York Timothy P, Eaves Lindon J, van den Oord Edwin J C G
Massey Cancer Center, Virginia Commonwealth University, Virginia Institute for Psychiatric and Behavioral Genetics, P.O. Box 980003, Richmond, VA 23298-0003, USA.
Stat Med. 2006 Apr 30;25(8):1355-67. doi: 10.1002/sim.2292.
In a wide variety of medical research scenarios one is interested in the question whether regression curves differ for subgroups in the sample. Examples are gender differences in the effect of drug treatment or the study of genotype-environment interactions. To address this question exploratory techniques are often required because detailed knowledge concerning the shape of the regression curves and how that shape differs across subgroups is lacking. In this article we explored the power of two such exploratory techniques: multivariate adaptive regression splines (MARS) and least squares curve fitting using polynomials. For this purpose simulations were performed using linear, logistic, and complex non-linear curves. The power obtained from MARS was on average 1.4 times higher than with polynomials. It was shown that power was higher even if the regression curve was linear, that gains increased with the complexity of the curve, and that for highly non-linear curves model-free methods such as MARS might be the only alternative.
在各种各样的医学研究场景中，人们会关注样本中不同亚组的回归曲线是否存在差异这一问题。例如药物治疗效果中的性别差异或基因 - 环境相互作用的研究。由于缺乏关于回归曲线形状以及该形状在不同亚组间如何不同的详细知识，解决这个问题通常需要探索性技术。在本文中，我们探讨了两种此类探索性技术的功效：多元自适应回归样条（MARS）和使用多项式的最小二乘曲线拟合。为此，使用线性、逻辑和复杂非线性曲线进行了模拟。从MARS获得的功效平均比多项式高1.4倍。结果表明，即使回归曲线是线性的，MARS的功效也更高，随着曲线复杂性的增加功效增益也增加，并且对于高度非线性曲线，诸如MARS之类的无模型方法可能是唯一的选择。
