Tests for Conditional Association Between an Ordinal Predictor and Continuous, Binomial, or Ordinal Outcomes

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Bryan E. Shepherd*+ and Chun Li
• Companies: Vanderbilt University and Vanderbilt University
• Keywords: ordinal data ; categorical data analysis ; regression ; residuals ; HIV

Abstract

Standard regression models treat ordered categorical predictors (X) as either continuous or categorical. The former approach requires assigning arbitrary numbers to ordinal categories; the latter ignores order information. We propose a new method for testing the association between continuous, binary, or ordered categorical outcomes (Y) and X, adjusting for covariates (Z). Our method tests the correlation between residuals of the regression of Y on Z and residuals of the regression of X on Z, using a new residual for ordinal variables. We show that under the null of independence between X and Y conditional on Z, our test statistics are asymptotically normal with mean 0 and estimable variance. Through simulations we show that our test statistics outperform standard regression approaches. We apply our methods to data from HIV-infected patients in Mozambique.