Guardabasso V, Munson P J, Rodbard D
Laboratory of Theoretical and Physical Biology, National Institute of Child Health and Human Development, Bethesda, Maryland 20892.
FASEB J. 1988 Mar 1;2(3):209-15. doi: 10.1096/fasebj.2.3.3350235.
We have developed a versatile new approach to the simultaneous analysis of families of curves, which combines the simplicity of empirical methods with several of the advantages of mathematical modeling, including objective comparison of curves and statistical hypothesis testing. The method uses weighted smoothing cubic splines; the degree of smoothing is adjusted automatically to satisfy constraints on curve chape (monotonicity, number of inflection points). By simultaneous analysis of a family of curves, one can extract the shape common to all the curves. Up to four linear scaling parameters are used to match the shape to each curve, and to provide optimal superimposition of the several curves. By applying constraints to these scaling factors, one can test a variety of hypotheses concerning comparisons of curves (e.g., identity, parallelism, or similarity of shape of two or more curves), and thus evaluate the effects of experimental manipulation. By optimal pooling of data one can avoid the need for arbitrary selection of a typical experiment, and can detect subtle but reproducible effects that might otherwise be overlooked. This approach can facilitate the development of an appropriate model. The method has been implemented in a Turbo-Pascal program for IBM-PC compatible microcomputers, and in FORTRAN-77 for the DEC-10 mainframe, and has been utilized successfully in a wide variety of applications.
我们开发了一种通用的新方法来同时分析曲线族，该方法将经验方法的简单性与数学建模的若干优点相结合，包括曲线的客观比较和统计假设检验。该方法使用加权平滑三次样条；平滑度会自动调整以满足对曲线形状的约束（单调性、拐点数量）。通过同时分析曲线族，可以提取所有曲线共有的形状。使用多达四个线性缩放参数来使形状与每条曲线匹配，并实现多条曲线的最佳叠加。通过对这些缩放因子施加约束，可以检验关于曲线比较的各种假设（例如，两条或多条曲线的一致性、平行性或形状相似性），从而评估实验操作的效果。通过对数据进行最佳汇总，可以避免随意选择典型实验的必要性，并能够检测到否则可能被忽视的细微但可重复的效果。这种方法可以促进合适模型的开发。该方法已在用于IBM-PC兼容微型计算机的Turbo-Pascal程序以及用于DEC-10大型机的FORTRAN-77中实现，并已成功应用于各种领域。
