Noah Simon

A Sparse-Group Lasso

For high-dimensional supervised learning problems, often using problem-specific assumptions can lead to greater accuracy. For problems with grouped covariates, which are believed to have sparse effects both on a group and within group level, we introduce a regularized model for linear regression with ℓ1 and ℓ2 penalties. We discuss the sparsity and other regularization properties of the optimal fit for this model, and show that it has the desired effect of group-wise and within group sparsity. We propose an algorithm to fit the model via accelerated generalized gradient descent, and extend this model and algorithm to convex loss functions. We also demonstrate the efficacy of our model and the efficiency of our algorithm on simulated data. This article has online supplementary material.

Systems analysis of sex differences reveals an immunosuppressive role for testosterone in the response to influenza vaccination

Significance There are marked differences between the sexes in their immune response to infections and vaccination, with females often having significantly higher responses. However, the mechanisms underlying these differences are largely not understood. Using a systems immunology approach, we have identified a cluster of genes involved in lipid metabolism and likely modulated by testosterone that correlates with the higher antibody-neutralizing response to influenza vaccination observed in females. Moreover, males with the highest testosterone levels and expression of related gene signatures exhibited the lowest antibody responses to influenza vaccination. This study generates a number of hypotheses on the sex differences observed in the human immune system and their relationship to mechanisms involved in the antibody response to vaccination. Females have generally more robust immune responses than males for reasons that are not well-understood. Here we used a systems analysis to investigate these differences by analyzing the neutralizing antibody response to a trivalent inactivated seasonal influenza vaccine (TIV) and a large number of immune system components, including serum cytokines and chemokines, blood cell subset frequencies, genome-wide gene expression, and cellular responses to diverse in vitro stimuli, in 53 females and 34 males of different ages. We found elevated antibody responses to TIV and expression of inflammatory cytokines in the serum of females compared with males regardless of age. This inflammatory profile correlated with the levels of phosphorylated STAT3 proteins in monocytes but not with the serological response to the vaccine. In contrast, using a machine learning approach, we identified a cluster of genes involved in lipid biosynthesis and previously shown to be up-regulated by testosterone that correlated with poor virus-neutralizing activity in men. Moreover, men with elevated serum testosterone levels and associated gene signatures exhibited the lowest antibody responses to TIV. These results demonstrate a strong association between androgens and genes involved in lipid metabolism, suggesting that these could be important drivers of the differences in immune responses between males and females.

New Insights and Faster Computations for the Graphical Lasso

We consider the graphical lasso formulation for estimating a Gaussian graphical model in the high-dimensional setting. This approach entails estimating the inverse covariance matrix under a multivariate normal model by maximizing the ℓ1-penalized log-likelihood. We present a very simple necessary and sufficient condition that can be used to identify the connected components in the graphical lasso solution. The condition can be employed to determine whether the estimated inverse covariance matrix will be block diagonal, and if so, then to identify the blocks. This in turn can lead to drastic speed improvements, since one can simply apply a standard graphical lasso algorithm to each block separately. Moreover, the necessary and sufficient condition provides insight into the graphical lasso solution: the set of connected nodes at any given tuning parameter value is a superset of the set of connected nodes at any larger tuning parameter value. This article has supplementary material online.

Adaptive enrichment designs for clinical trials

Modern medicine has graduated from broad spectrum treatments to targeted therapeutics. New drugs recognize the recently discovered heterogeneity of many diseases previously considered to be fairly homogeneous. These treatments attack specific genetic pathways which are only dysregulated in some smaller subset of patients with the disease. Often this subset is only rudimentarily understood until well into large-scale clinical trials. As such, standard practice has been to enroll a broad range of patients and run post hoc subset analysis to determine those who may particularly benefit. This unnecessarily exposes many patients to hazardous side effects, and may vastly decrease the efficiency of the trial (especially if only a small subset of patients benefit). In this manuscript, we propose a class of adaptive enrichment designs that allow the eligibility criteria of a trial to be adaptively updated during the trial, restricting entry to patients likely to benefit from the new treatment. We show that our designs both preserve the type 1 error, and in a variety of cases provide a substantial increase in power.

Quantitative SD-OCT Imaging Biomarkers as Indicators of Age-Related Macular Degeneration Progression

PURPOSE We developed a statistical model based on quantitative characteristics of drusen to estimate the likelihood of conversion from early and intermediate age-related macular degeneration (AMD) to its advanced exudative form (AMD progression) in the short term (less than 5 years), a crucial task to enable early intervention and improve outcomes. METHODS Image features of drusen quantifying their number, morphology, and reflectivity properties, as well as the longitudinal evolution in these characteristics, were automatically extracted from 2146 spectral-domain optical coherence tomography (SD-OCT) scans of 330 AMD eyes in 244 patients collected over a period of 5 years, with 36 eyes showing progression during clinical follow-up. We developed and evaluated a statistical model to predict the likelihood of progression at predetermined times using clinical and image features as predictors. RESULTS Area, volume, height, and reflectivity of drusen were informative features distinguishing between progressing and nonprogressing cases. Discerning progression at follow-up (mean, 6.16 months) resulted in a mean area under the receiver operating characteristic curve (AUC) of 0.74 (95% confidence interval [CI], 0.58, 0.85). The maximum predictive performance was observed at 11 months after a patients first early AMD diagnosis, with mean AUC 0.92 (95% CI, 0.83, 0.98). Those eyes predicted to progress showed a much higher progression rate than those predicted not to progress at any given time from the initial visit. CONCLUSIONS Our results demonstrate the potential ability of our model to identify those AMD patients at risk of progressing to exudative AMD from an early or intermediate stage.

Transcriptome Sequencing of a Large Human Family Identifies the Impact of Rare Noncoding Variants

Recent and rapid human population growth has led to an excess of rare genetic variants that are expected to contribute to an individual’s genetic burden of disease risk. To date, much of the focus has been on rare protein-coding variants, for which potential impact can be estimated from the genetic code, but determining the impact of rare noncoding variants has been more challenging. To improve our understanding of such variants, we combined high-quality genome sequencing and RNA sequencing data from a 17-individual, three-generation family to contrast expression quantitative trait loci (eQTLs) and splicing quantitative trait loci (sQTLs) within this family to eQTLs and sQTLs within a population sample. Using this design, we found that eQTLs and sQTLs with large effects in the family were enriched with rare regulatory and splicing variants (minor allele frequency < 0.01). They were also more likely to influence essential genes and genes involved in complex disease. In addition, we tested the capacity of diverse noncoding annotation to predict the impact of rare noncoding variants. We found that distance to the transcription start site, evolutionary constraint, and epigenetic annotation were considerably more informative for predicting the impact of rare variants than for predicting the impact of common variants. These results highlight that rare noncoding variants are important contributors to individual gene-expression profiles and further demonstrate a significant capability for genomic annotation to predict the impact of rare noncoding variants.

Fused Lasso Additive Model

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two datasets. Supplemental materials are available online, and the R package flam is available on CRAN.

Quotient Sets and Diophantine Equations

Abstract Quotient sets 핌/핌 = {u/u′ : u, u′ ∊ 핌} have been considered several times before in the Monthly. We consider more general quotient sets 핌/핍 and we apply our results to certain simultaneous Diophantine equations with side constraints.

Exploring medical diagnostic performance using interactive, multi-parameter sourced receiver operating characteristic scatter plots

Determining diagnostic criteria for specific disorders is often a tedious task that involves determining optimal diagnostic thresholds for symptoms and biomarkers using receiver-operating characteristic (ROC) statistics. To help this endeavor, we developed softROC, a user-friendly graphic-based tool that lets users visually explore possible ROC tradeoffs. The software requires MATLAB installation and an Excel file containing threshold symptoms/biological measures, with corresponding gold standard diagnoses for a set of patients. The software scans the input file for diagnostic and symptom/biomarkers columns, and populates the graphical-user-interface (GUI). Users select symptoms/biomarkers of interest using Boolean algebra as potential inputs to create diagnostic criteria outputs. The software evaluates subtests across the user-established range of cut-points and compares them to a gold standard in order to generate ROC and quality ROC scatter plots. These plots can be examined interactively to find optimal cut-points of interest for a given application (e.g. sensitivity versus specificity needs). Split-set validation can also be used to set up criteria and validate these in independent samples. Bootstrapping is used to produce confidence intervals. Additional statistics and measures are provided, such as the area under the ROC curve (AUC). As a testing set, softROC is used to investigate nocturnal polysomnogram measures as diagnostic features for narcolepsy. All measures can be outputted to a text file for offline analysis. The softROC toolbox, with clinical training data and tutorial instruction manual, is provided as supplementary material and can be obtained online at http://www.stanford.edu/~hyatt4/software/softroc or from the open source repository at http://www.github.com/informaton/softroc.

Convex hierarchical testing of interactions

We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that considers an interaction only when one or more of its constituent features has a nonzero main effect. The test is based on a convex optimization framework that seamlessly considers main effects and interactions together. We show—both in simulation and on a genomic dataset from the SAPPHIRe study—a potential gain in power and interpretability over a standard (non-hierarchical) interaction test.