Estimating and modeling the proportion cured of disease in population-based cancer studies

In population-based cancer studies, cure is said to occur when the mortality (hazard) rate in the diseased group of individuals returns to the same level as that expected in the general population. The cure fraction (the proportion of patients cured of disease) is of interest to patients and a useful measure to monitor trends in survival of curable disease. I will describe two types of cure model, namely, the mixture and nonmixture cure model (Sposto 2002); explain how they can be extended to incorporate the expected mortality rate (obtained from routine data sources); and discuss their implementation in Stata using the strsmix and strsnmix commands. In both commands there is the choice of parametric distribution (Weibull, generalized gamma, and log–logistic) and link function for the cure fraction (identity, logit, and log(–log)). As well as modeling the cure fraction it is possible to include covariates for the ancillary parameters for the parametric distributions. This ability is important, as it allows for departures from proportional excess hazards (typical in many population-based cancer studies). Both commands incorporate delayed entry and can therefore be used to obtain up-to-date estimates of the cure fraction by using period analysis (Smith et al. 2004). There is also an associated predict command that allows prediction of the cure fraction, relative survival, and the excess mortality rate with associated confidence intervals. For some cancers the parametric distributions listed above do not fit the data well, and I will describe how finite mixture distributions can be used to overcome this limitation. I will use examples from international cancer registries to illustrate the approach.