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

Therese Ml Andersson,Paul W Dickman,Sandra Eloranta,Paul C Lambert

doi:10.1186/1471-2288-11-96

Therese Ml Andersson, Paul W Dickman + Show 2 more

Open Access

https://doi.org/10.1186/1471-2288-11-96

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Abstract

BackgroundWhen 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.MethodsHere 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.ResultsWe 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.ConclusionsCure 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.

Highlights

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”
As cancer patient survival has improved for many cancer types, and many patients are cured of their disease, another important question is what proportion of patients are cured of their cancer
This paper shows how these problems could potentially be avoided by using flexible parametric survival models to estimate the cure proportion and the survival of the “uncured” in a population-based setting

Summary

Introduction

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”. 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. For most cancers the relative survival will reach a plateau some years after diagnosis, indicating that the mortality among the patients still alive is the same as expected in the general population This point is called the cure point and the patients still alive are considered “statistically cured”. It can sometimes be difficult to fit survival functions flexible enough to capture 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 [6]. Non-parametric or semi-parametric cure models have been suggested (e.g. [8-11]), but they do not use relative survival

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