Equivalence of Regression Curves
Equivalence of Regression Curves
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DOI：
10.1080/01621459.2017.1281813
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发表时间：
2018-03
影响因子：
3.7
通讯作者：
H. Dette;Kathrin Möllenhoff;S. Volgushev;F. Bretz
中科院分区：
文献类型：
--
作者：
H. Dette;Kathrin Möllenhoff;S. Volgushev;F. Bretz
摘要本文研究了描述两个不同组中的一个响应变量与若干协变量之间关系的两个参数模型m1、m2之间的差异是否实际上无关的问题，从而可以在合并样本的基础上进行推断。开发了统计方法来测试假设H 0：d（m1，m2）vs H1：d（m1，m2）<，以证明对于预定阈值，两条回归曲线m1，m2之间的等效性，其中d表示测量距离的距离m1和m2之间的距离。我们的方法是基于一个合适的估计这个距离的渐近性质。为了提高小样本情况下名义水平的近似性，开发了一种Bootstrap检验，该检验解决了区间假设的特定形式。特别是，数据必须在零假设下生成，这隐含地定义了参数向量的流形。通过仿真研究和数据实例说明了结果。它表明，新的方法大大提高了目前可用的方法的功率和近似的标称水平。
ABSTRACT This article investigates the problem whether the difference between two parametric models m1, m2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H0: d(m1, m2) ⩾ ϵ versus H1: d(m1, m2) < ϵ to demonstrate equivalence between the two regression curves m1, m2 for a prespecified threshold ϵ, where d denotes a distance measuring the distance between m1 and m2. Our approach is based on the asymptotic properties of a suitable estimator of this distance. To improve the approximation of the nominal level for small sample sizes, a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data have to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level.