Søgaard J, Gyrd-Hansen D
Odense University, Denmark.
Dev Health Econ Public Policy. 1998;6:51-74. doi: 10.1007/978-1-4615-5681-7_3.
The life expectancy gain produced by a reduction in mortality can be determined by three different methods with respect to the timing of the gained life-years. One method adds the life expectancy gain to the expected end of life. Another method places the gain at the time of occurrence of the mortality reduction. A third method distributes the gained life-years over the maximum lifespan according to the differences in survival probabilities after and before the reduction in mortality. The three methods are all used in the literature together with a quasi-deterministic and a probabilistic approach to the notion of life expectancy. The counted numbers of gained life-years are the same, but due to different timing of life expectancy gains the discounted numbers are different. Several discounting models are identified when combining the three methods of counting with the deterministic and the probabilistic approaches to life expectancy. Some are symmetrical, some are not. However, most importantly, they come out with potentially very large differences in the discounted number of gained life-years. They differ by a factor of approximately (1 + r)e(a)-1, where r is a constant discount rate and e(a) is remaining life expectancy at age a, when the reduction of mortality occurs. For a new-born, discounting at 7% p.a., one discounting model provides a present value that is 150 times larger than another discounting model, the other models being in between. The various counting and discounting models for life expectancy gains are presented formally, graphically, and with numerical examples using Danish male mortality data. We show how three different discounting models provide large differences in discounted life expectancy gains and hence cost-effectiveness ratios in an economic evaluation of a colorectal cancer screening programme in Denmark. These different discounting models co-exist in the evaluation literature. Choice of method is rarely made explicit. Sensitivity analysis with respect to this choice is even rarer. We argue that one counting-discounting model is sufficient and that this should be to discount the differences between the two survival probability curves.
就所获生命年的时间而言，死亡率降低所带来的预期寿命增长可通过三种不同方法来确定。一种方法是将预期寿命增长加到预期生命终点。另一种方法是将增长置于死亡率降低发生之时。第三种方法是根据死亡率降低前后生存概率的差异，将所获生命年分布在最长寿命期间。这三种方法在文献中都与预期寿命概念的准确定性方法和概率性方法一起使用。所计算出的所获生命年数量相同，但由于预期寿命增长的时间不同，贴现后的数量也不同。当将三种计算方法与预期寿命的确定性方法和概率性方法相结合时，可确定几种贴现模型。有些是对称的，有些则不是。然而，最重要的是，它们在所获生命年的贴现数量上可能会有非常大的差异。它们相差约(1 + r)e(a)-1倍，其中r是固定贴现率，e(a)是死亡率降低发生时年龄a的剩余预期寿命。对于新生儿，按每年7%贴现，一种贴现模型提供的现值比另一种贴现模型大150倍，其他模型则介于两者之间。使用丹麦男性死亡率数据，以正式、图形和数值示例的方式呈现了预期寿命增长的各种计算和贴现模型。我们展示了三种不同的贴现模型如何在丹麦结直肠癌筛查计划的经济评估中，在所获预期寿命增长的贴现以及因此的成本效益比方面产生巨大差异。这些不同的贴现模型在评估文献中并存。方法的选择很少明确说明。关于这种选择的敏感性分析更是罕见。我们认为一种计算 - 贴现模型就足够了，而且应该是对两条生存概率曲线之间的差异进行贴现。
