Test of Association Between Two Ordinal Variables While Adjusting for Covariates

• 成果类型: Article
• 署名作者: Li, Chun; Shepherd, Bryan E.
• 署名单位: Vanderbilt University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09386
• 发表日期: 2010
• 页码: 612-620
• 关键词: models

摘要

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.