A comparison of two methods for calculating expected mortality.
A comparison of two methods for calculating expected mortality.
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两种计算预期死亡率方法的比较。
DOI：
10.1002/sim.4780040114
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发表时间：
1985
影响因子：
2
通讯作者：
中科院分区：
文献类型：
--
作者：
作者的结论是，职业死亡率研究中使用的传统人年方法是不合理的。他们认为预期死亡率不应考虑研究组的生存经历。尽管这个提案具有一定的直观吸引力，但我们认为这种方法是不合适的，并且它们的表述不一致。哈茨等人。提出了人年法的另一种方法，他们称之为“预期”法，我们在这里称之为“精算法”。所提出的计算预期死亡率的精算方法只是个人风险的总和，风险在通常意义上定义为研究期间死亡的条件概率。该方法可得出随访结束时预期死亡的累积估计值。这样，预期死亡率是研究期长度的函数。另一方面，人年方法的基础是计算每人时间的比率（而不是风险）。因此，该方法考虑了研究组在整个研究期间相对于标准的生存经历的瞬时变化。我们和其他评论员一起认为，在检查长期死亡率数据时，这种方法更可取。 Hartz 等人的示例 3 实际上很好地说明了这个问题。在研究组中的所有 50 个人在 20 年随访的第一年全部死亡的队列中，精算方法的使用实际上忽略了这种不寻常的情况，并导致 16.6 例预期死亡。另一方面，与观测值 50 人相比，使用人年方法会导致预期只有 1 人死亡，这一结果更能描述本例中急剧超额死亡率。论文中的不一致之处在于试图解释根据两种方法计算的预期死亡率之间的差异。作者指出，当研究组的死亡率低于标准死亡率时，人年方法得出的预期死亡率估计值“太低”。实际上，一般来说，当研究组的死亡率低于标准人群时，人年法产生的预期死亡率高于精算法，而当研究组的死亡率较高时，则相反。对于特定原因死亡率，情况变得更加复杂，Hartz 等人没有考虑这一点。他们的示例 2 以及根据第 384 页上的实际数据进行的计算说明了这一点。
The authors conclude that the traditional person-years method used in occupational mortality studies cannot be justified. They contend that expected mortality should not take into account the survival experience of the study group. Although this proposal has a certain intuitive appeal, we submit that this approach is inappropriate and that their presentation is inconsistent. Hartz et al. present an alternative method to the person-years method, which they call the ‘prospective’method, and which we will here call the ‘actuarial method’. The proposed actuarial method of calculating expected mortality is simply a sum of individual risks, with risk defined in the usual sense as the conditional probability of dying during the period of study. This method results in a cumulative estimate of expected deaths at the end of follow-up. In this way the expected mortality is a function of the length of the study period. The basis for the person-years method, on the other hand, is the calculation of rates (as opposed to risks) per person-time. This method therefore takes into account instantaneous changes in the survival experience of the study group relative to the standard over the entire period of study. We, along with other commentators, believe that such a method is preferable when examining long-term mortality data. Hartz et al.’s example 3 actually illustrates the problem quite well. In a cohort where all 50 individuals in the study group die in the first year of a 20 year follow-up, use of the actuarial method virtually ignores this unusual situation and results in 16.6 expected deaths. Use of the person-years method, on the other hand, results in an expectation of only one death, compared to the observed value of 50, a result more descriptive of the dramatic excess mortality rate in this example.Inconsistencies in the paper occur with an attempt to explain the differences between the expected mortality calculated according to the two methods. The authors state that the person-years method results in estimates of expected mortality that are ‘too low’when the mortality rates in the study group are less than the standard rates. Actually, in general, the person-years method produces higher expected mortality than the actuarial method when the study group has lower mortality rates compared to the standard population, whereas the reverse is true when the study group has higher mortality rates. The situation becomes more complicated for cause-specific mortality, not considered by Hartz et a/. Their example 2 as well as their calculations from actual data on page 384 illustrate this point.
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DOI：
10.1016/0021-9681(70)90038-x
发表时间：
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期刊：
Journal of Chronic Diseases
影响因子：
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期刊：
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DOI：
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