curereg: Parametric regression models with cure fraction for survival...

In Rumenick/flexcure: Flexible Parametric Survival Models with Cure Fraction

Description

curereg fits parametric regression models with cure fraction for survival data. This function extends the flexsurvreg by the inclusion of the cure fraction in the formulation and adds the Marshall-Olkin extreme value distribution in the comprehensive roll of parametric distributions avaliable.

Usage

curereg(formula, cureformula = ~1, data, weights, timedist = "moeev",
  ncausedist = "poisson", subset, na.action, inits, method = "SANN", ...)

Arguments

formula	an object of class "formula" which expresses the model to be fitted. The response should be specified as an object of class survival obtained via Surv function and can be set as right, left and interval censored data. The ~ separates the response from the covariates which should be specified on the right side, for instance formula = Surv(time, status) ~ age + sex.
cureformula	a formula defining the cure rate model. In the case of no covariate effect on the cure rate, set cureformula = ~ 1 (default), and for instance cureformula = ~ age + sex to include coefficients age and sex additively. If cureformula = or cureformula = NULL the model will be fitted without any cure rate.
data	the data set of class data.frame or list which includes all the objects defined in formula and cureformula. In case unspecified data, the variables shoud be available in the workspace (see (.GlobalEnv)).
weights	optional prior weights for the data.
timedist	survival distribution for the non-cured individuals. This can be set as: "exp" (exponential), "weibull" (Weibull), "ev" (extreme value), "gamma" (Gamma),"lnorm" (Log-normal), "llogist" (Log-logistic), "moee" (extreme value (or exponential) in the Marshall-Olkin family), "moeev" (extreme value (or Weibull) in the Marshall-Olkin family, the default), "gengamma" (Generalised Gamma), "genf" (Generalised F). The exponential, Weibull, log-normal and log-logistic distributions have the same parameterization defined in dexp, dweibull, dlnorm from package base and dllogis from package flexsurv, respectively. respectively. These differ from the parametrization used in the package survreg. The generalised Gamma and Generalised F distributions follows the parametrisation in (dgengamma) and (dgenf), respectively, both available in flexsurv. For the Marshall-Olkin extreme value distribution see dmoeev.
ncausedist	distribution of the number of competing causes of the event. This can be set as ncausedist = "bernoulli" for the standard mixture model and ncausedist = "poisson" (default), for the promotion time model.
subset	optional numeric vector specifying the subset observations from the full data set.
na.action	a function indicating what should happen when NA's occur, with possible arguments na.omit and na.fail. The default is set by the na.action setting in options().
inits	optional list with the initial values for the parameters. This list should be set as inits = list(coef_cure = c(...), coef_time = c(...), others = c(...)) where coef_cure is the vector of coefficients for the cure model, coef_time is the vector of coefficients for the survival regression model and others is parameters that are not modeled by covariates. See the object curereg.dists or flexsurv.dists in the source for the exact methods used.
method	The optimisation method to be used. method = "BFGS" is the default however "Nelder-Mead", "CG", "L-BFGS-B" and "SANN" can also be used, For more information about the optimisation methods, see optim.
...	optional arguments for the optim and flexsurvreg functions. For situations where the default optim arguments results in lack of converge, consider use control=list(fnscale = value) with value a tolerance value with the same magnitude of the log-likelihood function. Usually that happens when the Hessian matrix is not positive definite at some step of the numerical optimisation. An useful tool detect this and verify a possible "slower" convergence is add an appropriate value for trace to the control. See optim for more information. The argument fixedpars of the flexsurvreg function allows the user to input a vector of indices representing the fixed parameters. The arbitrary values for those fixed parameters should have been specified in inits argument and remain fixed throughout the estimation process.

Details

Note that the arguments ncausedist and timedist set up the model to be fitted. This means that if ncausedist = "poisson" and timedist = "genf" the fitted model is obtained considering the promotion-time model with generalised F responses. The improper density function of this model is available in dgenfpt. If ncausedist = "bernoulli" and timedist = "genf" has been set then the fitted model is calculated considering the standard mixture model with generalised F responses. The improper density function of this model is available in dgenfms. d____ms and p____ms correspond to the improper density and probability functions for standard mixture models, respectively, where ____ can be any of the distributions in timedist. Similarly, d____pt and p____pt correspond to the improper density and probability functions for promotion time models.

The relationship between the linear predictor in formula and the time-to-event of the non-cured elements is logarithmic as in the accelerated failure time models (Lawless, 2003). However, for cureformula, if ncausedist = "bernoulli" the relationship is similar to a logistic regression model (family = binomial(link = " logit ") in glm) and if ncausedist = "poisson" is similar to a Poisson model with logarithmic link function (family = poisson(link = "log") in glm). See the references for more details.

Value

A list of class "curereg" containing information about the fitted model. Components of interest to users may include:

call	the matched call.
coefficients	a named vector of coefficients obtained via Maximum Likelihood (see Details).
std.error	a named vector of the estimated standard errors for the coefficients (see Details).
vcov	A matrix of the estimated covariances between the coefficient estimates in the predictor of the model.
loglik	log-likelihood.
AIC	AIC the (generalized) Akaike Information Criterion for the fitted model.

Author(s)

Rumenick Pereira da Silva [e-mail]

References

Jackson, C.H. Christopher Jackson (2015). flexsurv: Flexible Parametric Survival and Multi-State Models. R package version 0.7. https://CRAN.R-project.org/package=flexsurv.

Maller, R. A., & Zhou, X. (1996). Survival analysis with long-term survivors. New York: Wiley.

Lawless, J. F. (2011). Statistical models and methods for lifetime data (Vol. 362). John Wiley & Sons.

Ortega, E. M., Cancho, V. G., & Paula, G. A. (2009). Generalized log-gamma regression models with cure fraction. Lifetime Data Analysis, 15(1), 79-106.

Peng, Y., Dear, K. B., & Denham, J. W. (1998). A generalized F mixture model for cure rate estimation. Statistics in medicine, 17(8), 813-830.

See Also

confint.curereg for confidence intervals for the coefficients, curefraction for predict cure fractions from fitted curereg model, plot.curereg and lines.curereg to plot fitted survival, hazards and cumulative hazards from models fitted by curereg.

Examples

## fit Marshall-Olkin extended extreme value standart mixture model
data(e1684)
fitmo <- curereg(Surv(FAILTIME, FAILCENS) ~ TRT + SEX + AGE, cureformula = ~ TRT + SEX + AGE,
                data = e1684, timedist = "moeev", ncausedist = "bernoulli")

# Output of 'curereg' object
fitmo

# Extract Model Coefficients
coef(fitmo)

# Extract model coefficients:
# Terms: failure time distribution model
coef(fitmo, terms = "time")
# Terms: cure probability model
coef(fitmo, terms = "cure")

# Object summaries
summary(fitmo)

# Information criterion
AIC(fitmo) # Akaike information criterion
BIC(fitmo) # Bayesian information criterion

# Extract Log-Likelihood
logLik(fitmo)
# Calculate Variance-Covariance Matrix for a Fitted Model Object
vcov(fitmo)

Rumenick/flexcure documentation built on May 9, 2019, 10:37 a.m.