OBJECTIVES: Mixture models that include a curable and incurable fraction improve the fitting of mortality models to data. However, some cancers display transformational step changes in mortality rates. Sometimes this is due to transformations in the cancer itself such as in chronic myeloid leukaemia, but sometimes occurs when resistance to treatment develops, or when treatment options become exhausted. Here we test a modified mixture model to include a transformational step to calculate the excess mortality in specific cancers over time from diagnosis using relative mortality statistics, in order to improve the success rate of fitting.

METHODS: Relative survival data from the SEER database was used covering a wide range of specific cancers at different ages and stages. Relative survival data We introduce a logistic function to a mixture model that includes, curable and incurable fractions, in addition to a model of rising mortality with time to represent the unmodified natural history of the cancer, along with a counterfactual model of decreasing mortality with intervention, to model step changes in mortality rates in specific cancers. The transformational step is represented as a logistic function representing a scalar variable applied to a parallel model of mortality that supplements excess mortality after a certain time-point.

RESULTS: Using the examples of chronic lymphoid, chronic myeloid leukaemia and others, we demonstrate the failure to successfully fit a simple mixture model in comparison to successful fitting with the modified mixture model.

CONCLUSIONS: Introduction of a transformation model within a standard mixture model may improve fitting of excess mortality models to relative survival data when there are transformation step changes in mortality with time from diagnosis.