Lamson S H, Hook E B
Hum Genet. 1981;59(3):232-4. doi: 10.1007/BF00283670.
The maternal age dependence of Down's syndrome rates was analyzed by two mathematical models, a discontinuous (DS) slope model which fits different exponential equations to different parts of the 20-49 age interval and a CPE model which fits a function that is the sum of a constant and exponential term over this whole 20-49 range. The CPE model had been considered but rejected by Penrose, who preferred models postulating changes with age assuming either a power function X10, where X is age or a Poisson model in which accumulation of 17 events was the assumed threshold for the occurrence of Down's syndrome. However, subsequent analyses indicated that the two models preferred by Penrose did not fit recent data sets as well as the DS or CPE model. Here we report analyses of broadened power and Poisson models in which n (the postulated number of independent events) can vary. Five data sets are analyzed. For the power models the range of the optimal n is 11 to 13; for the Poisson it is 17 to 25. The DS, Poisson, and power models each give the best fit to one data set; the CPE, to two sets. No particular model is clearly preferable. It appears unlikely that, with a data set from any single available source, a specific etiologic hypothesis for the maternal age dependence of Down's syndrome can be clearly inferred by the use of these or similar regression models.
通过两个数学模型分析了唐氏综合征发病率与母亲年龄的相关性，一个是不连续（DS）斜率模型，它对20至49岁年龄区间的不同部分拟合不同的指数方程；另一个是CPE模型，它在整个20至49岁范围内拟合一个由常数项和指数项组成的函数。Penrose曾考虑过CPE模型，但将其否决，他更倾向于假设随年龄变化的模型，一种是幂函数X10（其中X为年龄），另一种是泊松模型，即假定17个事件的累积是唐氏综合征发生的阈值。然而，随后的分析表明，Penrose所偏好的这两个模型对近期数据集的拟合效果不如DS模型或CPE模型。在此我们报告了对扩展的幂模型和泊松模型的分析，其中n（假定的独立事件数）可以变化。分析了五个数据集。对于幂模型，最优n的范围是11至13；对于泊松模型，是17至25。DS模型、泊松模型和幂模型分别对一个数据集拟合效果最佳；CPE模型对两个数据集拟合效果最佳。没有一个特定的模型明显更优。使用这些或类似的回归模型，似乎不太可能从任何单一可用来源的数据集中明确推断出关于唐氏综合征发病率与母亲年龄相关性的特定病因假设。
