Test of Association Between Two Ordinal Variables While Adjusting for Covariates
Test of Association Between Two Ordinal Variables While Adjusting for Covariates
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DOI：
10.1198/jasa.2010.tm09386
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发表时间：
2010-06-01
影响因子：
3.7
通讯作者：
Shepherd, Bryan E.
中科院分区：
文献类型：
--
作者：
Li, Chun;Shepherd, Bryan E.
我们提出了一组新的检验统计量来检验两个有序分类变量X和Y在调整连续和/或分类协变量z之后的关联。对于每个受试者，我们然后计算给定z的X和Y的条件分布。如果调整z后X和Y之间没有关系，则这些条件分布将是独立的，并且受试者的（X， Y）的观测值预计遵循这些条件分布的乘积分布。我们考虑两种简单的方法来检验条件独立的null，这两种方法都平等地对待X和Y，因为它们不需要指定结果和预测变量。第一种方法将所有受试者的这些乘积分布相加，以获得（X， Y）的期望分布，然后将其与观察到的无条件分布（X， Y）进行对比。我们的第二种方法是从两个多项模型中计算“残差”，然后测试这些残差之间的相关性；我们为具有有序结果的模型定义了一个新的个人水平残差。我们提出了使用我们的检验统计量的经验分布或渐近分布来计算p值的方法。通过模拟，我们证明，与将X视为连续或分类预测器的比例赔率模型相比，我们的测试统计数据在功率和I型错误率方面表现良好。我们将我们的方法应用于儿童视力障碍研究和人类免疫缺陷病毒（HIV）感染妇女宫颈异常研究的数据。这篇文章的补充材料可以在网上找到。
We propose a new set of test statistics to examine the association between two ordinal categorical variables X and Y after adjusting for continuous and/or categorical covariates Z. Our approach first fits multinomial (e.g.. proportional odds) models of X and Y, separately, on Z. For each subject, we then compute the conditional distributions of X and Y given Z. If there is no relationship between X and Y after adjusting for Z. then these conditional distributions will be independent, and the observed value of (X, Y) for a subject is expected to follow the product distribution of these conditional distributions. We consider two simple ways of testing the null of conditional independence, both of which treat X and Y equally, in the sense that they do not require specifying an outcome and a predictor variable. The first approach adds these product distributions across all subjects to obtain the expected distribution of (X. Y) tinder the null and then contrasts it with the observed unconditional distribution of (X, Y). Our second approach computes "residuals" from the two multinomial models and then tests for correlation between these residuals; we define a new individual-level residual for models with ordinal outcomes. We present methods for computing p-values using either the empirical or asymptotic distributions of our test statistics. Through simulations, we demonstrate that our test statistics perform well in terms of power and Type I error rate when compared to proportional odds models which treat X as either a continuous or categorical predictor. We apply our methods to data from a study of visual impairment in children and to a study of cervical abnormalities in human immunodeficiency virus (HIV)-infected women. Supplemental materials for the article are available online.