A Greenwood formula for standard error of the age-standardised relative survival ratio

The age-standardised relative survival ratio is used to compare population-based cancer survival patterns when the population age structures differ. Traditionally, the direct standardisation method based on age-specific relative survival ratios has been used. In a new method [Brenner H, Arndt V, Gefeller O, Hakulinen T. An alternative approach to age adjustment of cancer survival rates. Eur J Cancer 2004;40:2317-22], weighted observations depending on the age structures of the study and standard populations are used to substitute the patients leading to a use of weighted counts. The relative survival ratio is then calculated in the conventional way. However, no standard error of the age-standardised relative survival estimate has been reported. In this paper, we introduce a generalisation of the well-known Greenwood formula for that purpose. This method is also applicable for the observed survival and particularly when the observed survival probabilities of the patient population differ by age stratum. The traditional Greenwood formula is a special case of the method when no specific weights are used and the observed survival probability is the same in each stratum. Data from the Finnish Cancer Registry are used for illustration.