Despite the fact that imbalance between case and control groups is prevalent in genome-wide association studies (GWAS), it is often overlooked. This imbalance is getting more significant and urgent as the rapid growth of biobanks and electronic health records have enabled the collection of thousands of phenotypes from large cohorts, in particular for diseases with low prevalence. The unbalanced binary traits pose serious challenges to traditional statistical methods in terms of both genomic selection and disease prediction. For example, the well-established linear mixed models (LMM) yield inflated type I error rates in the presence of unbalanced case-control ratios. In this article, we review multiple statistical approaches that have been developed to overcome the inaccuracy caused by the unbalanced case-control ratio, with the advantages and limitations of each approach commented. In addition, we also explore the potential for applying several powerful and popular state-of-the-art machine-learning approaches, which have not been applied to the GWAS field yet. This review paves the way for better analysis and understanding of the unbalanced case-control disease data in GWAS.

The rapid advancement of functional data in various application fields has increased the demand for advanced statistical approaches that can incorporate complex structures and nonlinear associations. In this article, we propose a novel functional random forests (FunFor) approach to model the functional data response that is densely and regularly measured, as an extension of the landmark work of Breiman, who introduced traditional random forests for a univariate response. The FunFor approach is able to predict curve responses for new observations and selects important variables from a large set of scalar predictors. The FunFor approach inherits the efficiency of the traditional random forest approach in detecting complex relationships, including nonlinear and high-order interactions. Additionally, it is a non-parametric approach without the imposition of parametric and distributional assumptions. Eight simulation settings and one real-data analysis consistently demonstrate the excellent performance of the FunFor approach in various scenarios. In particular, FunFor successfully ranks the true predictors as the most important variables, while achieving the most robust variable sections and the smallest prediction errors when comparing it with three other relevant approaches. Although motivated by a biological leaf shape data analysis, the proposed FunFor approach has great potential to be widely applied in various fields due to its minimal requirement on tuning parameters and its distribution-free and model-free nature. An R package named ’FunFor’, implementing the FunFor approach, is available at GitHub.

Feature screening plays a critical role in handling ultrahigh dimensional data analyses when the number of features exponentially exceeds the number of observations. It is increasingly common in biomedical research to have case-control (binary) response and an extremely large-scale categorical features. However, the approach considering such data types is limited in extant literature. In this article, we propose a new feature screening approach based on the iterative trend correlation (ITC-SIS, for short) to detect important susceptibility loci that are associated with the polycystic ovary syndrome (PCOS) affection status by screening 731,442 SNP features that were collected from the genome-wide association studies. We prove that the trend correlation based screening approach satisfies the theoretical strong screening consistency property under a set of reasonable conditions, which provides an appealing theoretical support for its outperformance. We demonstrate that the finite sample performance of ITC-SIS is accurate and fast through various simulation designs. ITC-SIS serves as a good alternative method to detect disease susceptibility loci for clinic genomic data.

Detection of important genes affecting lung adenocarcinoma (LUAD) is critical to finding effective therapeutic targets for this highly lethal cancer. However, many existing approaches have focused on single outcomes or phenotypic associations, which may not be as thorough as investigating molecular transcript levels within cells. In this article, we apply a novel multivariate rank-distance correlation-based gene selection procedure (MrDcGene) to LUAD multi-omics data downloaded from The Cancer Genome Atlas (TCGA). MrDcGene provides additional opportunities for detecting novel susceptibility genes as it leverages information from multiple platforms, while efficiently handling challenges such as high dimensionality, low signal-to-noise ratio, unknown distributions, and non-linear structures, etc. Notably, the MrDcGene method is able to detect two different scenarios, i.e., strong association strength with a few gene expressions and weak association strength with several gene expressions. After thoroughly exploring the association between gene expression (GE) and multiple other platforms, including reverse phase protein array (RPPA), miRNA, copy number variation (CNV) and DNA methylation (ME), we detect several novel genes that may play an important role in LUAD (ZNF133, CCDC159, YWHAZ, HNRNPR. ITPR2, PTHLH, and WIPI2). In addition, we quantitatively validate several other susceptibility genes that were reported in the literature using different methods and studies. The accuracy of the MrDcGene approach is theoretically assured and empirically demonstrated by the simulation studies.

Feature screening approaches are effective in selecting active features from data with ultrahigh dimensionality and increasing complexity; however, the majority of existing feature screening approaches are either restricted to a univariate response or rely on some distribution or model assumptions. In this article, we propose a novel sure independence screening approach based on the multivariate rank distance correlation (MrDc-SIS). The MrDc-SIS achieves multiple desirable properties such as being distribution-free, completely nonparametric, scale-free, robust for outliers or heavy tails, and sensitive for hidden structures. Moreover, the MrDc-SIS can be used to screen either univariate or multivariate responses and either one dimensional or multi-dimensional predictors. We establish the asymptotic sure screening consistency property of the MrDc-SIS under a mild condition by lifting previous assumptions about the finite moments. Simulation studies demonstrate that MrDc-SIS outperforms three other closely relevant approaches under various settings. We also apply the MrDc-SIS approach to a multi-omics ovarian carcinoma data downloaded from The Cancer Genome Atlas (TCGA).