View source: R/fit.cure.model.R
fit.cure.model | R Documentation |
This function fits parametric cure models using simple parametric distributions.
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 )
formula |
Formula for modelling the cure proportion. The left hand side
has to be of the form |
data |
Data frame in which to interpret the variable names in |
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 |
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 |
link.mix |
Character. Specifies the link function for the mixture parameter in a
weibull-weibull mixture model and weibull-exponential model. |
control |
List of control parameters passed to |
method |
Optimization method passed to |
init |
Initial values for the maximum likelihood optimization. If not provided, the optimization will start in 0. |
If type = "mixture"
, the function fits the model,
S(t|z) = π(z) + [1 - π(z)] S_u(t|z),
and if type = "nmixture"
, the function fits the model,
S(t|z) = π(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 θ_i in the below survival functions.
Exponential model:
S_u(t) = \exp≤ft(-t θ_1\right).
Weibull model:
S_u(t) = \exp≤ft(-θ_1 t^{θ_2}\right).
Log-normal model:
S_u(t) = 1 - Φ≤ft(\frac{\log(t) - θ_1}{θ_2}\right).
Weibull-exponential mixture model:
S_u(t) = θ_1\exp≤ft(-θ_2 t^{θ_3}\right) + (1 - θ_1)\exp≤ft(-θ_4 t\right).
Weibull-Weibull mixture model:
S_u(t) = θ_1\exp≤ft(-θ_2 t^{θ_3}\right) + (1 - θ_1)\exp≤ft(-θ_4 t^{θ_5}\right).
Generalized modified Weibull distribution:
S_u(t) = 1-≤ft(1 - \exp≤ft(-θ_1 t ^ θ_2 \exp(θ_3 t)\right)\right) ^ θ_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 θ_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
An object of class cm
containing the estimated parameters of the cure model.
The appropriate link functions taken on π and the θ_i's are linear in the covariates corresponding to their respective parameter estimates.
##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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.