Discussion of "Optimal test procedures for multiple hypotheses controlling the familywise expected loss" by Willi Maurer, Frank Bretz, and Xiaolei Xun.
Discussion of "Optimal test procedures for multiple hypotheses controlling the familywise expected loss" by Willi Maurer, Frank Bretz, and Xiaolei Xun.
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Willi Maurer、Frank Bretz 和 Xiaolei Xun 讨论“控制家庭预期损失的多重假设的最优检验程序”。
DOI：
10.1111/biom.13908
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发表时间：
2023
期刊：
影响因子：
1.9
通讯作者：
Banerjee,Sudipto
中科院分区：
文献类型：
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作者：
Banerjee,Sudipto
我祝贺作者（毛尔、Bretz和Xun）写了一篇有趣的文章，并感谢编辑们给我机会讨论这篇文章。作者追求一个经典的决策理论的方法，定义合适的损失函数为一个给定的决策规则。他们控制的familywise预期损失，而不是更习惯的familywise错误率（FWER），根据数据的抽样分布。作者认为FWER可能不适合某些现实世界的临床决策环境，并注意到在常规临床应用中假设的数量相对较少，因此采用有限行动的观点，并寻求最大限度地减少假阴性的测量，但要受到一定的影响。误报受到任何参数配置的给定阈值的限制。我的讨论将集中在一些不太传统的环境中，而不是对所提出的方法进行批判性分析，这些环境正在见证越来越多的多假设检验的使用，在我看来，经典的决策理论方法（如作者所采用的方法）可能无法无缝地呈现自己。我的讨论并不是为了掩盖经典的决策理论方法，而是为了在经典方法可能过于限制时，进一步探索完全基于模型的贝叶斯方法。更具体地说，我将考虑空间数据分析在公共卫生中的应用，其中一个试图检测相邻地区之间的影响差异。这种应用程序的一个突出特点是，多个测试寻求未观察到的相关空间随机效应，需要从空间模型估计。让我们考虑空间疾病映射，其中区域聚集体（如疾病的计数或比率）映射到明确划定的行政单位（如州内的县或人口普查区或邮政编码），以更好地了解疾病的地理变异（Koch，2005; Lawson，2013，2018; Lawson等人，2016）。令表示针对= 1，.，的区域中的感兴趣的疾病结果。𝑖我们假设一个典型的广义线性混合模型设置，其中，λ λ遵循具有典型链接的指数族分布λ（E（λ λ））=λ Tλλ+λ λ，（1）其中，λ是区域λ内特定解释变量的λ× 1向量，λλ是与解释变量对应的斜率，λ λ是与区域λ对应的空间随机效应。解释变量可以包括疾病的风险因素或需要考虑的潜在混杂因素。空间依赖性被引入到空间随机效应的× 1向量中，=（ 1， 2，...，）T，使用图上的随机模型，其中节点对应于区域，并且两个节点之间的边将它们作为邻居。𝜙𝑛𝑛实例包括使用无向图的马尔可夫随机场（Besag，1974; Besag等人，1991; Kissling & Carl，2008;芸香& Held，2005）或定向非循环图形自回归（DAGAR）模型（Datta等人，2019年）。
I congratulate the authors (Mauer, Bretz, and Xun) on an interesting article and thank the Editors for the opportunity to discuss the work. The authors pursue a classical decision-theoretic approach by defining suitable loss functions for a given decision rule. They control the familywise expected loss, rather than the more customary familywise error rate (FWER), based upon the sampling distribution of the data. Arguing that FWER may not be appropriate in certain real-world clinical decision settings and noting that the number of hypotheses is relatively small in customary clinical applications, the authors adopt a finite actions perspective and seek to minimize a measure of false negatives subject to some measure of false positives being bounded by a given threshold for any parameter configuration. Instead of offering a critical analysis of the proposed approach, my discussion will focus on some less traditional settings that are witnessing increasing use of multiple hypothesis tests and where, in my opinion, a classical decision-theoretic approach such as the one adopted by the authors’ may not render itself seamlessly. My discussion is not intended to disparage the classical decisiontheoretic approach, but to foment further explorations into fully model-based Bayesian approaches when the classical approach may be too restrictive. More specifically, I will consider applications of spatial data analysis in public health where one seeks to detect differences in effects among neighboring regions. A salient feature of such applications is that multiple tests are sought on unobserved correlated spatial random effects that need to be estimated from a spatial model. Let us consider spatial disease mapping, where regional aggregates such as counts or rates from a disease are mapped over clearly delineated administrative units such as counties or census tracts or zip codes in a state to better understand geographic variation of diseases (Koch, 2005; Lawson, 2013, 2018; Lawson et al., 2016). Let 𝑦𝑖 denote a disease outcome of interest in region 𝑖 for 𝑖= 1,…, 𝑛. We assume a typical generalized linear mixed model setting where 𝑦𝑖 follows a distribution from the exponential family with canonical link 𝑔 (E (𝑦𝑖))= 𝒙T 𝑖 𝜷+ 𝜙𝑖,(1) where 𝒙𝑖𝑑 is a 𝑝× 1 vector of explanatory variables specific within region 𝑖, 𝜷 are the slopes corresponding to the explanatory variables and 𝜙𝑖 is a spatial random effect corresponding to region 𝑖. The explanatory variables can comprise risk factors for the disease or potential confounders that need to be reckoned with. Spatial dependence is introduced in the 𝑛× 1 vector of spatial random effects, 𝝓=(𝜙1, 𝜙2,…, 𝜙𝑛) T, using stochastic models on graphs, where the nodes correspond to regions and an edge between two nodes relate them as neighbors. Examples include Markov random fields using undirected graphs (Besag, 1974; Besag et al., 1991; Kissling & Carl, 2008; Rue & Held, 2005) or directed acyclic graphical autoregression (DAGAR) models (Datta et al., 2019).