Assessing the Effect of an Unobserved Covariate in Regression Analysis

• Activity Number: 190
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Yeo Jung Park*+ and Kerby Shedden
• Companies: University of Michigan and University of Michigan
• Keywords: Regression ; Unobserved variable effect ; Moment based method ; Gene association study ; EEG

Abstract

Multiple regression analysis is one of the most widely used methods in applied research to understand the relationship between an outcome and observed variables. In such analysis, it is possible that a single unobserved variable explains the entire regression relationship between an outcome and observed predictors. We propose a moment based approach to learn under which circumstances this alternative explanation for an observed association is possible. Under the hypothesis that only an unobserved variable has nonzero effect, the moments contain following three unknown quantities: the distribution and effect size of the unobserved variable, and the net dependence between the unobserved and observed variables. The funtional relationship of these three quantities characterizes the behavior of the unobserved variable's effect. We provide a simulation study based on genetic association study and two real data applications in electroencephalography (EEG) from multiple brain channels and DNA from 16 genetic regions.