A nonparametric maximum likelihood approach for survival data with observed cured subjects, left truncation and right-censoring

Measures of explained variation under the mixture cure model for survival data

Explained variation is well understood under linear regression models and has been extended to models for survival data. In this article, we consider the mixture cure models. We propose two approaches to define explained variation under the mixture cure models, one based on the Kullback-Leibler information gain and the other based on residual sum of squares. We show that the proposed measures have desired properties as measures of explained variation, similar to those under other regression models. A simulation study is conducted to demonstrate the properties of the proposed measures. They are also applied to real data analyses to illustrate the use of explained variation.

Fitting parametric cure models in R using the packages cuRe and rstpm2

BACKGROUND AND OBJECTIVE

Within medical research, cure models are useful for analyzing time-to-event data in the scenario where a proportion of the analyzed individuals are expected to never experience the event of interest. Cure models are also useful for modelling the relative survival in scenarios where a proportion of the individuals are expected to eventually experience a mortality rate similar to that of the general population. Here we present two R packages, cuRe and rstpm2, that provide researchers with several tools for performing statistical inference using parametric cure models.

METHODS

Cure models are commonly used to estimate 1) the proportion of individuals that are cured and 2) the event-time distribution of individuals who are not cured. This can be done using simple parametric distributions for the event-time distribution of the uncured, but our implementations also enable fitting of more flexible spline-based cure models. The parametric framework of both packages ensures that cure models for the relative survival can easily be used.

RESULTS

The cuRe package contains two main functions for estimating parametric mixture cure models; one based on simple parametric distributions (e.g. Weibull or exponential) and one utilizing a spline-based formulation of the cure model. The rstpm2 package enables estimation of spline-based latent cure models, i.e., cure models with no explicit parameters modelling the proportion of cured individuals.

CONCLUSIONS

Through the R-packages cuRe and rstpm2, a wide range of different parametric cure models can be fitted. The cuRe package also contains a number of useful post-estimation procedures for computing the time to statistical cure and conditional probability of cure, which may spread the use of cure models in medical research.