A Quadratically Regularized Functional Canonical Correlation Analysis for Identifying the Global Structure of Pleiotropy with NGS Data

Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore multiple levels of representations of genetic variants, learn their internal patterns involved in the disease development, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new framework referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the nine competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and nine other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the nine other statistics.Comment: 64 pages including 12 figure

Changes from Classical Statistics to Modern Statistics and Data Science

A coordinate system is a foundation for every quantitative science, engineering, and medicine. Classical physics and statistics are based on the Cartesian coordinate system. The classical probability and hypothesis testing theory can only be applied to Euclidean data. However, modern data in the real world are from natural language processing, mathematical formulas, social networks, transportation and sensor networks, computer visions, automations, and biomedical measurements. The Euclidean assumption is not appropriate for non Euclidean data. This perspective addresses the urgent need to overcome those fundamental limitations and encourages extensions of classical probability theory and hypothesis testing , diffusion models and stochastic differential equations from Euclidean space to non Euclidean space. Artificial intelligence such as natural language processing, computer vision, graphical neural networks, manifold regression and inference theory, manifold learning, graph neural networks, compositional diffusion models for automatically compositional generations of concepts and demystifying machine learning systems, has been rapidly developed. Differential manifold theory is the mathematic foundations of deep learning and data science as well. We urgently need to shift the paradigm for data analysis from the classical Euclidean data analysis to both Euclidean and non Euclidean data analysis and develop more and more innovative methods for describing, estimating and inferring non Euclidean geometries of modern real datasets. A general framework for integrated analysis of both Euclidean and non Euclidean data, composite AI, decision intelligence and edge AI provide powerful innovative ideas and strategies for fundamentally advancing AI. We are expected to marry statistics with AI, develop a unified theory of modern statistics and drive next generation of AI and data science.Comment: 37 page

Implication of next-generation sequencing on association studies

<p>Abstract</p> <p>Background</p> <p>Next-generation sequencing technologies can effectively detect the entire spectrum of genomic variation and provide a powerful tool for systematic exploration of the universe of common, low frequency and rare variants in the entire genome. However, the current paradigm for genome-wide association studies (GWAS) is to catalogue and genotype common variants (5% < MAF). The methods and study design for testing the association of low frequency (0.5% < MAF ≤ 5%) and rare variation (MAF ≤ 0.5%) have not been thoroughly investigated. The 1000 Genomes Project represents one such endeavour to characterize the human genetic variation pattern at the MAF = 1% level as a foundation for association studies. In this report, we explore different strategies and study designs for the near future GWAS in the post-era, based on both low coverage pilot data and exon pilot data in 1000 Genomes Project.</p> <p>Results</p> <p>We investigated the linkage disequilibrium (LD) pattern among common and low frequency SNPs and its implication for association studies. We found that the LD between low frequency alleles and low frequency alleles, and low frequency alleles and common alleles are much weaker than the LD between common and common alleles. We examined various tagging designs with and without statistical imputation approaches and compare their power against de novo resequencing in mapping causal variants under various disease models. We used the low coverage pilot data which contain ~14 M SNPs as a hypothetical genotype-array platform (Pilot 14 M) to interrogate its impact on the selection of tag SNPs, mapping coverage and power of association tests. We found that even after imputation we still observed 45.4% of low frequency SNPs which were untaggable and only 67.7% of the low frequency variation was covered by the Pilot 14 M array.</p> <p>Conclusions</p> <p>This suggested GWAS based on SNP arrays would be ill-suited for association studies of low frequency variation.</p