COBRAC: a fast implementation of convex biclustering with compression.

SUMMARY: Biclustering is a generalization of clustering used to identify simultaneous grouping patterns in observations (rows) and features (columns) of a data matrix. Recently, the biclustering task has been formulated as a convex optimization problem. While this convex recasting of the problem has attractive properties, existing algorithms do not scale well. To address this problem and make convex biclustering a practical tool for analyzing larger data, we propose an implementation of fast convex biclustering called COBRAC to reduce the computing time by iteratively compressing problem size along with the solution path. We apply COBRAC to several gene expression datasets to demonstrate its effectiveness and efficiency. Besides the standalone version for COBRAC, we also developed a related online web server for online calculation and visualization of the downloadable interactive results. AVAILABILITY AND IMPLEMENTATION: The source code and test data are available at https://github.com/haidyi/cvxbiclustr or https://zenodo.org/record/4620218. The web server is available at https://cvxbiclustr.ericchi.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Discovering Geometry in Data Arrays.

Modern technologies produce a deluge of complicated data. In neuroscience, for example, minimally invasive experimental methods can take recordings of large populations of neurons at high resolution under a multitude of conditions. Such data arrays possess non-trivial interdependencies along each of their axes. Insights into these data arrays may lay the foundations of advanced treatments for nervous system disorders. The potential impacts of such data, however, will not be fully realized unless the techniques for analyzing them keep pace. Specifically, there is an urgent, growing need for methods for estimating the low-dimensional structure and geometry in big and noisy data arrays. This article reviews a framework for identifying complicated underlying patterns in such data and also recounts the key role that the Department of Energy Computational Sciences Graduate Fellowship played in setting the stage for this work to be done by the author.

Assessor- and participant-blinded, randomized controlled trial of dense cranial electroacupuncture stimulation plus body acupuncture for neuropsychiatric sequelae of stroke.

AIM: Acupuncture has benefits in the rehabilitation of neuropsychiatric sequelae of stroke. This study was aimed to evaluate the effectiveness of dense cranial electroacupuncture stimulation plus body acupuncture (DCEAS+BA) in treating poststroke depression (PSD), functional disability, and cognitive deterioration. METHODS: In this assessor- and participant-blinded, randomized controlled trial, 91 stroke patients who initially had PSD were randomly assigned to either DCEAS+BA (n = 45) or minimum acupuncture stimulation as controls (n = 46) for three sessions per week over 8 consecutive weeks. The primary outcome was baseline-to-end-point change in score of the 17-item Hamilton Depression Rating Scale. Secondary outcomes included the Montgomery-Åsberg Depression Rating Scale for depressive symptoms, the Barthel Index for functional disability, and the Montreal Cognitive Assessment for cognitive function. RESULTS: DCEAS+BA-treated patients showed strikingly greater end-point reduction than MAS-treated patients in scores of the three symptom domains. The clinical response rate, defined as an at least 50% baseline-to-end-point reduction in 17-item Hamilton Depression Rating Scale score, was markedly higher in the DCEAS+BA-treated group than that of controls (40.0% vs 17.4%, P = 0.031). Incidence of adverse events was not different in the two groups. Subgroup analysis revealed that DCEAS+BA with electrical stimulation on forehead acupoints was more apparent in reducing Barthel-Index-measured disability than that without electrical stimulation. CONCLUSION: DCEAS+BA, particularly with electrical stimulation on forehead acupoints, reduces PSD, functional disability, and cognitive deterioration of stroke patients. It can serve as an effective rehabilitation therapy for neuropsychiatric sequelae of stroke.

Multiway Graph Signal Processing on Tensors: Integrative analysis of irregular geometries.

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.

Bayesian methods for analysis of biosimilar phase III trials.

A biologic is a product made from living organisms. A biosimilar is a new version of an already approved branded biologic. Regulatory guidelines recommend a totality-of-the-evidence approach with stepwise development for a new biosimilar. Initial steps for biosimilar development are (a) analytical comparisons to establish similarity in structure and function followed by (b) potential animal studies and a human pharmacokinetics/pharmacodynamics equivalence study. The last step is a phase III clinical trial to confirm similar efficacy, safety, and immunogenicity between the biosimilar and the biologic. A high degree of analytical and pharmacokinetics/pharmacodynamics similarity could provide justification for an eased statistical threshold in the phase III trial, which could then further facilitate an overall abbreviated approval process for biosimilars. Bayesian methods can help in the analysis of clinical trials, by adding proper prior information into the analysis, thereby potentially decreasing required sample size. We develop proper prior information for the analysis of a phase III trial for showing that a proposed biosimilar is similar to a reference biologic. For the reference product, we use a meta-analysis of published results to set a prior for the probability of efficacy, and we propose priors for the proposed biosimilar informed by the strength of the evidence generated in the earlier steps of the approval process. A simulation study shows that with few exceptions, the Bayesian relative risk analysis provides greater power, shorter 90% credible intervals with more than 90% frequentist coverage, and better root mean squared error.

Improving the power to establish clinical similarity in a Phase 3 efficacy trial by incorporating prior evidence of analytical and pharmacokinetic similarity.

To improve patients' access to safe and effective biological medicines, abbreviated licensure pathways for biosimilar and interchangeable biological products have been established in the US, Europe, and other countries around the world. The US Food and Drug Administration and European Medicines Agency have published various guidance documents on the development and approval of biosimilars, which recommend a "totality-of-the-evidence" approach with a stepwise process to demonstrate biosimilarity. The approach relies on comprehensive comparability studies ranging from analytical and nonclinical studies to clinical pharmacokinetic/pharmacodynamic (PK/PD) and efficacy studies. A clinical efficacy study may be necessary to address residual uncertainty about the biosimilarity of the proposed product to the reference product and support a demonstration that there are no clinically meaningful differences. In this article, we propose a statistical strategy that takes into account the similarity evidence from analytical assessments and PK studies in the design and analysis of the clinical efficacy study in order to address residual uncertainty and enhance statistical power and precision. We assume that if the proposed biosimilar product and the reference product are shown to be highly similar with respect to the analytical and PK parameters, then they should also be similar with respect to the efficacy parameters. We show that the proposed methods provide correct control of the type I error and improve the power and precision of the efficacy study upon the standard analysis that disregards the prior evidence. We confirm and illustrate the theoretical results through simulation studies based on the biosimilars development experience of many different products.

δ- and γ-tocopherols inhibit phIP/DSS-induced colon carcinogenesis by protection against early cellular and DNA damages.

Tocopherols, the major forms of vitamin E, are a family of fat-soluble compounds that exist in alpha (α-T), beta (ß-T), gamma (γ-T), and delta (δ-T) variants. A cancer preventive effect of vitamin E is suggested by epidemiological studies. However, past animal studies and human intervention trials with α-T, the most active vitamin E form, have yielded disappointing results. A possible explanation is that the cancer preventive activity of α-T is weak compared to other tocopherol forms. In the present study, we investigated the effects of δ-T, γ-T, and α-T (0.2% in diet) in a novel colon cancer model induced by the meat-derived dietary carcinogen, 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) and promoted by dextran sodium sulfate (DSS)-induced colitis in CYP1A-humanized (hCYP1A) mice. PhIP/DSS treatments induced multiple polypoid tumors, mainly tubular adenocarcinomas, in the middle to distal colon of the hCYP1A mice after 10 wk. Dietary supplementation with δ-T and γ-T significantly reduced colon tumor formation and suppressed markers of oxidative and nitrosative stress (i.e., 8-oxo-dG and nitrotyrosine) as well as pro-inflammatory mediators (i.e., NF-κB p65 and p-STAT3) in tumors and adjacent tissues. By administering δ-T at different time periods, we obtained results suggesting that the inhibitory effect of δ-T against colon carcinogenesis is mainly due to protection against early cellular and DNA damages caused by PhIP. α-T was found to be ineffective in inhibiting colon tumors and less effective in attenuating the molecular changes. Altogether, we demonstrated strong cancer preventive effects of δ-T and γ-T in a physiologically relevant model of human colon cancer. © 2016 Wiley Periodicals, Inc.

Convex biclustering.

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying structure in high-dimensional genomic data motivates this work. In this context, biclustering enables us to identify subsets of genes that are co-expressed only within a subset of experimental conditions. We present a convex formulation of the biclustering problem that possesses a unique global minimizer and an iterative algorithm, COBRA, that is guaranteed to identify it. Our approach generates an entire solution path of possible biclusters as a single tuning parameter is varied. We also show how to reduce the problem of selecting this tuning parameter to solving a trivial modification of the convex biclustering problem. The key contributions of our work are its simplicity, interpretability, and algorithmic guarantees-features that arguably are lacking in the current alternative algorithms. We demonstrate the advantages of our approach, which includes stably and reproducibly identifying biclusterings, on simulated and real microarray data.

Obesity promotes PhIP-induced small intestinal carcinogenesis in hCYP1A-db/db mice: involvement of mutations and DNA hypermethylation of Apc.

Obesity is associated with an increased risk of cancer. To study the promotion of dietary carcinogen-induced gastrointestinal cancer by obesity, we employed 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) to induce intestinal tumorigenesis in CYP1A-humanized (hCYP1A) mice, in which mouse Cyp1a1/1a2 was replaced with human CYP1A1/1A2 Obesity was introduced in hCYP1A mice by breeding with Lepr(db/+) mice to establish the genetically induced obese hCYP1A-Lepr(db/db) mice or by feeding hCYP1A mice a high-fat diet. PhIP induced the formation of small intestinal tumors at the ages of weeks 28-40 in obese hCYP1A mice, but not in lean hCYP1A mice. No tumors were found in colon and other gastrointestinal organs in the lean or obese mice. Using immunohistochemistry (IHC), we found strong positive staining of NF-κB p65, pSTAT3 and COX2 as well as elevated levels of nuclear ß-catenin (Ctnnb1) in small intestinal tumors, but not in normal tissues. By sequencing Apc and Ctnnb1 genes, we found that most PhIP-induced small intestinal tumors in obese mice carried only a single heterozygous mutation in Apc By bisulfite-sequencing of CpG islands of Apc, we found DNA hypermethylation in a CpG cluster located in its transcription initiation site, which most likely caused the inactivation of the wild-type Apc allele. Our findings demonstrate that PhIP-induced small intestinal carcinogenesis in hCYP1A-db/db mice is promoted by obesity and involves Apc mutation and inactivation by DNA hypermethylation. This experimental result is consistent with the association of obesity and the increased incidence of small intestinal cancer in humans in recent decades.

Genotype imputation via matrix completion.

Most current genotype imputation methods are model-based and computationally intensive, taking days to impute one chromosome pair on 1000 people. We describe an efficient genotype imputation method based on matrix completion. Our matrix completion method is implemented in MATLAB and tested on real data from HapMap 3, simulated pedigree data, and simulated low-coverage sequencing data derived from the 1000 Genomes Project. Compared with leading imputation programs, the matrix completion algorithm embodied in our program MENDEL-IMPUTE achieves comparable imputation accuracy while reducing run times significantly. Implementation in a lower-level language such as Fortran or C is apt to further improve computational efficiency.

Convex clustering: an attractive alternative to hierarchical clustering.

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/.

Nonparametric tests for evaluation of biosimilarity in variability of follow-on biologics.

As more biologic products are going off patent protection, the development of follow-on biologic products (also known as biosimilars) has gained much attention from both the biotechnology industry and regulatory agencies. Unlike small molecules, the development of biologic products is not only more complicated but also sensitive to a small change in procedure/environment during the manufacturing process. In practice, biologics are expected to have much larger variation, which will potentially impact the product quality and potency. Thus, it is suggested that the assessment of biosimilarity between biologic products should take variability into consideration, in addition to average biosimilarity of endpoints of interest. In this article, we propose the use of nonparametric tests for evaluation of biosimilarity in variability between the follow-on biologic product and the reference product. Extensive simulations are conducted to compare the relative performance of the proposed methods with the adapted parametric F-test in terms of correctly concluding biosimilarity in variability. Under normality assumption, the proposed nonparametric tests are found to be comparably well with the adapted F-test. However, the proposed methods are more robust when the assumption is violated.

Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties.

Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications - discriminant analysis and EM clustering - in this sampling regime.

A Brief Survey of Modern Optimization for Statisticians.

Modern computational statistics is turning more and more to high-dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include nondifferentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience.

Distance majorization and its applications.

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization.

In a recent issue of this journal, Mordukhovich, Nam, and Salinas pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem, one is given k + 1 closed convex sets in ℝ d equipped with its Euclidean norm and asked to find the point in the last set such that the sum of the distances to the first k sets is minimal. In later work, the authors generalize the Heron problem even further, relax its convexity assumptions, study its theoretical properties, and pursue subgradient algorithms for solving the convex case. Here, we revisit the original problem solely from the numerical perspective. By exploiting the majorization-minimization (MM) principle of computational statistics and rudimentary techniques from differential calculus, we are able to construct a very fast algorithm for solving the Euclidean version of the generalized Heron problem.

An adapted F-test for homogeneity of variability in follow-on biological products.

In recent years, follow-on biological products (biosimilars) have received much attention from both the biotechnology industry and the regulatory agencies, especially after the passage of the 2010 healthcare reform bill. Unlike the traditional small-molecule drug products, the development of biological products is not only more complicated but also sensitive to small changes (both mean and variation) in procedure/environment during the manufacturing process because of some fundamental differences between drug products and biological products. A small change will have an impact on the quality of the product and consequently the treatment effect. Thus, in addition to the assessment of biosimilarity in average, it was suggested that biosimilarity in variability between biological products should be assessed. In this article, we propose an adapted F-test for homogeneity of variances to assess biosimilarity in variability. We study the performance and concordance of the proposed adapted F-test and compare it with probability-based method by extensive Monte Carlo simulations.

Impact of variability on the choice of biosimilarity limits in assessing follow-on biologics.

With larger variation in biological products compared with small molecular drugs, it is suggested that the assessment of biosimilarity of follow-on biologics (FOBs) should take variability into consideration in addition to average as standard in bioequivalence tests in small molecule drugs. Recent research on assessing variability in biosimilarity of FOBs has focused on direct assessment of variances, individual biosimilar index aggregating average and variability, and comparison of the entire distributions. However, the choice of biosimilarity limits for evaluating FOBs has not been investigated in the literature. In this article, we first explore the impact of variability on biosimilarity limits for the average biosimilarity assessment. On the basis of the derived relationship between variability and biosimilarity limit that result in the same power given all other parameters fixed, we propose several scaled biosimilarity limits to incorporate highly variable biological products.

The evaluation of biosimilarity index based on reproducibility probability for assessing follow-on biologics.

Unlike small molecule drug products, biological products are therapeutic agents producted using of a living system or organism. Thus, the development of biologic products is a very different and complicated process that is sensitive to environmental factors such as light and temperature. Therefore, the therapeutic effect of follow-on biologic products may not be equivalent to the innovative products even though the average biosimilarity has been established. Thus, Chow et al. suggested that the assessment of biosimilarity between biologic products should be conducted on the basis of variability in 2010. In this article, we propose a biosimilar index that is derived on the basis of estimated reproducibility probability approach and Bayesian approach, respectively. We conducted simulation studies to empirically investigate the relationship of reproducibility probability under various parameter combinations. The simulation results demonstrate that the proposed method based on biosimilar index can reflect the characteristics and impact of variability on the therapeutic effect of biologic products.

A Sharper Computational Tool for L2E Regression.

Building on previous research of Chi and Chi (2022), the current paper revisits estimation in robust structured regression under the L2E criterion. We adopt the majorization-minimization (MM) principle to design a new algorithm for updating the vector of regression coefficients. Our sharp majorization achieves faster convergence than the previous alternating proximal gradient descent algorithm (Chi and Chi, 2022). In addition, we reparameterize the model by substituting precision for scale and estimate precision via a modified Newton's method. This simplifies and accelerates overall estimation. We also introduce distance-to-set penalties to enable constrained estimation under nonconvex constraint sets. This tactic also improves performance in coefficient estimation and structure recovery. Finally, we demonstrate the merits of our improved tactics through a rich set of simulation examples and a real data application.