

t: The input data.
d: The input censoring indicator.
lambda: The estimates for the mixing proportions.
scaling: The estimates for the components scaling.
posterior: An \(n\times k\) matrix of posterior probabilities for observation, after convergence of the algorithm.
loglik: The (pseudo) log-likelihood value at convergence of the algorithm.
all.loglik: The sequence of log-likelihood values over iterations.
all.lambda: The sequence of mixing proportions over iterations.
all.scaling: The sequence of scaling parameter over iterations.
meanpost: Posterior probabilities averaged over iterations.
survival: Kaplan-Meier last iteration estimate (a stepfun object).
hazard: Hazard rate last iteration estimate evaluated at final.t.
final.t: Last iteration unscaled sample (see reference).
s.hat: Kaplan-Meier average estimate.
t.hat: Ordered unscaled sample, for testing purpose.
avg.od: For testing purpose only.
hazard.hat: Hazard rate average estimate on t.hat.
batch.t: Batch sample (not ordered), see reference.
batch.d: Associated event indicators just rep(d,batchsize), for testing purpose.
sumNaNs: Internal control of numerical stability.
ft: A character vector giving the name of the function.

Arguments

t: A vector of \(n\) real positive lifetime (possibly censored) durations. If d is not NULL then a vector of random censoring times c occurred, so that \(x= min(x,c)\) and \(d = I(x <= c)\).
d: The vector of censoring indication, where 1 means observed lifetime data, and 0 means censored lifetime data.
lambda: Initial value of mixing proportions. If NULL, then lambda is set to rep(1/k,k).
scaling: Initial value of scaling between components, set to 1 if NULL.
centers: initial centers for initial call to kmeans for initialization.
kernelft: .
bw: Bandwidth in the kernel hazard estimates.
averaged: averaged.
epsilon: Tolerance limit.
maxit: The number of iterations allowed.
batchsize: The batchsize (see reference below).
verb: If TRUE, print updates for every iteration of the algorithm as it runs

Author

Didier Chauveau

References

Bordes, L., and Chauveau, D. (2016), Stochastic EM algorithms for parametric and semiparametric mixture models for right-censored lifetime data, Computational Statistics, Volume 31, Issue 4, pages 1513-1538. https://link.springer.com/article/10.1007/s00180-016-0661-7

Examples

Run this code

if (FALSE) {
n=500 # sample size
m=2 # nb components
lambda=c(0.4, 0.6) # parameters
meanlog=3; sdlog=0.5; scale=0.1
set.seed(12)
# simulate a scaled mixture of lognormals
x <- rlnormscalemix(n, lambda, meanlog, sdlog, scale)
cs=runif(n,20,max(x)+400) # Censoring (uniform) and incomplete data
t <- apply(cbind(x,cs),1,min)
d <- 1*(x <= cs)
tauxc <- 100*round( 1-mean(d),3)
cat(tauxc, "percents of data censored.\n")

c0 <- c(25, 180) # data-driven initial centers (visible modes)
sc0 <- 25/180    # and scaling
s <- spRMM_SEM(t, d, scaling = sc0, centers = c0, bw = 15, maxit = 100)

plotspRMM(s) # default
summary(s)   # S3 method for class "spRMM"
}

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