Holmes A P, Blair R C, Watson J D, Ford I
Department of Statistics, University of Glasgow, Scotland.
J Cereb Blood Flow Metab. 1996 Jan;16(1):7-22. doi: 10.1097/00004647-199601000-00002.
The analysis of functional mapping experiments in positron emission tomography involves the formation of images displaying the values of a suitable statistic, summarising the evidence in the data for a particular effect at each voxel. These statistic images must then be scrutinised to locate regions showing statistically significant effects. The methods most commonly used are parametric, assuming a particular form of probability distribution for the voxel values in the statistic image. Scientific hypotheses, formulated in terms of parameters describing these distributions, are then tested on the basis of the assumptions. Images of statistics are usually considered as lattice representations of continuous random fields. These are more amenable to statistical analysis. There are various shortcomings associated with these methods of analysis. The many assumptions and approximations involved may not be true. The low numbers of subjects and scans, in typical experiments, lead to noisy statistic images with low degrees of freedom, which are not well approximated by continuous random fields. Thus, the methods are only approximately valid at best and are most suspect in single-subject studies. In contrast to the existing methods, we present a nonparametric approach to significance testing for statistic images from activation studies. Formal assumptions are replaced by a computationally expensive approach. In a simple rest-activation study, if there is really no activation effect, the labelling of the scans as "active" or "rest" is artificial, and a statistic image formed with some other labelling is as likely as the observed one. Thus, considering all possible relabellings, a p value can be computed for any suitable statistic describing the statistic image. Consideration of the maximal statistic leads to a simple nonparametric single-threshold test. This randomisation test relies only on minimal assumptions about the design of the experiment, is (almost) exact, with Type I error (almost) exactly that specified, and hence is always valid. The absence of distributional assumptions permits the consideration of a wide range of test statistics, for instance, "pseudo" t statistic images formed with smoothed variance images. The approach presented extends easily to other paradigms, permitting nonparametric analysis of most functional mapping experiments. When the assumptions of the parametric methods are true, these new nonparametric methods, at worst, provide for their validation. When the assumptions of the parametric methods are dubious, the nonparametric methods provide the only analysis that can be guaranteed valid and exact.
正电子发射断层扫描中功能映射实验的分析涉及形成显示合适统计量值的图像，该统计量总结了数据中每个体素处特定效应的证据。然后必须仔细检查这些统计图像，以定位显示出具有统计学显著效应的区域。最常用的方法是参数法，它假设统计图像中体素值具有特定形式的概率分布。然后根据这些假设，对用描述这些分布的参数表述的科学假设进行检验。统计图像通常被视为连续随机场的格点表示。这更便于进行统计分析。这些分析方法存在各种缺点。所涉及的许多假设和近似可能并不成立。在典型实验中，受试者和扫描次数较少，导致统计图像噪声大且自由度低，无法很好地用连续随机场近似。因此，这些方法充其量只是近似有效，在单受试者研究中最值得怀疑。与现有方法不同，我们提出了一种用于激活研究中统计图像显著性检验的非参数方法。形式假设被一种计算成本高昂的方法所取代。在一个简单的静息 - 激活研究中，如果真的没有激活效应，将扫描标记为“激活”或“静息”是人为的，用其他一些标记形成的统计图像与观察到的图像可能性相同。因此，考虑所有可能的重新标记，可以为描述统计图像的任何合适统计量计算p值。考虑最大统计量会导致一个简单的非参数单阈值检验。这种随机化检验仅依赖于关于实验设计的最小假设，是（几乎）精确的，I型错误（几乎）恰好是指定的，因此总是有效的。不存在分布假设允许考虑广泛的检验统计量，例如，用平滑方差图像形成的“伪”t统计图像。所提出的方法很容易扩展到其他范式，允许对大多数功能映射实验进行非参数分析。当参数方法的假设成立时，这些新的非参数方法在最坏的情况下为其提供验证。当参数方法的假设可疑时，非参数方法提供唯一可以保证有效和精确的分析。
