Investigation of Smooth and Non-smooth Penalties for Regularized Model Selection in Regression.

In this thesis, new approaches for using regularized regression in model selection are proposed, and we characterize the circumstances in which regularized regression improves our ability to discriminate models. First, we propose a variable selection method for regression models with interactions, using L1 regularization to automatically enforces heredity constraints. Theoretical study shows that asymptotically the proposed method performs as well as when the true model is known in advance under some regularity conditions. Numerical results show that the method performs favorably in terms of prediction and variable selection compared to some other recently developed methods. Second, regularized regression methods including ridge regression, the Lasso and the elastic net are investigated in terms of their abilities to rank the predictors in a regression model based on the sizes of their effects. Intuitively, regularization should be most useful when strong collinearity is present, however, we find that not all models with collinearity benefit from regularization. We were able to characterize situations in which regularization is either helpful, harmful, or neutral for ranking performance, and defined a sense in which regularization improves performance more often than not. By analytical and numerical studies, we show that L2-regularization outperforms L1-regularization for ranking performance, especially when the effects are weak, partly because when univariate analysis is optimal, ridge regression can better approximate univariate analysis than the Lasso. Our results also imply that the best regression estimator for variable ranking and for prediction may differ. This work may have implications for genetic mapping and other analyses involving regression methods with weak effects and collinear regressors.Ph.D.StatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64649/1/nami_1.pd

Least angle and ℓ1\ell_1 penalized regression: A review

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO ($\ell_1$-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research.Comment: Published in at http://dx.doi.org/10.1214/08-SS035 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org

17β-Estradiol supplementation changes gut microbiota diversity in intact and colorectal cancer-induced ICR male mice

The composition of the gut microbiota is influenced by sex hormones and colorectal cancer (CRC). Previously, we reported that 17 beta -estradiol (E2) inhibits azoxymethane/dextran sulfate sodium (AOM/DSS)-induced tumorigenesis in male mice. Here, we investigated whether the composition of the gut microbiota is different between male and female, and is regulated by estrogen as a secondary outcome of previous studies. We established four groups of mice based on the sex and estrogen status [ovariectomized (OVX) female and E2-treated male]. Additionally, three groups of males were established by treating them with AOM/DSS, and E2, after subjecting them to AOM/DSS treatment. The mice were sacrificed at 21 weeks old. The composition of the gut microbiota was analyzed using 16S rRNA metagenomics sequencing. We observed a significant increase in the microbial diversity (Chao1 index) in females, males supplemented with E2, and males treated with AOM/DSS/E2 compared with normal males. In normal physiological condition, sex difference and E2 treatment did not affect the ratio of Firmicutes/Bacteroidetes (F/B). However, in AOM/DSS-treated male mice, E2 supplementation showed significantly lower level of the F/B ratio. The ratio of commensal bacteria to opportunistic pathogens was higher in females and E2-treated males compared to normal males and females subjected to OVX. Unexpectedly, this ratio was higher in the AOM/DSS group than that determined in other males and the AOM/DSS/E2 group. Our findings suggest that estrogen alters the gut microbiota in ICR (CrljOri:CD1) mice, particularly AOM/DSS-treated males, by decreasing the F/B ratio and changing Shannon and Simpson index by supply of estrogen. This highlights another possibility that estrogen could cause changes in the gut microbiota, thereby reducing the risk of developing CRC.

Identification of correlated genetic variants jointly associated with rheumatoid arthritis using ridge regression

Abstract Using the North American Rheumatoid Arthritis Consortium genome-wide association dataset, we applied ridged, multiple least-squares regression to identify genetic variants with apparent unique contributions to variation of anti-cyclic citrullinated peptide (anti-CCP), a newly identified clinical risk factor for development of rheumatoid arthritis. Within a 2.7-Mbp region on chromosome 6 around the well studied HLA-DRB1 locus, ridge regression identified a single-nucleotide polymorphism that was associated with anti-CCP variation when including the additive effects of other single-nucleotide polymorphisms in a multivariable analysis, but that showed only a weak direct association with anti-CCP. This suggests that multivariable methods can be used to identify potentially relevant genetic variants in regions of interest that would be difficult to detect based on direct associations.http://deepblue.lib.umich.edu/bitstream/2027.42/117369/1/12919_2009_Article_2814.pd

17β-Estradiol strongly inhibits azoxymethane/dextran sulfate sodium-induced colorectal cancer development in Nrf2 knockout male mice

© 2020 The Author(s)Nuclear factor erythroid 2-related factor 2 (Nrf2) has dual effects on inflammation and cancer progression depending on the microenvironment. Estrogens have a protective effect on colorectal cancer (CRC) development. The aim of this study was to investigate CRC development in Nrf2 knockout (KO) mice. Azoxymethane (AOM) and dextran sulfate sodium (DSS)-treated wild-type (WT) and Nrf2 KO male mice were sacrificed at weeks 2 and 16 after AOM injection with/without 17β-estradiol (E2) treatment during week 1. Disease activity index and colon tissue damage at week 2 showed strong attenuation following E2 administration in WT mice but to a lesser extent in Nrf2 KO male mice. At week 16, E2 significantly diminished AOM/DSS-induced adenoma/cancer incidence at distal colon in the Nrf2 KO group, but not in the WT. Furthermore, mRNA or protein levels of NF-κB-related mediators (i.e., iNOS, TNF-α, and IL-1β) and Nrf2-related antioxidants (i.e., NQO1 and HO-1) were significantly lower in the Nrf2 KO group regardless of E2 treatment compared to the WT. The expression of estrogen receptor beta (ERβ) was higher in the Nrf2 KO group than in the WT. In conclusion, estrogen further inhibits CRC by upregulating ERβ-related alternate pathways in the absence of Nrf2.

Dependent Lung Opacity at Thin-Section CT: Evaluation by Spirometrically-Gated CT of the Influence of Lung Volume

ObjectiveTo evaluate the influence of lung volume on dependent lung opacity seen at thin-section CT.Materials and methodsIn thirteen healthy volunteers, thin-section CT scans were performed at three levels (upper, mid, and lower portion of the lung) and at different lung volumes (10, 30, 50, and 100% vital capacity), using spirometric gated CT. Using a three-point scale, two radiologists determined whether dependent opacity was present, and estimated its degree. Regional lung attenuation at a level 2 cm above the diaphragm was determined using semiautomatic segmentation, and the diameter of a branch of the right lower posterior basal segmental artery was measured at each different vital capacity.ResultsAt all three anatomic levels, dependent opacity occurred significantly more often at lower vital capacities (10, 30%) than at 100% vital capacity (p = 0.001). Visually estimated dependent opacity was significantly related to regional lung attenuation (p < 0.0001), which in dependent areas progressively increased as vital capacity decreased (p < 0.0001). The presence of dependent opacity and regional lung attenuation of a dependent area correlated significantly with increased diameter of a segmental arterial branch (r = 0.493 and p = 0.0002; r = 0.486 and p = 0.0003, respectively).ConclusionVisual estimation and CT measurements of dependent opacity obtained by semiautomatic segmentation are significantly influenced by lung volume and are related to vascular diameter