Centro de Matematica - Universidade do Minho

Cancer survival analysis is of major importance in the evaluation of cancer care practices provided to populations. International comparison of survival probabilities from cancer should take into account differences in patient?s population age structure since survival from cancer is often age dependent. This is usually achieved through direct age-standardization using a common age distribution standard such as the International Cancer Survival Standards. The direct age-standardization implies the estimation of survival for each age group. Often, the extreme age groups (youngest or oldest, depending on the cancer) are sparse and their net survival estimates are either very unstable or even impossible to obtain a few years after diagnosis.

Net survival, the survival that would be observed in the absence of causes of death not related to the disease in study, can be estimated using the Pohar-Perme estimator or a modelling approach. If the model is correctly specified, both methods should produce the same estimate. When age is considered as a continuous variable and the excess hazard is modelled with flexible functions (e.g. splines), net survival of each individual can be thinly predicted for any time since diagnosis. The net survival of a given age group is obtained as the mean of the individual net survival of the subjects in this age group. Although a flexible modelling approach is used, net survival estimate of each age group depends on the observed number of subjects in each group as well as on their observed age-distribution. This will again lead to unstable net survival estimates when the data are sparse even if the model allows to smoothly predict exact individual net survivals. Age group-specific estimates given by the non-parametric Pohar-Perme estimator are also very unstable on such datasets.

An alternative approach to the estimation of age-standardized net survival would be to predict survival (model-based) for a reference age in each age group or for a reference age instead of averaging the individual?s survival.

The main aim of this study was to evaluate and compare methods for the estimation of age standardized net survival when data are sparse. We compared three different approaches. Two model-based estimators of survival and the non-parametric estimator proposed by Pohar-Perme. In the first model-based approach, net survival was estimated averaging individual survivals within each age group. In the second, survival was estimated at a reference age in each age group. A flexible parametric model on the log hazard scale was used to model the excess hazard. We compared empirically the three approaches on small randomly selected samples from a large simulated dataset under different scenarios of age and year of diagnosis dependence.