Naouma Hanaa, Pataky Todd C
Bioengineering Course/Graduate School of Science and Technology, Shinshu University, Ueda, Nagano, Japan.
Department of Human Health Sciences/Graduate School of Medicine, Kyoto University, Kyoto, Japan.
PeerJ. 2019 Dec 10;7:e8189. doi: 10.7717/peerj.8189. eCollection 2019.
The inflation of falsely rejected hypotheses associated with multiple hypothesis testing is seen as a threat to the knowledge base in the scientific literature. One of the most recently developed statistical constructs to deal with this problem is the false discovery rate (FDR), which aims to control the proportion of the falsely rejected null hypotheses among those that are rejected. FDR has been applied to a variety of problems, especially for the analysis of 3-D brain images in the field of Neuroimaging, where the predominant form of statistical inference involves the more conventional control of false positives, through Gaussian random field theory (RFT). In this study we considered FDR and RFT as alternative methods for handling multiple testing in the analysis of 1-D continuum data. The field of biomechanics has recently adopted RFT, but to our knowledge FDR has not previously been used to analyze 1-D biomechanical data, nor has there been a consideration of how FDR vs. RFT can affect biomechanical interpretations.
We reanalyzed a variety of publicly available experimental datasets to understand the characteristics which contribute to the convergence and divergence of RFT and FDR results. We also ran a variety of numerical simulations involving smooth, random Gaussian 1-D data, with and without true signal, to provide complementary explanations for the experimental results.
Our results suggest that RFT and FDR thresholds (the critical test statistic value used to judge statistical significance) were qualitatively identical for many experimental datasets, but were highly dissimilar for others, involving non-trivial changes in data interpretation. Simulation results clarified that RFT and FDR thresholds converge as the true signal weakens and diverge when the signal is broad in terms of the proportion of the continuum size it occupies. Results also showed that, while sample size affected the relation between RFT and FDR results for small sample sizes (<15), this relation was stable for larger sample sizes, wherein only the nature of the true signal was important.
RFT and FDR thresholds are both computationally efficient because both are parametric, but only FDR has the ability to adapt to the signal features of particular datasets, wherein the threshold lowers with signal strength for a gain in sensitivity. Additional advantages and limitations of these two techniques as discussed further. This article is accompanied by freely available software for implementing FDR analyses involving 1-D data and scripts to replicate our results.
与多重假设检验相关的错误拒绝假设的膨胀被视为对科学文献知识库的一种威胁。最近开发的用于处理此问题的统计结构之一是错误发现率（FDR），其旨在控制在被拒绝的假设中错误拒绝的零假设的比例。FDR已应用于各种问题，特别是在神经成像领域对三维脑图像的分析中，在该领域统计推断的主要形式涉及通过高斯随机场理论（RFT）对假阳性进行更传统的控制。在本研究中，我们将FDR和RFT视为在一维连续数据的分析中处理多重检验的替代方法。生物力学领域最近采用了RFT，但据我们所知，FDR以前尚未用于分析一维生物力学数据，也没有人考虑过FDR与RFT如何影响生物力学解释。
我们重新分析了各种公开可用的实验数据集，以了解导致RFT和FDR结果趋同和分歧的特征。我们还进行了各种数值模拟，涉及有和没有真实信号的平滑、随机高斯一维数据，以对实验结果提供补充解释。
我们的结果表明，对于许多实验数据集，RFT和FDR阈值（用于判断统计显著性的临界检验统计量值）在定性上是相同的，但对于其他数据集则高度不同，这涉及数据解释中的重大变化。模拟结果表明，当真实信号减弱时，RFT和FDR阈值会收敛，而当信号在其占据的连续体大小比例方面较宽时，它们会发散。结果还表明，虽然样本大小在小样本量（<15）时会影响RFT和FDR结果之间的关系，但对于较大样本量，这种关系是稳定的，其中只有真实信号的性质是重要的。
RFT和FDR阈值在计算上都很高效，因为它们都是参数性的，但只有FDR有能力适应特定数据集的信号特征，其中阈值会随着信号强度降低以提高灵敏度。这两种技术的其他优点和局限性将进一步讨论。本文附带了用于实现涉及一维数据的FDR分析的免费软件以及用于复制我们结果的数据脚本。
