Haybittle J L
MRC Cancer Trials Office, Cambridge, UK.
Int J Epidemiol. 1998 Oct;27(5):885-9. doi: 10.1093/ije/27.5.885.
Change in life expectancy may be more readily appreciated by a lay person as a measure of risk than the standardized mortality ratio (SMR).
The linear increase in the logarithm of the age-specific mortality rates with age (the Gompertz function) is used to deduce formulae connecting SMR with change in life expectancy. Their validity is checked by a comparison between the 1992 and 1952 mortality data for England and Wales, and between smokers and non-smokers in the American Cancer Society's second Cancer Prevention Study.
It is shown that the Gompertz function is a good fit to mortality data for England and Wales from age 30 years upwards. Changes in life expectancy at ages 15, 25, 45 and 65 are presented for values of SMR from 0.5 to 3. A very simple formula connecting the two is valid at ages 15 and 25, and provides a reasonable approximation at age 45.
The Gompertz relationship can be used to calculate the change in life expectancy corresponding to a particular SMR over a greater range than have previous methods, and, although subject to some uncertainties, can provide a quick method of judging the change in life expectancy that is associated with a given SMR value.
对于非专业人士而言，预期寿命的变化作为一种风险衡量指标，可能比标准化死亡率（SMR）更容易理解。
利用特定年龄死亡率的对数随年龄的线性增长（冈珀茨函数）来推导将SMR与预期寿命变化联系起来的公式。通过比较1992年和1952年英格兰和威尔士的死亡率数据，以及美国癌症协会第二次癌症预防研究中吸烟者和非吸烟者的数据，来检验这些公式的有效性。
结果表明，冈珀茨函数非常适合30岁及以上英格兰和威尔士的死亡率数据。给出了SMR值从0.5到3时，15岁、25岁、45岁和65岁时预期寿命的变化情况。一个将两者联系起来的非常简单的公式在15岁和25岁时有效，在45岁时提供了合理的近似值。
冈珀茨关系可用于计算与特定SMR相对应的预期寿命变化，其适用范围比以前的方法更广，并且尽管存在一些不确定性，但可以提供一种快速方法来判断与给定SMR值相关的预期寿命变化。
