Analysis of Covariance in General Factorial Designs Through Multiple Contrast Tests Under Variance Heteroscedasticity.

IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY
Matthias Becher, Ludwig A Hothorn, Frank Konietschke
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引用次数: 0

Abstract

A common goal in clinical trials is to conduct tests on estimated treatment effects adjusted for covariates such as age or sex. Analysis of Covariance (ANCOVA) is often used in these scenarios to test the global null hypothesis of no treatment effect using an F $$ F $$ -test. However, in several samples, the F $$ F $$ -test does not provide any information about individual null hypotheses and has strict assumptions such as variance homoscedasticity. We extend the method proposed by Konietschke et al. ["Analysis of Covariance Under Variance Heteroscedasticity in General Factorial Designs," Statistics in Medicine 40 (2021): 4732-4749] to a multiple contrast test procedure (MCTP), which allows us to test arbitrary linear hypotheses and provides information about the global- as well as the individual null hypotheses. Further, we can calculate compatible simultaneous confidence intervals for the individual effects. We derive a small sample size approximation of the distribution of the test statistic via a multivariate t-distribution. As an alternative, we introduce a Wild-bootstrap method. Extensive simulations show that our methods are applicable even when sample sizes are small. Their application is further illustrated within a real data example.

方差异方差条件下多重对比检验一般析因设计的协方差分析。
临床试验的一个共同目标是对经协变量(如年龄或性别)调整后的估计治疗效果进行测试。协方差分析(ANCOVA)通常在这些情况下使用F $$ F $$检验来检验无治疗效果的全局零假设。然而,在一些样本中,F $$ F $$ -检验不提供任何关于单个零假设的信息,并且有严格的假设,如方差均方差。我们将Konietschke等人提出的方法扩展为多重对比检验程序(MCTP)。[“一般析因设计中方差异方差下的协方差分析”,医学统计40(2021):4732-4749],这使我们能够检验任意线性假设,并提供有关全局和个体零假设的信息。此外,我们可以计算个体效应的相容同时置信区间。我们通过多元t分布推导出检验统计量分布的小样本近似值。作为一种替代方法,我们引入了野生引导方法。大量的模拟表明,我们的方法即使在样本量很小的情况下也是适用的。在一个真实的数据示例中进一步说明了它们的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Statistics in Medicine
Statistics in Medicine 医学-公共卫生、环境卫生与职业卫生
CiteScore
3.40
自引率
10.00%
发文量
334
审稿时长
2-4 weeks
期刊介绍: The journal aims to influence practice in medicine and its associated sciences through the publication of papers on statistical and other quantitative methods. Papers will explain new methods and demonstrate their application, preferably through a substantive, real, motivating example or a comprehensive evaluation based on an illustrative example. Alternatively, papers will report on case-studies where creative use or technical generalizations of established methodology is directed towards a substantive application. Reviews of, and tutorials on, general topics relevant to the application of statistics to medicine will also be published. The main criteria for publication are appropriateness of the statistical methods to a particular medical problem and clarity of exposition. Papers with primarily mathematical content will be excluded. The journal aims to enhance communication between statisticians, clinicians and medical researchers.
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