Parametric Cure Models
In flexsurvcure: Flexible Parametric Cure Models

Introduction

Parametric cure models are a type of parametric survival model model in which it is assumed that there are a proportion of subjects who will not experience the event. In a mixture cure model, these 'cured' and 'uncured' subjects are modeled separately, with the cured individuals subject to no excess risk and the uncured individuals subject to excess risk modeled using a parametric survival distribution. In a non-mixture model, a parametric survival distribution is scaled such that survival asymptotically approaches the cure fraction.

Mixture Cure Model

The following code fits a mixture cure model to the bc dataset from flexsurv using a Weibull distribution and a logistic link function for the cure fraction:

library(flexsurvcure)
cure_model <- flexsurvcure(Surv(rectime, censrec)~group, data=bc, link="logistic", dist="weibullPH", mixture=T)
print(cure_model)

Model results can be displayed graphically using the plot S3 method:

plot(cure_model)

Predicted survival probabilities can also be generated using the summary S3 method:

summary(cure_model, t=seq(from=0,to=3000,by=1000), type="survival", tidy=T)

More complex models may be fitted by adding covariates to the parametric distribution used to model the uncured individuals. This is done by passing a list of formula, named according to the parameters affected, through the anc argument:

cure_model_complex <- flexsurvcure(Surv(rectime, censrec)~group, data=bc, link="logistic", dist="weibullPH", mixture=T, anc=list(scale=~group))
print(cure_model_complex)
plot(cure_model_complex)

Non-Mixture Cure Model

Non-mixture cure models can be fit by passing mixture=FALSE to flexsurvcure:

library(flexsurvcure)
cure_model_nmix <- flexsurvcure(Surv(rectime, censrec)~group, data=bc, link="loglog", dist="weibullPH", mixture=F)
print(cure_model_nmix)