Estimating and modelling cure in population-based cancer studies within the framework of flexible parametric survival models

Abstract

Background: When the mortality among a cancer patient group returns to the same level as in the general population, that is, the patients no longer experience excess mortality, the patients still alive are considered "statistically cured". Cure models can be used to estimate the cure proportion as well as the survival function of the "uncured". One limitation of parametric cure models is that the functional form of the survival of the "uncured" has to be specified. It can sometimes be hard to find a survival function flexible enough to fit the observed data, for example, when there is high excess hazard within a few months from diagnosis, which is common among older age groups. This has led to the exclusion of older age groups in population-based cancer studies using cure models.

Methods: Here we have extended the flexible parametric survival model to incorporate cure as a special case to estimate the cure proportion and the survival of the "uncured". Flexible parametric survival models use splines to model the underlying hazard function, and therefore no parametric distribution has to be specified.

Results: We have compared the fit from standard cure models to our flexible cure model, using data on colon cancer patients in Finland. This new method gives similar results to a standard cure model, when it is reliable, and better fit when the standard cure model gives biased estimates.

Conclusions: Cure models within the framework of flexible parametric models enables cure modelling when standard models give biased estimates. These flexible cure models enable inclusion of older age groups and can give stage-specific estimates, which is not always possible from parametric cure models.

Figure 1

Sensitivity to knot placement. Ederer II life table estimates of relative survival and predicted survival from flexible parametric cure models with different knot locations and number of knots.

Figure 2

Comparing predicted survival. Predicted survival and cure proportions (%) from non-mixture models and flexible parametric cure models, compared to life table estimates of relative survival.

Figure 3

Comparing predicted cure proportions. Predicted cure proportion (%) with 95% confidence intervals from a flexible parametric cure model and a non-mixture cure model.

Figure 4

Comparing predicted median survival times. Predicted median survival time (years) of "uncured" with 95% confidence intervals from a flexible parametric cure model and a non-mixture cure model.

Figure 5

An example of a high cure proportion. Predicted survival and cure proportion (%) for localised cancer from flexible parametric cure models, compared to life table estimates of relative survival.