*! version 1.0.2 13jul2012

help stmix also see: stmix postestimation

Title

stmix -- Parametric mixture survival models

Syntax

stmix [varlist] [if] [in] [, options]

Model
distribution(weibexp) Weibull-exponential survival distribution

distribution(we) synonym for distribution(weibexp)

distribution(weibweib) Weibull-Weibull survival distribution

distribution(ww) synonym for distribution(weibweib)

lambda1(varlist) covariates for the scale parameter of the first component distribution

gamma1(varlist) covariates for the shape parameter of the first component distribution

lambda2(varlist) covariates for the scale parameter of the second component distribution

gamma2(varlist) covariates for the shape parameter of the second component distribution

pmix(varlist) covariates for the mixture parameter

Reporting
nohr do not report hazard ratios

showinit display output from initial value model fits

showcons list constraints in output

keepcons do not drop constraints used in ml routine

level(#) set confidence level; default is level(95)

Maximization options
initmat(matrix_name) pass a matrix of initial values}

noinit do not fit the initial value model}

pmixconstraint(#) gives the value of which logit(pmix) is contrained to when obtaining initial values; default is 0

maximize_options control the maximization process; seldom used

You must stset your data before using stmix; see [ST] stset.

Weights are not currently supported.

Factor variables are not currently supported.

Description

stmix fits 2-component parametric mixture survival models. Distribution choices include Weibull-Weibull or Weibull-exponential. stmix can be
used with single- or multiple-record or single- or multiple-failure st data.

The component parametric models are additive on the survival scale, so for example, under a 2-component mixture Weibull-Weibull model:

S_0(t) = pmix * exp(-lambda1 * t ^ gamma1) + (1 - pmix) * exp(-lambda2 * t ^ gamma2)

Proportional hazards can be induced via:

h(t) = -d(ln(S_0(t))/dt * exp(XB)

Options

Model

distribution(string) specifies the parametric mixture distribution. Choices include a Weibull-exponential, weibexp/we, or a Weibull-Weibull,
weibweib/ww.

lambda1(varlist) covariates to include in the linear predictor of the scale parameter of the first component distribution. This is ln(lambda1) for all
models.

gamma1(varlist) covariates to include in the linear predictor of the shape parameter of the first component distribution. This is ln(gamma1) for all
models.

lambda2(varlist) covariates to include in the linear predictor of the scale parameter of the second component distribution. This is ln(lambda2) for all models.

gamma2(varlist) covariates to include in the linear predictor of the shape parameter of the second component distribution. This is ln(gamma2) and is only allowed under a mixture
weibweib model.

pmix(varlist) covariates to include in the linear predictor of the mixture parameter.

Reporting

nohr may be specified at estimation or upon redisplaying results, specifies that coefficients rather than exponentiated coefficients be displayed,
i.e., that coefficients rather than hazard ratios be displayed. This option affects only how coefficients are displayed, not how they are estimated.

showinit displays the output from the inital value model fit, whereby the mixture parameter is constrained to 0 (on the logit scale).

showcons displays the constraints used by stmix.

keepcons do not drop the constraints used in the ml routine.

level(#) specifies the confidence level, as a percentage, for confidence intervals. The default is level(95) or as set by set level.

Maximization

initmat(matrix_name) pass a matrix of initial values to the full model.

noinit do not fit the initial value model.

pmixconstraint(#) gives the value of the contraint on the mixture parameter when obtaining initial values. Default is 0 (on the logistic scale).

maximize_options; difficult, technique(algorithm_spec),
iterate(#), [no]log, trace, gradient,
showstep, hessian, shownrtolerance, tolerance(#),
ltolerance(#) gtolerance(#), nrtolerance(#),
nonrtolerance, from(init_specs); see [R] maximize. These
options are seldom used, but the difficult option may be useful if there
are convergence problems.

Remark

Note: Covariate effects can be interpreted as hazard ratios only if lambda1, gamma1, lambda2, gamma2 and pmix are left empty.

Example

Setup

webuse brcancer

stset rectime, failure(censrec = 1) scale(365.25)

Mixture Weibull-Weibull proportional hazards model

stmix hormon, dist(ww)

Authors

Michael J. Crowther, University of Leicester, UK. E-mail: michael.crowther@le.ac.uk.

Paul C. Lambert, University of Leicester, UK. E-mail: paul.lambert@le.ac.uk.

Please report any errors you may find.

References

McLachlan, G. J. & McGiffin, D. C. On the role of finite mixture models in survival analysis. Stat Methods Med Res, 1994, 3, 211-226.

Gelfand, A. E.; Ghosh, S. K.; Christiansen, C.; Soumerai, S. B. & McLaughlin, T. J. Proportional hazards models: a latent competing risk approach Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000, 49, 385-397.

Also see

Online: stmix postestimation