Semiparametric Modeling with Applications to Powerful Testing for Gene-Environment Interactions

• Activity Number: 165
• Type: Invited
• Date/Time: Monday, August 4, 2008 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Raymond Carroll*+ and Arnab Maity and Nilanjan Chatterjee and Enno Mammen
• Companies: Texas A&M University and Texas A&M University and National Cancer Institute and University of Mannheim
• Keywords: Repeated measures ; Genetic epidemiology ; Nonparametric regression ; Semiparametric methods ; Score testing

Abstract

Motivated from the problem of testing for genetic effects on complex traits in the presence of gene-environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 d.f form of interaction between parametrically and nonparametrically modeled covariates. We find that the score-test in this type of model, as recently developed by Chatterjee et al. (2007) in the fully parametric setting, is biased and requires undersmoothing to be valid in the presence of nonparametric components. Moreover, in the presence of repeated outcomes, the asymptotic distribution of the score test depends on the estimation of functions which are defined as solutions of complex integral equations, making implementation difficult and computationally taxing. We develop adjusted score statistics which are unbiased and asymptotically efficient for this problem.