Signs of Residuals for Testing Regression Coefficients in Quantile Regression

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sergey Tarima* and John Meurer and Peter Tarassenko and Rodney Sparapani
• Companies: Medical College of Wisconsin and The Medical College of Wisconsin and Tomsk State University and Medical College of Wisconsin
• Keywords: conditionally exact test ; quantile regression ; signs of residuals

Abstract

We introduce a family of tests for regression coefficients based on signs of quantile regression residuals. In our approach we first fit a quantile regression for the model where an independent variable of interest is not included in the set of model predictors (the null model). Then, signs of residuals of this null model are tested for association with the predictor of interest. This conditionally exact testing procedure is applicable for randomized studies. Further, we extend this testing procedure to observational data when co-linearity between the variable of interest and other model predictors is possible. In the presence of possible co-linearity, tests for conditional association controlling for other model predictors are used. Monte-Carlo simulation studies show superior performance of the introduced tests over all eight tests implemented in the R package "quantreg". These simulations explore situations when normality of regression coefficients is not yet reached, ex. lognormal distribution for lower and upper quantiles. An illustrative example shows the use of the proposed tests for investigating associations with hemoglobin A1C quantiles among type 2 diabetes patients.