Advances in molecular “omics” technologies have motivated new methodologies for the integration of multiple sources of high‐content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different cohorts on a single platform). This is limiting for data that take the form of bidimensionally linked matrices (eg, multiple cohorts measured on multiple platforms), which are increasingly common in large‐scale biomedical studies. In this paper, we propose bidimensional integrative factorization (BIDIFAC) for integrative dimension reduction and signal approximation of bidimensionally linked data matrices. Our method factorizes data into (a) globally shared, (b) row‐shared, (c) column‐shared, and (d) single‐matrix structural components, facilitating the investigation of shared and unique patterns of variability. For estimation, we use a penalized objective function that extends the nuclear norm penalization for a single matrix. As an alternative to the complicated rank selection problem, we use results from the random matrix theory to choose tuning parameters. We apply our method to integrate two genomics platforms (messenger RNA and microRNA expression) across two sample cohorts (tumor samples and normal tissue samples) using the breast cancer data from the Cancer Genome Atlas. We provide R code for fitting BIDIFAC, imputing missing values, and generating simulated data.
In genome-wide association studies (GWAS), it has been increasingly recognized that, as a complementary approach to standard single SNP analyses, it may be beneficial to analyze a group of functionally related SNPs together. Among the existent population-based SNP-set association tests, two adaptive tests, the aSPU test and the aSPUpath test, offer a powerful and general approach at the gene- and pathway-levels by data-adaptively combining the results across multiple SNPs (and genes) such that high statistical power can be maintained across a wide range of scenarios. We extend the aSPU and the aSPUpath test to familial data under the framework of the generalized linear mixed models (GLMMs), which can take account of both subject relatedness and possible population structure. As in population-based GWAS, the proposed aSPU and aSPUpath tests require only fitting a single and common GLMM (under the null hypothesis) for all the SNPs, thus are computationally efficient and feasible for large GWAS data. We illustrate our approaches in identifying genes and pathways associated with alcohol dependence in the Minnesota Twin Family Study. The aSPU test detected a gene associated with the trait, in contrast to none by the standard single SNP analysis. Our aSPU test also controlled Type I errors satisfactorily in a small simulation study. We provide R code to conduct the aSPU and aSPUpath tests for familial and other correlated data.
DNA methylation plays an important role in normal human development and disease. In epigenome-wide association studies (EWAS), a univariate test for association between a phenotype and each cytosine-phosphate-guanine (CpG) site has been widely used. Given the number of CpG sites tested in EWAS, a stringent significance cutoff is required to adjust for multiple testing; in addition, multiple nearby CpG sites may be associated with the phenotype, which is ignored by a univariate test. These two factors may contribute to the power loss of a univariate test. As an alternative, we propose applying an adaptive gene-based test that is powerful in genome-wide association studies (GWAS), called aSPUw, to EWAS for simultaneous testing on multiple CpG sites within or near a gene. We show its application to the GAW20 methylation data set.
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