phmclust {mixPHM}

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. (2009). Multivariate Weibull mixtures with proportional hazard restrictions for dwell time based session clustering with incomplete data. Journal of the Royal Statistical Society, Series C (Applied Statistics), 58(5), 619-639.

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)