包含重复测量应用的一般线性多变量模型的功效计算。
Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications.
作者信息
Muller Keith E, Lavange Lisa M, Ramey Sharon Landesman, Ramey Craig T
机构信息
Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599.
Center for Medical, Environmental, and Energy Statistics, Research Triangle Institute, Research Triangle Park, NC 27709, and Adjunct Assistant Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599. This work was conducted while she was Head, Design and Statistics Unit, Frank Porter Graham Child Development Center, University of North Carolina, Chapel Hill, NC.
出版信息
J Am Stat Assoc. 1992 Dec 1;87(420):1209-1226. doi: 10.1080/01621459.1992.10476281.
Recently developed methods for power analysis expand the options available for study design. We demonstrate how easily the methods can be applied by (1) reviewing their formulation and (2) describing their application in the preparation of a particular grant proposal. The focus is a complex but ubiquitous setting: repeated measures in a longitudinal study. Describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis. Discussion of the example also highlights issues that typically must be considered in designing a study. First, we discuss the motivation for using detailed power calculations, focusing on multivariate methods in particular. Second, we survey available methods for the general linear multivariate model (GLMM) with Gaussian errors and recommend those based on approximations. The treatment includes coverage of the multivariate and univariate approaches to repeated measures, MANOVA, ANOVA, multivariate regression, and univariate regression. Third, we describe the design of the power analysis for the example, a longitudinal study of a child's intellectual performance as a function of mother's estimated verbal intelligence. Fourth, we present the results of the power calculations. Fifth, we evaluate the tradeoffs in using reduced designs and tests to simplify power calculations. Finally, we discuss the benefits and costs of power analysis in the practice of statistics. We make three recommendations: Align the design and hypothesis of the power analysis with the planned data analysis, as best as practical.Embed any power analysis in a defensible sensitivity analysis.Have the extent of the power analysis reflect the ethical, scientific, and monetary costs. We conclude that power analysis catalyzes the interaction of statisticians and subject matter specialists. Using the recent advances for power analysis in linear models can further invigorate the interaction.
最近开发的功效分析方法扩展了研究设计的可用选项。我们通过（1）回顾其公式和（2）描述其在一份特定资助申请准备中的应用，来展示这些方法应用起来是多么容易。重点是一个复杂但普遍存在的情况：纵向研究中的重复测量。描述研究申请的制定过程可以展示进行有效功效分析所需的步骤。对该示例的讨论还突出了研究设计中通常必须考虑的问题。首先，我们讨论使用详细功效计算的动机，尤其关注多变量方法。其次，我们调查针对具有高斯误差的一般线性多变量模型（GLMM）的可用方法，并推荐基于近似值的方法。论述内容涵盖了重复测量、多变量方差分析（MANOVA）、单变量方差分析（ANOVA）、多变量回归和单变量回归的多变量和单变量方法。第三，我们描述该示例的功效分析设计，这是一项关于儿童智力表现作为母亲估计语言智力函数的纵向研究。第四，我们给出功效计算的结果。第五，我们评估使用简化设计和检验来简化功效计算时的权衡。最后，我们讨论功效分析在统计学实践中的益处和成本。我们提出三条建议：尽可能使功效分析的设计和假设与计划的数据分析保持一致。将任何功效分析嵌入到合理的敏感性分析中。使功效分析的程度反映伦理、科学和金钱成本。我们得出结论，功效分析促进了统计学家和主题专家之间的互动。利用线性模型中功效分析的最新进展可以进一步加强这种互动。
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