Liddell F D
J Epidemiol Community Health. 1984 Mar;38(1):85-8. doi: 10.1136/jech.38.1.85.
The standardised mortality ratio is the ratio of deaths observed, D, to those expected, E, on the basis of the mortality rates of some reference population. On the usual assumptions--that D was generated by a Poisson process and that E is based on such large numbers that it can be taken as without error--the long established, but apparently little known, link between the Poisson and chi 2 distributions provides both an exact test of significance and expressions for obtaining exact (1-alpha) confidence limits on the SMR. When a table of the chi 2 distribution gives values for 1-1/2 alpha and 1/2 alpha with the required degrees of freedom, the procedures are not only precise but very simple. When the required values of chi 2 are not tabulated, only slightly less simple procedures are shown to be highly reliable for D greater than 5; they are more reliable for all D and alpha than even the best of three approximate methods. For small D, all approximations can be seriously unreliable. The exact procedures are therefore recommended for use wherever the basic assumptions (Poisson D and fixed E) apply.
标准化死亡比是观察到的死亡数D与基于某些参考人群死亡率预期的死亡数E之比。基于通常的假设——即D由泊松过程产生，且E基于如此大量的数据以至于可视为无误差——泊松分布与卡方分布之间早已确立但显然鲜为人知的联系，既提供了一种精确的显著性检验，也给出了用于获得标准化死亡比精确的（1 - α）置信区间的表达式。当卡方分布表给出具有所需自由度的1 - 1/2α和1/2α值时，这些程序不仅精确而且非常简单。当所需的卡方值未列表时，对于D大于5的情况，仅稍欠简单的程序就被证明是高度可靠的；对于所有的D和α，它们比三种近似方法中最好的方法还要可靠。对于小的D，所有近似方法都可能严重不可靠。因此，建议在基本假设（泊松分布的D和固定的E）适用的任何地方使用精确程序。
