phmclust {mixPHM}R Documentation

Fits mixtures of proportional hazard models

Description

This function allows for the computation of proportional hazards models with different distribution assumptions on the underlying baseline hazard. Several options for imposing proportionality restrictions on the hazards are provided. This function offers several variations of the EM-algorithm regarding the posterior computation in the M-step.

Usage

phmclust(x, K, method = "separate", Sdist = "weibull", cutpoint = NULL, EMstart = NA, 
EMoption = "classification", EMstop = 0.01, maxiter = 100)

Arguments

x Data frame or matrix of dimension n*p with survival times (NA's allowed).
K Number of mixture components.
method Imposing proportionality restrictions on the hazards: With "separate" no restrictions are imposed, "main.g" relates to a group main effect, "main.p" to variable main effects. "main.gp" reflects the proportionality assumption over groups and variables. "int.gp" allows for interactions between groups and variables.
Sdist Various survival distrubtions such as "weibull", "exponential", and "rayleigh".
cutpoint Integer value with upper bound for observed dwell times. Above this cutpoint, values are regarded as censored. If NULL, no censoring is performed
EMstart Vector of length n with starting values for group membership, NA indicates random starting values.
EMoption "classification" is based on deterministic cluster assignment, "maximization" on deterministic assignment, and "randomization" provides a posterior-based randomized cluster assignement.
EMstop Stopping criterion for EM-iteration.
maxiter Maximum number of iterations.

Details

The method "separate" corresponds to an ordinary mixture model. "main.g" imposes proportionality restrictions over variables (i.e., the group main effect allows for free-varying variable hazards). "main.p" imposes proportionality restrictions over groups (i.e., the variable main effect allows for free-varying group hazards). If clusters with only one observation are generated, the algorithm stops.

Value

Returns an object of class mws with the following values:

K Number of components
iter Number of EM iterations
method Proportionality restrictions used for estimation
Sdist Assumed survival distribution
likelihood Log-likelihood value for each iteration
pvisit Matrix of prior probabilities due to NA structure
se.pvisit Standard errors for priors
shape Matrix with shape parameters
scale Matrix with scale parameters
group Final deterministic cluster assignment
posteriors Final probabilistic cluster assignment
npar Number of estimated parameters
aic Akaike information criterion
bic Bayes information criterion
clmean Matrix with cluster means
se.clmean Standard errors for cluster means
clmed Matrix with cluster medians

References

Mair, P., and Hudec, M. (2008). Analysis of dwell times in Web Usage Mining. Proceedings of the 31st Annual Conference of the German Classification Society on Data Analysis, Machine Learning, and Applications.

Collett, D. (2003). Modelling Survival Data in Medical Research. Boca Raton, FL: Chapman & Hall.

Celaux, G., and Govaert, G. (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, 315-332.

See Also

stableEM, msBIC

Examples


data(webshop)

## Fitting a Weibll mixture model (3 components) is fitted with classification EM 
## Observations above 600sec are regarded as censored

res1 <- phmclust(webshop, K = 3, cutpoint = 600)
res1
summary(res1)

## Fitting a Rayleigh Weibull proportional hazard model (2 components, proportional over groups)
res2 <- phmclust(webshop, K = 2, method = "main.p", Sdist = "rayleigh") 
res2
summary(res2)


[Package mixPHM version 0.7.0 Index]