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1.  A regularized Hotelling’s T2 test for pathway analysis in proteomic studies 
Recent proteomic studies have identified proteins related to specific phenotypes. In addition to marginal association analysis for individual proteins, analyzing pathways (functionally related sets of proteins) may yield additional valuable insights. Identifying pathways that differ between phenotypes can be conceptualized as a multivariate hypothesis testing problem: whether the mean vector μ of a p-dimensional random vector X is μ0. Proteins within the same biological pathway may correlate with one another in a complicated way, and type I error rates can be inflated if such correlations are incorrectly assumed to be absent. The inflation tends to be more pronounced when the sample size is very small or there is a large amount of missingness in the data, as is frequently the case in proteomic discovery studies. To tackle these challenges, we propose a regularized Hotelling’s T2 (RHT) statistic together with a non-parametric testing procedure, which effectively controls the type I error rate and maintains good power in the presence of complex correlation structures and missing data patterns. We investigate asymptotic properties of the RHT statistic under pertinent assumptions and compare the test performance with four existing methods through simulation examples. We apply the RHT test to a hormone therapy proteomics data set, and identify several interesting biological pathways for which blood serum concentrations changed following hormone therapy initiation.
doi:10.1198/jasa.2011.ap10599
PMCID: PMC3755504  PMID: 23997374
proteomics; pathway analysis; regularization; Hotelling’s T2
2.  Partial Correlation Estimation by Joint Sparse Regression Models 
In this paper, we propose a computationally efficient approach —space(Sparse PArtial Correlation Estimation)— for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer data set and identify a set of hub genes which may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.
doi:10.1198/jasa.2009.0126
PMCID: PMC2770199  PMID: 19881892
concentration network; high-dimension-low-sample-size; lasso; shooting; genetic regulatory network

Results 1-2 (2)