Additive Properties of Crude, Age Specific and Age Adjusted Rates for Cancer Incidence and Mortality

Background: In National Cancer Registry Programme (NCRP) reports, various rates are routinely provided for 50 cancer sites of males and 54 cancer sites of females. Very often, depending on our interest, we wish to see these rates for group of cancers like head and neck cancers, oral cancers, and reproductive cancers. In such a situation, the desired rates are calculated independently from the actual data and reported. The question is can we derive the rates for groups of cancers from the published reports when the data is provided only for the individual sites?
Objective: In the present paper, an attempt is made to explore the mathematical properties of various rates to derive them directly for the group of cancer sites from the published data when the rates are provided only for the individual sites. Source of data: The cancer incidence data collected by two urban Population Based Cancer Registries (PBCRs), under the network of NCRP for the period of 2006-08 was considered for the study purposes. The Registries included were: Bangalore and Bhopal.
Results: In the present communication, we have shown that the crude rate (CR), age specific rates and age-adjuste rates (AAR) all possess additive properties. This means, given the above rates for individual sites, the above rates can be calculated for groups of sites by simply adding them. In terms of formula it can be stated that CR(Site1+Site2+++ SiteN) = CR(Site1)+CR(Site2)+++ CR(SiteN). This formula holds good for age specific rates as well as for AAR. This property facilitates the calculation of various rates for defined groups of cancers by simply adding the above rates for individual sitesfrom which they are made up.