Motivated by research problems arising in the analysis of gut microbiome and metagenomic data, we consider variable selection and estimation in high-dimensional regression with compositional covariates. We propose an ℓ₁ regularization method for the linear log-contrast model that respects the unique features of compositional data. We formulate the proposed procedure as a constrained convex optimization problem and introduce a coordinate descent method of multipliers for efficient computation. In the high-dimensional setting where the dimensionality grows at most exponentially with the sample size, model selection consistency and $$\ell _{\infty }$$ bounds for the resulting estimator are established under conditions that are mild and interpretable for compositional data. The numerical performance of our method is evaluated via simulation studies and its usefulness is illustrated by an application to a microbiome study relating human body mass index to gut microbiome composition.

To investigate cigarette smoking in cutaneous lupus erythematosus (CLE). Prospective longitudinal cohort study. Urban cutaneous autoimmune disease clinic. A total of 218 individuals with CLE or systemic lupus erythematosus and lupus nonspecific skin disease seen between January 5, 2007, and July 30, 2010. Cutaneous Lupus Erythematosus Disease Area and Severity Index (CLASI) scores to assess disease severity and response to treatment and Skindex 29+3 scores to assess patient quality of life. Current smokers with lupus erythematosus had higher median CLASI scores (9.5) than did never (7.0) and past (6.0) smokers with CLE (P = .02). Current smokers had higher median scores on all the Skindex 29+3 subsets. Current smokers taking hydroxychloroquine sulfate had higher quinacrine hydrochloride use than did nonsmokers (P = .04). Two to 7 months after enrollment, current smokers (median CLASI change, -3) treated with only antimalarial agents improved more than never (1) and past (0) smokers (P = .02). Eight months or more after enrollment, current smokers (CLASI change, 3.5) treated with antimalarial drugs plus at least 1 additional immunomodulator improved less than never (-1.5) and past (0) smokers (P = .04). Current smokers with lupus erythematosus had worse disease, had worse quality of life, and were more often treated with a combination of hydroxychloroquine and quinacrine than were nonsmokers. Never and past smokers showed greater improvement when treated with antimalarial agents plus at least 1 additional immunomodulator. Current smokers had greater improvement when treated with antimalarial drugs only.

Introduction: Aromatase inhibitor-associated arthralgia (AIAA) is a common and often debilitating symptom in breast cancer survivors. Since joint symptoms have been related to estrogen deprivation through the menopausal transition, we hypothesized that genetic polymorphisms in CYP19A1, the final enzyme in estrogen synthesis, may be associated with the occurrence of AIAA. Methods: We performed a cross-sectional study of postmenopausal women with stage 0 to III breast cancer receiving adjuvant aromatase inhibitor (AI) therapy. Patient-reported AIAA was the primary outcome. DNA was genotyped for candidate CYP19A1 polymorphisms. Serum estrogen levels were evaluated by radioimmunoassay. Multivariate analyses were performed to examine associations between AIAA and genetic variants controlling for possible confounders. Results: Among 390 Caucasian participants, 50.8% reported AIAA. Women carrying at least one 8-repeat allele had lower odds of AIAA (adjusted odds ratio (AOR) 0.41, 95% confidence interval (CI) 0.21 to 0.79, P = 0.008) after adjusting for demographic and clinical covariates. Estradiol and estrone were detectable in 47% and 86% of subjects on AIs, respectively. Although these post-AI levels were associated with multiple genotypes, they were not associated with AIAA. In multivariate analyses, women with more recent transition into menopause (less than five years) were significantly more likely to report AIAA than those greater than ten years post-menopause (AOR 3.31, 95% CI 1.72 to 6.39, P < 0.001). Conclusions: Functional polymorphism in CYP19A1 and time since menopause are associated with patient-reported AIAA, supporting the hypothesis that the host hormonal environment contributes to the pathophysiology of AAIA. Prospective investigation is needed to further delineate relationships between host genetics, changing estrogen levels and AIAA.

In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be much larger than the sample size. Motivated by such modern applications, we consider the problem of variable selection and estimation in high-dimensional sparse instrumental variables models. To overcome the difficulty of high dimensionality and unknown optimal instruments, we propose a two-stage regularization framework for identifying and estimating important covariate effects while selecting and estimating optimal instruments. The methodology extends the classical two-stage least squares estimator to high dimensions by exploiting sparsity using sparsity-inducing penalty functions in both stages. The resulting procedure is efficiently implemented by coordinate descent optimization. For the representative L₁ regularization and a class of concave regularization methods, we establish estimation, prediction, and model selection properties of the two-stage regularized estimators in the high-dimensional setting where the dimensionality of covariates and instruments are both allowed to grow exponentially with the sample size. The practical performance of the proposed method is evaluated by simulation studies and its usefulness is illustrated by an analysis of mouse obesity data. Supplementary materials for this article are available online.

We consider estimation and variable selection in high-dimensional Cox regression when a prior knowledge of the relationships among the covariates, described by a network or graph, is available. A limitation of the existing methodology for survival analysis with high-dimensional genomic data is that a wealth of structural information about many biological processes, such as regulatory networks and pathways, has often been ignored. In order to incorporate such prior network information into the analysis of genomic data, we propose a network-based regularization method for high-dimensional Cox regression; it uses an ℓ1-penalty to induce sparsity of the regression coefficients and a quadratic Laplacian penalty to encourage smoothness between the coefficients of neighboring variables on a given network. The proposed method is implemented by an efficient coordinate descent algorithm. In the setting where the dimensionality p can grow exponentially fast with the sample size n, we establish model selection consistency and estimation bounds for the proposed estimators. The theoretical results provide insights into the gain from taking into account the network structural information. Extensive simulation studies indicate that our method outperforms Lasso and elastic net in terms of variable selection accuracy and stability. We apply our method to a breast cancer gene expression study and identify several biologically plausible subnetworks and pathways that are associated with breast cancer distant metastasis.