Yashin A I, Manton K G, Stallard E
J Math Biol. 1986;24(2):119-40. doi: 10.1007/BF00275995.
Analyses of human mortality data classified according to cause of death frequently are based on competing risk theory. In particular, the times to death for different causes often are assumed to be independent. In this paper, a competing risk model with a weaker assumption of conditional independence of the times to death, given an assumed stochastic covariate process, is developed and applied to cause specific mortality data from the Framingham Heart Study. The results generated under this conditional independence model are compared with analogous results under the standard marginal independence model. Under the assumption that this conditional independence model is valid, the comparison suggests that the standard model overestimates by 4% the effect on life expectancy at age 30 due to the hypothetical elimination of cancer and by 7% the effect for cardiovascular/cerebrovascular disease. By age 80 the overestimates were 11% for cancer and 16% for heart disease. These results suggest the importance of avoiding the marginal independence assumption when appropriate data are available--especially when focusing on mortality at advanced ages.
根据死因分类的人类死亡率数据分析通常基于竞争风险理论。特别是，不同死因的死亡时间通常被假定为相互独立。在本文中，我们开发了一种竞争风险模型，该模型在给定一个假定的随机协变量过程的情况下，对死亡时间的条件独立性假设较弱，并将其应用于弗雷明汉心脏研究的特定死因死亡率数据。将在这种条件独立性模型下生成的结果与标准边际独立性模型下的类似结果进行比较。在假定这种条件独立性模型有效的前提下，比较结果表明，标准模型因假设消除癌症而高估了30岁时预期寿命的影响4%，因心血管/脑血管疾病而高估了7%。到80岁时，癌症的高估率为11%，心脏病的高估率为16%。这些结果表明，在有适当数据可用时，尤其是关注老年死亡率时，避免边际独立性假设的重要性。
