fit.cure.model: Parametric cure model

In cuRe: Parametric Cure Model Estimation

Parametric cure model

Description

This function fits parametric cure models using simple parametric distributions.

Usage

fit.cure.model(
  formula,
  data,
  formula.surv = NULL,
  type = c("mixture", "nmixture"),
  dist = c("weibull", "exponential", "lognormal", "weiwei", "weiexp", "gmw"),
  link = c("logit", "loglog", "identity", "probit"),
  bhazard = NULL,
  covariance = TRUE,
  link.mix = c("logit", "loglog", "identity", "probit"),
  control = list(maxit = 10000),
  method = "Nelder-Mead",
  init = NULL
)

Arguments

formula	Formula for modelling the cure proportion. The left hand side has to be of the form Surv(time, status).
data	Data frame in which to interpret the variable names in formula and formula.surv.
formula.surv	List of formulas for each parameter in the parametric distribution (see details).
type	A character indicating the type of cure model. Possible values are mixture (default) and nmixture.
dist	The parametric distribution of the survival of the uncured.
link	Character. Specifies the link function of the cure proportion.
bhazard	Background hazard.
covariance	Logical. If TRUE (default), the covariance matrix is computed.
link.mix	Character. Specifies the link function for the mixture parameter in a weibull-weibull mixture model and weibull-exponential model. Only used when dist = "weiwei" and dist = "weiexp".
control	List of control parameters passed to optim.
method	Optimization method passed to optim.
init	Initial values for the maximum likelihood optimization. If not provided, the optimization will start in 0.

Details

If type = "mixture", the function fits the model,

S(t|z) = \pi(z) + [1 - \pi(z)] S_u(t|z),

and if type = "nmixture", the function fits the model,

S(t|z) = \pi(z)^{\widetilde F(t)},

where z is a vector of covariates. The formula.surv argument is used to model S_u(t) (1 - \widetilde F(t)). It is a list of formulas with as many entries as there are parameters in the chosen parametric distribution. If not specified, all formulas are assumed to be ~1. The ith formula, i.e., formula.surv[[i]] refers to \theta_i in the below survival functions.

Exponential model:

S_u(t) = \exp\left(-t \theta_1\right).

Weibull model:

S_u(t) = \exp\left(-\theta_1 t^{\theta_2}\right).

Log-normal model:

S_u(t) = 1 - \Phi\left(\frac{\log(t) - \theta_1}{\theta_2}\right).

Weibull-exponential mixture model:

S_u(t) = \theta_1\exp\left(-\theta_2 t^{\theta_3}\right) + (1 - \theta_1)\exp\left(-\theta_4 t\right).

Weibull-Weibull mixture model:

S_u(t) = \theta_1\exp\left(-\theta_2 t^{\theta_3}\right) + (1 - \theta_1)\exp\left(-\theta_4 t^{\theta_5}\right).

Generalized modified Weibull distribution:

S_u(t) = 1-\left(1 - \exp\left(-\theta_1 t ^ \theta_2 \exp(\theta_3 t)\right)\right) ^ \theta_4.

In the Weibull-exponential and Weibull-Weibull mixture models, the link function for the mixture component is controlled by link.mix. The remaining parameters are modelled using an exponential link function except \theta_1 in the log-normal model, which is modelled using the identity. Parameters are not transformed back to the original scale in the outputted object and related print.cm and summary.cm functions

Value

An object of class cm containing the estimated parameters of the cure model. The appropriate link functions taken on \pi and the \theta_i's are linear in the covariates corresponding to their respective parameter estimates.

Examples

##Use data cleaned version of the colon cancer data from the rstpm2 package
data("colonDC")
set.seed(2)
colonDC <- colonDC[sample(1:nrow(colonDC), 500), ]

##Extract general population hazards
colonDC$bhaz <- general.haz(time = "FU", rmap = list(age = "agedays", sex = "sex", year= "dx"),
                            data = colonDC, ratetable = survexp.dk)


###Without covariates
##Fit weibull mixture cure model
fit.wei <- fit.cure.model(Surv(FUyear, status) ~ 1, data = colonDC, bhazard = "bhaz",
                          type = "mixture", dist = "weibull", link = "logit")

##Plot various summaries of the model (see ?predict.cm)
plot(fit.wei)
plot(fit.wei, time = seq(0, 40, length.out = 100))
plot(fit.wei, type = "hazard")
plot(fit.wei, type = "survuncured")
plot(fit.wei, type = "probcure")

#Fit a weibull-weibull mixture cure model
fit.weiwei <- fit.cure.model(Surv(FUyear, status) ~ 1, data = colonDC, bhazard = "bhaz",
                          type = "mixture", dist = "weiwei", link = "logit")

#Compare to the weibull model
plot(fit.wei, ci = FALSE)
plot(fit.weiwei, add = TRUE, col = 2, ci = FALSE)

###With covariates
##Fit weibull mixture cure model with age effect for both components of the Weibull model
fit <- fit.cure.model(Surv(FUyear, status) ~ age, data = colonDC, bhazard = "bhaz",
                      formula.surv = list(~ age, ~ age),
                      type = "mixture", dist = "weibull", link = "logit")

##Plot model for age 50 and 60
plot(fit, newdata = data.frame(age = 60),
     time = seq(0, 15, length.out = 100), ci = FALSE)
plot(fit, newdata = data.frame(age = 50),
     time = seq(0, 15, length.out = 100), ci = FALSE, add = TRUE, col = 2)

plot(fit, newdata = data.frame(age = 60),
     time = seq(0, 15, length.out = 100), ci = FALSE, type = "hazard")
plot(fit, newdata = data.frame(age = 50),
     time = seq(0, 15, length.out = 100), ci = FALSE, type = "hazard", add = TRUE, col = 2)

cuRe documentation built on July 9, 2023, 7 p.m.