Estimating the crude probability of death due to cancer and other causes using relative survival models.

Relative survival is used extensively in population-based cancer studies to measure patient survival correcting for causes of death not related to the disease of interest. An advantage of relative survival is that it provides a measure of mortality associated with a particular disease, without the need for information on cause of death. Relative survival provides a measure of net mortality, i.e. the probability of death due to cancer in the absence of other causes. This is a useful measure, but it is also of interest to measure crude mortality, i.e. the probability of death due to cancer in the presence of other causes. A previous approach to estimate the crude probability of death in population-based cancer studies used life table methods, but we show how the estimates can be obtained after fitting a relative survival model. We adopt flexible parametric models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects. We illustrate the approach using an example of men diagnosed with prostate cancer in England and Wales showing the differences in net and crude survival for different ages.