A penalized linear mixed model with generalized method of moments for complex phenotype prediction

Linear mixed models have long been the method of choice for risk prediction analysis on high-dimensional genomic data. However, it remains computationally challenging to simultaneously model a large amount of genetic variants that can be noise or have predictive effects of complex forms. In this work, we have developed a penalized linear mixed model with generalized method of moments (pLMMGMM) estimators for prediction analysis. pLM-MGMM is built within the linear mixed model framework, where random effects are used to model the joint predictive effects from all genetic variants within a region. Fundamentally different from existing methods that usually focus on linear relationships and use empirical criteria for feature screening, pLMMGMM can jointly consider a large number of genetic regions and efficiently select those harboring variants with both linear and non-linear predictive effects. Through theoretical investigations, we have shown that our method has the selection consistency, estimation consistency and asymptotic normality. Through extensive simulations and the analysis of PET-imaging outcomes, we have demonstrated that pLMMGMM outperformed existing models and it can accurately detect regions that harbor risk factors with various forms of predictive effects.