多响应的分组Hotelling's T^2检验
Group Hotelling's T^2 Test for Comparing Multiple Endpoints
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摘要: 两样本的多响应比较在实际中应用非常广泛. 当样本不服从正态分布时, Hotelling's T^2检验(HT)的功效普遍不高.为了解决这一问题, 本文提出了分组Hotelling's T^2检验(GHT),即对数据进行逆正态变换后, 在每一组中进行HT,然后基于每组的p值构造统计量并取最大值. 大量模拟表明,GHT比HT和其他已有检验更加稳健. 最后,应用于血浆肾素活性和大脑衰老数据进一步验证GHT的有效性.Abstract: Comparisons between two samples with multiple endpoints are often encountered in many real applications and Hotelling's T^2 test (HT) may suffer from loss of efficiency when multivariate normality assumption is violated. To overcome this issue, we propose a group Hotelling's T^2 test (GHT) where HT is conducted within each group after inverse normal transformation and then use the maximum value among combined statistics based on p-values at the group-level. Extensive simulations show that GHT is more robust than HT and some other existing procedures. Finally, the applications to plasma-renin activity in serum study and the ageing human brain further demonstrate the performance of GHT.