Comparison of mathematical models for the maternal age dependence of Down's syndrome rates

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.