Genetic prediction of complex traits with polygenic scores: a statistical review

Accurate genetic prediction of complex traits can facilitate disease screening, improve early intervention, and aid in the development of personalized medicine. Genetic prediction of complex traits requires the development of statistical methods that can properly model polygenic architecture and construct a polygenic score (PGS). We present a comprehensive review of 46 methods for PGS construction. We connect the majority of these methods through a multiple linear regression framework which can be instrumental for understanding their prediction performance for traits with distinct genetic architectures. We discuss the practical considerations of PGS analysis as well as challenges and future directions of PGS method development. We hope our review serves as a useful reference both for statistical geneticists who develop PGS methods and for data analysts who perform PGS analysis.

The reciprocal Bayesian LASSO

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model selection relative to traditional shrinkage methods. Here we consider a fully Bayesian formulation of the rLASSO problem, which is based on the observation that the rLASSO estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters are assigned independent inverse Laplace priors. Bayesian inference from this posterior is possible using an expanded hierarchy motivated by a scale mixture of double Pareto or truncated normal distributions. On simulated and real datasets, we show that the Bayesian formulation outperforms its classical cousin in estimation, prediction, and variable selection across a wide range of scenarios while offering the advantage of posterior inference. Finally, we discuss other variants of this new approach and provide a unified framework for variable selection using flexible reciprocal penalties. All methods described in this article are publicly available as an R package at: https://github.com/himelmallick/BayesRecipe.

Genetic risk factors for colorectal cancer in multiethnic Indonesians

Colorectal cancer is a common cancer in Indonesia, yet it has been understudied in this resource-constrained setting. We conducted a genome-wide association study focused on evaluation and preliminary discovery of colorectal cancer risk factors in Indonesians. We administered detailed questionnaires and collecting blood samples from 162 colorectal cancer cases throughout Makassar, Indonesia. We also established a control set of 193 healthy individuals frequency matched by age, sex, and ethnicity. A genome-wide association analysis was performed on 84 cases and 89 controls passing quality control. We evaluated known colorectal cancer genetic variants using logistic regression and established a genome-wide polygenic risk model using a Bayesian variable selection technique. We replicate associations for rs9497673, rs6936461 and rs7758229 on chromosome 6; rs11255841 on chromosome 10; and rs4779584, rs11632715, and rs73376930 on chromosome 15. Polygenic modeling identified 10 SNP associated with colorectal cancer risk. This work helps characterize the relationship between variants in the SCL22A3, SCG5, GREM1, and STXBP5-AS1 genes and colorectal cancer in a diverse Indonesian population. With further biobanking and international research collaborations, variants specific to colorectal cancer risk in Indonesians will be identified.

A data augmentation approach for a class of statistical inference problems

We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.