Principal Interactions Analysis for Repeated Measures Data: Application to Gene-Gene, Gene-Environment Interactions

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Bhramar Mukherjee and Yi-An Ko*+ and Tyler J. VanderWeele and Anindya Roy and Sung Kyun Park and Jinbo Chen
• Companies: University of Michigan and University of Michigan and Harvard University and University of Maryland at Baltimore County and University of Michigan and University of Pennsylvania
• Keywords: column interaction ; epistasis ; intraclass correlation ; likelihood ratio test ; non-additivity ; Wishart matrix

Abstract

Modeling gene-gene, gene-environment interactions with repeated measures data on a quantitative trait is considered. Classical models proposed by Tukey and Mandel using cell means of a two-way classification array are effective to detect interactions in presence of main effects, but they fail under misspecified interaction structures. We explore additive main effects and multiplicative interaction (AMMI) models, which are based on a singular value decomposition of the cell means residual matrix after fitting additive main effects. AMMI models provide summaries of subject-specific and time-varying contributions to the leading principal components of the interaction matrix and allow geometric representation of the structure. We call this analysis "Principal Interactions Analysis" (PIA). It is illustrated using data from a longitudinal cohort study. Simulation studies were carried out under classical and common epistasis models to reveal PIA properties in comparison with the classical alternatives. AMMI performs reasonably across a spectrum of interaction models. AMMI test, however, may not be very powerful for common epistasis models unless epistasis occurs without main effects.