This proposal develops novel statistical methods to select a small group of molecules from high-throughput data such as microarray and proteomic data from cancer research. The challenge of the study is the ultrahigh dimensionality inherited in these studies, particular when gene-gene interactions are introduced. The ultrahigh dimensionality has large impact on statistical computation, methodological developments, and theoretical studies. The challenge will be dealt by using the proposed novel independence screening methods, which also addresses the computational demand and stability, and the issues of stochastic error accumulation in ultra-high dimensional statistical inferences. An iterative independence screening method is introduced to find hidden signature genes that are marginally unimportant but jointly extremely important to the clinical outcomes. It also enables us to eliminate redundant molecules that are marginally highly but jointly weakly associated with clinical outcomes. With number of features surely reduced to a manageable level, penalized pseudo-likelihood methods will be introduced to further select relevant genes. In addition, methods for finding synergetic groups of molecules are introduced. The idea of independence screening and its iterated version will be applied to various statistical problems from the analysis of high throughput data, ranging from ultrahigh dimensional regression and classification to the analysis of survival time, estimation of genewide variance, and normalization of microarrays. The efficacy of the proposed methods will be evaluated via asymptotic theory and simulation studies. Data sets from on-going biomedical studies on cancer such as breast cancer, multiple myeloma, neuroblastoma, lung tumor, and liver carcigogen will be critically analyzed using the newly developed statistical and bioinformatic tools.
Statistical Methods for Ultrahigh-dimensional Biomedical Data PI: Jianqing Fan This proposal develops novel statistical and bioinformatic tools for finding genes and proteins that are associated with clinical outcomes. Data sets from on-going biomedical studies on cancer such as breast cancer, multiple myeloma, neuroblastoma, lung tumor, and liver carcinogen will be critically analyzed using the newly developed statistical and bioinformatic tools. The research findings will have strong impact on understanding molecular mechanisms of cancer and developing therapeutic targets.
|Fan, Jianqing; Liu, Han; Wang, Weichen (2018) LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS. Ann Stat 46:1383-1414|
|Chen, Zhao; Fan, Jianqing; Li, Runze (2018) Error Variance Estimation in Ultrahigh-Dimensional Additive Models. J Am Stat Assoc 113:315-327|
|Li, Quefeng; Cheng, Guang; Fan, Jianqing et al. (2018) Embracing the Blessing of Dimensionality in Factor Models. J Am Stat Assoc 113:380-389|
|Fan, Jianqing; Shao, Qi-Man; Zhou, Wen-Xin (2018) ARE DISCOVERIES SPURIOUS? DISTRIBUTIONS OF MAXIMUM SPURIOUS CORRELATIONS AND THEIR APPLICATIONS. Ann Stat 46:989-1017|
|Battey, Heather; Fan, Jianqing; Liu, Han et al. (2018) DISTRIBUTED TESTING AND ESTIMATION UNDER SPARSE HIGH DIMENSIONAL MODELS. Ann Stat 46:1352-1382|
|Zhou, Wen-Xin; Bose, Koushiki; Fan, Jianqing et al. (2018) A NEW PERSPECTIVE ON ROBUST M-ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING. Ann Stat 46:1904-1931|
|Fan, Jianqing; Liu, Han; Sun, Qiang et al. (2018) I-LAMM FOR SPARSE LEARNING: SIMULTANEOUS CONTROL OF ALGORITHMIC COMPLEXITY AND STATISTICAL ERROR. Ann Stat 46:814-841|
|Avella-Medina, Marco; Battey, Heather S; Fan, Jianqing et al. (2018) Robust estimation of high-dimensional covariance and precision matrices. Biometrika 105:271-284|
|Aït-Sahalia, Yacine; Fan, Jianqing; Laeven, Roger J A et al. (2017) Estimation of the Continuous and Discontinuous Leverage Effects. J Am Stat Assoc 112:1744-1758|
|Wang, Weichen; Fan, Jianqing (2017) Asymptotics of empirical eigenstructure for high dimensional spiked covariance. Ann Stat 45:1342-1374|
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