Crombie I K, Cramer N
J Epidemiol Community Health. 1980 Sep;34(3):223-8. doi: 10.1136/jech.34.3.223.
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.
I = btk（其中I是年龄t时的发病率，b和k为常数），研究了人口结构对五岁年龄组特定发病率的影响。五年发病率与五年期中间年份的一年发病率存在系统性差异。这种差异取决于人口规模和发病率随年龄的变化。因此，在20 - 24岁年龄段，五年发病率比中期的一年发病率高估约4%，但这种高估逐渐减少，在75 - 79岁时变为低估0.5%。因此，一年发病率和五年发病率得出的拟合年龄发病率曲线斜率不同；发病率方程中k的值对于一年发病率约大0.7%。发达国家和不发达国家的人口结构明显不同，且发现这些结构会影响五年发病率，但影响幅度从不超过0.5%。实际人口一年年龄结构的不规则性对观察到的五年发病率的影响也很小，约为0.5%。然而，当通过记录多个日历年的肿瘤来计算发病率时，这些不规则性会给估算合适的分母人口带来困难。使用普查人口，即使是观察期中间年份的普查人口，误差也可能超过2%。一个好的方法是计算观察期的年平均人口，通过对相邻两次普查之间的年份人口进行插值来估算中间年份的人口。
