Alternating Optimization for G × E Modelling With Weighted Genetic and Environmental Scores: Examples From the MAVAN Study

• Published in: Psychological methods 2019-04, Vol.24 (2), p.196-216
• Main Authors: Jolicoeur-Martineau, Alexia, Wazana, Ashley, Szekely, Eszter, Steiner, Meir, Fleming, Alison S., Kennedy, James L., Meaney, Michael J., Greenwood, Celia M. T.
• Format: Article
• Language: English
• Subjects: Adult; Affective Symptoms - epidemiology; Affective Symptoms - etiology; Affective Symptoms - genetics; Child Development - physiology; Child, Preschool; Depression - epidemiology; Environment; Exposure; Female; Gene-Environment Interaction; Genetics; Genotypes; Human; Humans; Infant; Linear Regression; Mathematical Modeling; Models, Biological; Models, Statistical; Pregnancy; Pregnancy Complications - epidemiology; Simulation; Statistical Weighting
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/met0000175

Motivated by the goal of expanding currently existing Genotype × Environment interaction (G × E) models to simultaneously include multiple genetic variants and environmental exposures in a parsimonious way, we developed a novel method to estimate the parameters in a G × E model, where G is a weighted sum of genetic variants (genetic score) and E is a weighted sum of environments (environmental score). The approach uses alternating optimization, an iterative process where the genetic score weights, the environmental score weights, and the main model parameters are estimated in turn, assuming the other parameters are constant. This technique can be used to construct relatively complex interaction models that are constrained to a particular structure, and hence contain fewer parameters. We present the model as a 2-way interaction longitudinal mixed model, for which ordinary linear regression is a special case, but it can easily be extended to be compatible with k-way interaction models and generalized linear mixed models. The model is implemented in R (LEGIT package) and using SAS macros (LEGIT_SAS). Through simulations, we demonstrate the power and validity of this approach even with small sample sizes. Furthermore, we present examples from the Maternal Adversity, Vulnerability, and Neurodevelopment (MAVAN) study where we improve significantly upon already existing models using alternating optimization. Translational Abstract Traditional attempts to understand how genes and environment interact consider a single variation of a gene and a single aspect of the environment at a time. In this article, we present a model which considers multiple genes and environments at the same time: the Latent Environment and Genetic InTeraction (LEGIT). It assumes that each gene and each aspect of the environment has a relative contribution. LEGIT is constructed through an iterative process which we call "alternating optimization." It estimates, in turn, the contribution of the genes, the contribution of the environments and how they interact with each other. LEGIT models are more complex and generally more powerful than traditional approaches. Through simulations, we demonstrate the power and validity of the approach even with fewer study participants. Furthermore, we present examples from the Maternal Adversity, Vulnerability, and Neurodevelopment (MAVAN) study where we improve significantly upon already existing models. Programming code is provided in R (LEGIT package) and