Testing equality of relative survival patterns based on aggregated data

The relative survival rate is defined as the ratio of the survival rate observed in a patient group under consideration to the survival rate expected in a group of people similar to the patient group at the beginning of the follow-up interval, with respect to all possible factors (e.g., age and sex) affecting survival, except the disease under study. Survival from cancer and other chronic diseases is often measured by this quantity, which is adjusted for the effect of mortality attributable to competing risks of death. In this paper, maximum likelihood ratio tests are constructed on the basis of aggregated data for testing the equality of relative survival rates between patient groups against proportional hazards and general alternative hypotheses. The tests are applied to the Finnish nationwide data on colon cancer patients with nonlocalized tumors as reported to the Finnish Cancer Registry. Simulation studies show that the maximum likelihood ratio tests compare favorably with alternative methods proposed earlier. Moreover, the maximum likelihood ratio tests are more extensive in coverage and are based on more applicable alternative hypotheses than the other test statistics. Finally, an extension to proportional hazards regression models of the relative survival rates is suggested.