Multikernel linear mixed model with adaptive lasso for complex phenotype prediction

Abstract

Linear mixed models (LMMs) and their extensions have been widely used for high‐dimensional genomic data analyses. While LMMs hold great promise for risk prediction research, the high dimensionality of the data and different effect sizes of genomic regions bring great analytical and computational challenges. In this work, we present a multikernel linear mixed model with adaptive lasso (KLMM‐AL) to predict phenotypes using high‐dimensional genomic data. We develop two algorithms for estimating parameters from our model and also establish the asymptotic properties of LMM with adaptive lasso when only one dependent observation is available. The proposed KLMM‐AL can account for heterogeneous effect sizes from different genomic regions, capture both additive and nonadditive genetic effects, and adaptively and efficiently select predictive genomic regions and their corresponding effects. Through simulation studies, we demonstrate that KLMM‐AL outperforms most of existing methods. Moreover, KLMM‐AL achieves high sensitivity and specificity of selecting predictive genomic regions. KLMM‐AL is further illustrated by an application to the sequencing dataset obtained from the Alzheimer's disease neuroimaging initiative.

A Penalized Linear Mixed Model with Generalized Method of Moments for Complex Phenotype Prediction

“…Converging evidence has shown that not all genetic variants and regions are predictive (Wen and Lu, 2020;Wen et al, 2016;Li, Lu and Wen, 2020;Speed and Balding, 2014;Weissbrod, Geiger and Rosset, 2016). Including noise can reduce the robustness and accuracy of the prediction model.…”

“…L 1 penalty is a commonly used technique for simultaneously selecting predictors and estimating their effect sizes. For example, Wen and Lu (2020) added an L 1 penalty to the log likelihood function of LMMs to simultaneously select predictive regions and estimate their effect sizes:…”

“…As converging evidences have suggested that epistasis widely exist (Buil et al, 2015;Moore and Williams, 2009), Weissbrod, Geiger and Rosset (2016) further generalizes the MultiBLUP via embedding cumulative predictive effects from each region into the reproducing kernel Hilbert space, where a pre-specified kernel function is used to construct variance-covariance matrices for each region, making it capable of capturing non-linear predictive effects. Recently, Wen and Lu (2020) incorporated the multi-kernel learnings into the LMMs, where complex predictive effects can be efficiently captured. While the advances in LMM-based methods offer greater flexibility in modeling complex diseases, their levels of successes are largely limited, mainly due to the high computational cost when a large number of random effects are used to accommodate different types of predictive effects.…”

“…L 1 penalization is a common technique used for simultaneously selecting predictive variables and estimating their effect sizes (Ghosh and Chinnaiyan, 2005;Ma, Song and Huang, 2007;Wu et al, 2009;Sun and Wang, 2012). Recently, it is introduced to LMM-based risk prediction models, where penalties are imposed on the random effect terms to allow for consistent and efficient selection of predictive regions (i.e., random effects) (Wen and Lu, 2020;Li, Lu and Wen, 2020). While these advances can reduce the impact of noise and improve prediction accuracy, their parameter estimations can be computationally demanding.…”

“…More kernels (e.g., the RBF kernels) can be added to the candidate kernel set to efficiently model various types of predictive effects. By using random effects to capture cumulative predictive effects and kernelizing the covariance matrices, our proposed method not only reduces the model parameters, but also offers a very flexible framework for modeling traits with various underlying genetic architecture (Wen and Lu, 2020;Li, Lu and Wen, 2020).…”