Indirect standardization and multiplicative models for rates, with reference to the age adjustment of cancer incidence and relative frequency data

Abstract

By assuming that a simple multiplicative relationship exists between the age-specific mortality or morbidity rates for several populations, one is led to comparison of these populations using indirectly standardized mortality or morbidity ratios (SMR) where the age-specific rates for all populations combined are used as standards. Adjustments to these ratios are needed in case of large differences among the populations in both age-specific rates and age structures. This method is appropriate when insufficient data are available for direct standardization or when numbers of cases in individual age groups are so small as to make directly standardized rates unstable. It is oriented towards the internal comparison of specific sets of populations rather than production of synoptic figures for official publication. Extensions of the multiplicative hypothesis to the simultaneous analysis of multiple causes of mortality or morbidity suggest the use of a standardized relative mortality ratio (SRMR) for making comparisons when age-specific population denominators are not available. These methods are used to study several sets of cancer incidence and relative frequency data.