Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 41 / 5 / a / Solution

A standard setting is relative survival in cancer registries. Patients' all-cause mortality is compared with mortality expected from population life tables matched for factors such as attained age, sex and calendar year. These provide the known individual background hazards $h_B^{(i)}$; the remaining common excess hazard $h_E$ describes mortality above that expected background.

This is useful when causes of death are incomplete or unreliable: all observed deaths can be used without deciding which were caused by the cancer. It also separates changes in background population mortality from excess mortality in the diseased cohort. The reference life tables must be appropriate, and a common excess hazard is a modeling assumption, not automatic. A relative survivor function can then describe the cohort's excess survival, but interpreting it as the effect of a causal elimination of the disease requires further assumptions.