A new cure model accounting for extra non-cancer mortality: Validation and application to real data

Abstract

The proportion of cancer patients cured of the disease is estimated with standard cure models assuming they have the same risk of death as the general population [1] . These patients, however often maintain an extra risk of dying compared to the overall population, which we assume is due to other causes than cancer [2] . The aim of the work was to develop and validate an extended cure model incorporating the estimated patients’ relative risk of death from other causes (α) compared to that observed in the general population. We extended the mixture cure model considering Weibull relative survival of the uncured by including a relative risk αwhich muliptlies the mortality observed in the general population. The parameters were estimated using maximum likelihood method for individual data and unweighted least square for grouped data. The extended model was evaluated through a simulation study of the performance and robustness. The validity of parameters estimated by both the standard and the extended cure models was evaluated on a set of simulations based on scenarios mirroring the behavior of lung and breast cancer from real data with 1000 samples of different sizes (500–20,000 cases each), with different values of α, with different length of follow-up, with set-ups where all the assumptions are verified or where some of them are not verified (survival of uncured patients does not follow a Weibull distribution; extra non-cancer death risk is dependent of age at diagnosis or randomly varies across patients). The models were also applied to real data: colon cancer data from the FRANCIM common database. When the assumptions were satisfied, the extended cure models correctly estimated the parameters and their standard errors, providing excellent coverage, in all scenario. The standard model underestimated the proportion of cured by 7% when α = 1.2, and by 40% when α = 2.0. Age effect on the proportion of cured was heavily overestimated. Among the extended models, the maximum likelihood estimation on individual data outperformed the unweighted least square for grouped data. When some of the assumptions were violated, parameter estimates by both extended models appeared fairly robust. Applied to real colon cancer data (e.g. in men), the extended models estimated close values of α respectively 1.28 (95% confidence interval [1.16–1.40] for grouped data and 1.23 [1.12–1.35] for individual data) and cure fraction (respectively 57.2% [54.3–60.1%] and 55.7%[53.3–58.1%]), higher than that of the conventional model (51.0% [48.5–53.5%] for grouped data and 51.6% [50.0–53.3%] for individual data). In individual data analyses, AIC was smaller for the extended model (55748) than for the conventional model (55760). The present analysis suggests that conventional indicators overestimate cancer-specific death and underestimate cure fraction for cancer survivors. The extended models are more efficient to estimate net survival in presence of an extra risk of dying.