Five-year age-specific incidence rates. I. Their nature and limitations

The effect of population structure on five-year age-specific incidence rates was investigated using the one-year population data from life tables and a theoretical age incidence curve of the form: I = btk - where I is the incidence at age t, and b and k are constants. The five-year incidence rates differed systematically from the one-year rates of the central year of the five-year period. This difference depended on the change with age of both the population size and the incidence rate. Thus at ages 20-24 the five-year rate overestimates the mid-period one-year rate by about 4%, but the overestimate progressively decreases to become an underestimate of 0.5% at ages 75-79. In consequence the one-year and five-year rates produce fitted age incidence curves with different slopes; the value of k in the incidence equation is about 0.7% greater for the one-year rates. The population structures of developed and underdeveloped countries are markedly different and these were found to affect the five-year incidence rates, but never by more than 0.5%. The effect of the irregularities in one-year age structure of real populations on the observed five-year rates is also small, of the order of 0.5%. However, when incidence rates are calculated by recording tumours over several calendar years, these irregularities can create difficulties for the estimation of the appropriate denominator population. The use of the census population, even that of the central year of the observation period, can be in error by over 2%. A good method is to calculate the mean annual population of the observation period, estimating the intercensal year populations by interpolation between flanking censuses.