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

Abstract

Linear mixed models have long been the method of choice for risk prediction analysis on high-dimensional data, where random effect terms are used to capture predictive effects from multiple markers. However, it remains computationally challenging to simultaneously model a large number of variables that can be noise or have predictive effects of complex forms. In this thesis, we first develop a penalized linear mixed model with generalized method of moments estimators for prediction analyses. The proposed method adopts the generalized method of moments estimators to improve computational efficiency and uses the L1 penalty to select predictors. We show that generalized method of moments estimators have oracle properties, including variable selection consistency, estimation consistency, and asymptotic normality. We further develop a hybrid screening rule that constitutes of the sequential strong rule and the enhanced dual polytope projection rule to reduce data dimension and improve computational efficiency. The proposed hybrid screening rule projects solutions to the objective function of the proposed penalized linear mixed model into the dual space, and then uses the sequential strong rule and the enhanced dual polytope projection rule to detect inactive variables in the space. We show that the hybrid screening rule aligns well with the proposed downstream prediction model, and it can correctly and efficiently discard a large number of variables with no predictive effects in the corresponding penalized linear mixed model. Lastly, we incorporate multiple kernels into the proposed penalized linear mixed model to model high-dimensional multi-omics data, where the interactive roles of multi-omics data and their complex types of predictive effects are captured. Through extensive simulation studies, we have demonstrated that the proposed methods are computationally efficient and can be applied to genome-wide data. They can capture predictive effects of complex forms and outperform competing linear mixed models. In the prediction analyses of PET-imaging outcomes using high-dimensional omics data, we find that the proposed method has better prediction performance than commonly used methods, and our analyses show that genetic variants on APOE, APOC1, TOMM40 and FADS3 genes are highly predictive.