SOME LARGE-SAMPLE DISTRIBUTION-FREE ESTIMATORS AND TESTS FOR MULTIVARIATE PARTIALLY INCOMPLETE DATA FROM 2 POPULATIONS
SOME LARGE-SAMPLE DISTRIBUTION-FREE ESTIMATORS AND TESTS FOR MULTIVARIATE PARTIALLY INCOMPLETE DATA FROM 2 POPULATIONS
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DOI：
10.1002/sim.4780110903
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发表时间：
1992-06-30
影响因子：
2
通讯作者：
LACHIN, JM
中科院分区：
文献类型：
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作者：
LACHIN, JM
多变量观测最常见的例子是随着时间的推移重复测量的情况。分析两组K重复测量最常用的两种方法是K自由度(D.F.)T2 Manova F检验和受试者内1自由度方差F检验。两者都需要来自正态分布人群的完整样本。在这篇文章中，我描述了备选的K和1D.F.无需分布的程序，允许随机丢失观测数据。其中包括均值的大样本分析，带有Mann-Whitney参数估计的魏和拉钦多变量Wilcoxon检验，以及基于魏和约翰逊的多变量U统计量的多变量Hodges-Lehmann位置移位估计器。这些方法中的每一种都提供了群体差异大小的无分布的K变量估计，该估计可用作群体差异的总体检验的基础。这些测试包括K D.F。综合类T2检验，1D.F.限制性假设的检验，例如随机排序的魏-拉钦多元单边检验，以及基于平均组差异的最小方差广义最小二乘(GLS)估计的一般关联性检验。然后描述协变量分层调整的GLS估计和组间差异的检验。这种方法还为受试者内部和受试者之间的影响提供了同质性(交互)测试。我通过对按性别分层的两组患者重复测量胆固醇的分析来说明这些分析。这种分析提供了对通过结合时间(重复测量)和地层上的组差异而获得的处理效果的总体无分布汇总估计和测试。
The most common instance of multivariate observations is the case of repeated measures over time. The two most widely used methods for the analysis of K repeated measures for two groups are the K degrees of freedom (d.f.) T2 MANOVA F-test and the within-subjects 1 degree of freedom ANOVA F-test. Both require complete samples from normally distributed populations. In this paper, I describe alternative K and 1 d.f. distribution-free procedures which allow for randomly missing observations. These include a large-sample analysis of means, the Wei and Lachin multivariate Wilcoxon test with estimates of the Mann-Whitney parameter, and a multivariate Hodges-Lehmann location shift estimator based on the multivariate U-statistic of Wei and Johnson. Each of these methods provides a distribution-free K-variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences. These tests include the K d.f. omnibus T2-like test, 1 d.f. tests of restricted hypotheses, such as the Wei-Lachin multivariate one-sided test of stochastic ordering, and the test of general association based on a minimum variance generalized least squares (GLS) estimate of the average group difference. I then describe covariate stratified-adjusted GLS estimates and tests of group differences. This approach also provides tests of homogeneity (interaction) for within-subjects and between-subjects effects. I illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients, stratified by sex. Such analyses provide an overall distribution-free summary estimate and test of the treatment effect obtained by combining the group differences over both time (repeated measures) and strata.