Estimating and modeling cure within the framework of flexible parametric survival models

Cure models can be used to simultaneously estimate the proportion of cancer patients who are eventually cured of their disease and the survival of those who remain "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 fit survival functions flexible enough to capture high mortality rates within a few months from a diagnosis or a high cure proportion (e.g., over 90). If instead the flexible parametric survival models implemented in stpm2 could be used, then these problems could potentially be avoided. Flexible parametric survival models are fit on the log cumulative hazard scale using restricted cubic splines for the baseline. When cure is reached, the excess hazard rate (the difference in the observed all-cause mortality rate among the patients compared with that expected in the general population) is zero, and the cumulative excess hazard is constant. By incorporating an extra constraint on the log cumulative excess hazard after the last knot so that we force it not only to be linear but also to have zero slope, we are able to estimate the cure proportion. The flexible parametric survival model can be written as a special case of a nonmixture cure model, but with a more flexible distribution, which also enables estimation of the survival of "uncured" patients. We have updated the user-written stpm2 command for flexible parametric models and added a cure option as well as postestimation predictions of the cure proportion and survival of the "uncured". We will compare the use of flexible parametric cure models implemented in stpm2 with standard parametric cure models implemented in strsmix and strsnmix.