Frailty modelling for the excess hazard.

Long-term excess hazards for cancer survival sometimes tend to zero or become negative even though we expect them to be positive. This may be explained by selection at diagnosis; individuals with certain cancers may have an increased risk of dying of other diseases in general. Then comparing with population mortality rates is not correct. Alternatively, we may have a continuous selection of the most robust individuals after diagnosis. When there are unobserved heterogeneity, and those with highest risk of dying of cancer also have the highest risk of dying of other diseases, this will cause selection after diagnosis. This may be modelled by multivariate frailty variables, and a corrected excess hazard may be estimated. In two examples, these corrected excess hazards give a better estimate when comparing to the cause-specific cancer mortality. Actually, this study questions the usefulness of long-term excess hazard rates.