Statistical Methods for Analyzing Large Scale Biological Data

Abstract

With the development of high-throughput biomedical technologies in recent years, the size of a typical biological dataset is increasing at a fast pace, especially in the genomics, proteomics and metabolomics literatures. Typically, these large datasets contain a huge amount of information on each subject, where the number of subjects can range from small to often extremely large. The challenges of analyzing these large datasets are twofold, namely the problem of high-dimensionality, and the heavy computational burden associated with analyzing them. The goal of this dissertation is to develop statistical and computational methods to address some of these challenges in order to provide researchers with analytical tools that are scalable to handle these large datasets, as well as able to solve the issues arising from high-dimensionality. In Chapter II, we study the asymptotic behaviors of principal component analysis (PCA) in high-dimensional data under the generalized spiked population model. We propose a series of methods for the consistent estimation of the population eigenvalues, angles between the sample and population eigenvectors, correlation coefficients between the sample and population principal component (PC) scores, and the shrinkage-bias adjustment for the predicted PC scores. In Chapter III, we investigate the over-fitting problem of partial least squares (PLS) regression with high-dimensional predictors, which can result in the predicted and observed outcomes being almost identical, even when the outcome is independent of the predictor. We further discuss a shrinkage-bias problem similar to the shrinkage-bias in high-dimensional PCA, and propose a two-stage PLS (TPLS) method that can address both of these problems. In Chapter IV, we focus on the large-scale genome-wide or phenome-wide association studies (GWASs or PheWASs) of the electronic health records (EHR) or biobank-based binary phenotypes. Due to the severe case-control imbalance in most of the EHR or biobank-based binary phenotypes, the existing methods cannot provide a scalable and accurate way to analyze them. We develop a computationally efficient single-variant test, that is ~100 times faster than the state of the art Firth's test, and can provide well-calibrated p values even for phenotypes with extremely unbalanced case-control ratios. Further, our test can adjust for non-genetic covariates, and can retain similar power as the Firth's test. In Chapter V, we show that due to the severe case-control imbalance in most of the biobank-based binary phenotypes, applying the traditional Z-score-based method to meta-analyze the association results across multiple biobank-based association studies, can result in conservative or anti-conservative p values. We propose two alternative meta-analysis methods that can provide well-calibrated meta-analysis p values, even when the individual studies are extremely unbalanced in their case-control ratios. Our first method involves sharing an approximation of the distribution of the score test statistic from each study using cubic Hermite splines, and the second method involves sharing the overall genotype counts from each study. In summary, the purpose of this dissertation is to develop statistical and computational methods that can efficiently utilize the ever-growing nature of modern biological datasets, and facilitate researchers by addressing some of the problems associated with the high-dimensionality of the datasets, as well as by reducing the heavy computational burden of analyzing these large datasets.