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The breeder's equation, Δ z ¯ = G ß   , allows us to understand how genetics (the genetic covariance matrix, G) and the vector of linear selection gradients ß interact to generate evolutionary trajectories. Estimation of ß using multiple regression of trait values on relative fitness revolutionized the way we study selection in laboratory and wild populations. However, multicollinearity, or correlation of predictors, can lead to very high variances of and covariances between elements of ß, posing a challenge for the interpretation of the parameter estimates. This is particularly relevant in the era of big data, where the number of predictors may approach or exceed the number of observations. A common approach to multicollinear predictors is to discard some of them, thereby losing any information that might be gained from those traits. Using simulations, we show how, on the one hand, multicollinearity can result in inaccurate estimates of selection, and, on the other, how the removal of correlated phenotypes from the analyses can provide a misguided view of the targets of selection. We show that regularized regression, which places data-validated constraints on the magnitudes of individual elements of ß, can produce more accurate estimates of the total strength and direction of multivariate selection in the presence of multicollinearity and limited data, and often has little cost when multicollinearity is low. We also compare standard and regularized regression estimates of selection in a reanalysis of three published case studies, showing that regularized regression can improve fitness predictions in independent data. Our results suggest that regularized regression is a valuable tool that can be used as an important complement to traditional least-squares estimates of selection. In some cases, its use can lead to improved predictions of individual fitness, and improved estimates of the total strength and direction of multivariate selection.

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Gene expression plays a pivotal role in various diseases, contributing significantly to their mechanisms. Most GWAS risk loci are in non-coding regions, potentially affecting disease risk by altering gene expression in specific tissues. This expression is notably tissue-specific, with genetic variants substantially influencing it. However, accurately detecting the expression Quantitative Trait Loci (eQTL) is challenging due to limited heritability in gene expression, extensive linkage disequilibrium (LD), and multiple causal variants. The single variant association approach in eQTL analysis is limited by its susceptibility to capture the combined effects of multiple variants, and a bias towards common variants, underscoring the need for a more robust method to accurately identify causal eQTL variants. To address this, we developed an algorithm, CausalEQTL, which integrates L 0 +L 1 penalized regression with an ensemble approach to localize eQTL, thereby enhancing prediction performance precisely. Our results demonstrate that CausalEQTL outperforms traditional models, including LASSO, Elastic Net, Ridge, in terms of power and overall performance. Furthermore, analysis of heart tissue data from the GTEx project revealed that eQTL sites identified by our algorithm provide deeper insights into heart-related tissue eQTL detection. This advancement in eQTL mapping promises to improve our understanding of the genetic basis of tissue-specific gene expression and its implications in disease. The source code and identified causal eQTLs for CausalEQTL are available on GitHub: https://github.com/zhc-moushang/CausalEQTL.

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Large-scale observational health databases are increasingly popular for conducting comparative effectiveness and safety studies of medical products. However, increasing number of patients poses computational challenges when fitting survival regression models in such studies. In this paper, we use graphics processing units (GPUs) to parallelize the computational bottlenecks of massive sample-size survival analyses. Specifically, we develop and apply time- and memory-efficient single-pass parallel scan algorithms for Cox proportional hazards models and forward-backward parallel scan algorithms for Fine-Gray models for analysis with and without a competing risk using a cyclic coordinate descent optimization approach. We demonstrate that GPUs accelerate the computation of fitting these complex models in large databases by orders of magnitude as compared to traditional multi-core CPU parallelism. Our implementation enables efficient large-scale observational studies involving millions of patients and thousands of patient characteristics. The above implementation is available in the open-source R package Cyclops (Suchard et al., 2013).

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Fitting penalized models for the purpose of merging the estimation and model selection problem has become commonplace in statistical practice. Of the various regularization strategies that can be leveraged to this end, the use of the l0 norm to penalize parameter estimation poses the most daunting model fitting task. In fact, this particular strategy requires an end user to solve a non-convex NP-hard optimization problem irregardless of the underlying data model. For this reason, the use of the l0 norm as a regularization strategy has been woefully under utilized. To obviate this difficulty, a strategy to solve such problems that is generally accessible by the statistical community is developed. The approach can be adopted to solve l0 norm penalized problems across a very broad class of models, can be implemented using existing software, and is computationally efficient. The performance of the method is demonstrated through in-depth numerical experiments and through using it to analyze several prototypical data sets.

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The widespread application of engineered nanoparticles (NPs) in various industries has demonstrated their effectiveness over the years. However, modifications to NPs' physicochemical properties can lead to toxicological effects. Therefore, understanding the toxicity behaviour of NPs is crucial. In this paper, regularized regression models, such as ridge, LASSO, and elastic net, were constructed to predict the cytotoxicity of various engineered NPs. The dataset utilized in this study was compiled from several journals published between 2010 and 2022. Data exploration revealed missing values, which were addressed through listwise deletion and kNN imputation, resulting in two complete datasets. The ridge, LASSO, and elastic net models achieved F1 scores ranging from 91.81% to 92.65% during internal validation and 92.89% to 93.63% during external validation on Dataset 1. On Dataset 2, the models attained F1 scores between 92.16% and 92.43% during internal validation and 92% and 92.6% during external validation. These results indicate that the developed models effectively generalize to unseen data and demonstrate high accuracy in classifying cytotoxicity levels. Furthermore, the cell type, material, cell source, cell tissue, synthesis method, and coat or functional group were identified as the most important descriptors by the three models across both datasets.

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OBJECTIVE: Subjective illness perception (IP) can differ from physician's clinical assessment results. Herein, we explored patient's IP during coronavirus disease 2019 (COVID-19) recovery. METHODS: Participants of the prospective observation CovILD study (ClinicalTrials.gov: NCT04416100) with persistent somatic symptoms or cardiopulmonary findings one year after COVID-19 were analyzed (n = 74). Explanatory variables included demographic and comorbidity, COVID-19 course and one-year follow-up data of persistent somatic symptoms, physical performance, lung function testing, chest computed tomography and trans-thoracic echocardiography. Factors affecting IP (Brief Illness Perception Questionnaire) one year after COVID-19 were identified by regularized modeling and unsupervised clustering. RESULTS: In modeling, 33% of overall IP variance (R2) was attributed to fatigue intensity, reduced physical performance and persistent somatic symptom count. Overall IP was largely independent of lung and heart findings revealed by imaging and function testing. In clustering, persistent somatic symptom count (Kruskal-Wallis test: η2 = 0.31, p < .001), fatigue (η2 = 0.34, p < .001), diminished physical performance (χ2 test, Cramer V effect size statistic: V = 0.51, p < .001), dyspnea (V = 0.37, p = .006), hair loss (V = 0.57, p < .001) and sleep problems (V = 0.36, p = .008) were strongly associated with the concern, emotional representation, complaints, disease timeline and consequences IP dimensions. CONCLUSION: Persistent somatic symptoms rather than abnormalities in cardiopulmonary testing influence IP one year after COVID-19. Modifying IP represents a promising innovative approach to treatment of post-COVID-19 condition. Besides COVID-19 severity, individual IP should guide rehabilitation and psychological therapy decisions.

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Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

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Children show substantial variation in the rate of physical, cognitive, and social maturation as they traverse adolescence and enter adulthood. Differences in developmental paths are thought to underlie individual differences in later life outcomes, however, there remains a lack of consensus on the normative trajectory of cognitive maturation in adolescence. To address this problem, we derive a Cognitive Maturity Index (CMI), to estimate the difference between chronological and cognitive age predicted with latent factor estimates of inhibitory control, risky decision-making and emotional processing measured with standard neuropsychological instruments. One hundred and forty-one children from the Adolescent Development Study (ADS) were followed longitudinally across three time points from ages 11-14, 13-16, and 14-18. Age prediction with latent factor estimates of cognitive skills approximated age within ±10 months (r = 0.71). Males in advanced puberty displayed lower cognitive maturity relative to peers of the same age; manifesting as weaker inhibitory control, greater risk-taking, desensitization to negative affect, and poor recognition of positive affect.

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The process of identifying and quantifying metabolites in complex mixtures plays a critical role in metabolomics studies to obtain an informative interpretation of underlying biological processes. Manual approaches are time-consuming and heavily reliant on the knowledge and assessment of nuclear magnetic resonance (NMR) experts. We propose a shifting-corrected regularized regression method, which identifies and quantifies metabolites in a mixture automatically. A detailed algorithm is also proposed to implement the proposed method. Using a novel weight function, the proposed method is able to detect and correct peak shifting errors caused by fluctuations in experimental procedures. Simulation studies show that the proposed method performs better with regard to the identification and quantification of metabolites in a complex mixture. We also demonstrate real data applications of our method using experimental and biological NMR mixtures.

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miRNA are regulators of cell phenotype, and there is clear evidence that these small posttranscriptional modifiers of gene expression are involved in defining a cellular response across states of development and disease. Classical methods for elucidating the repressive effect of a miRNA on its targets involve controlling for the many factors influencing miRNA action, and this can be achieved in cell lines, but misses tissue and organism level context which are key to a miRNA function. Also, current technology to carry out this validation is limited in both generalizability and throughput. Methodologies with greater scalability and rapidity are required to better understand the function of these important species of RNA. To this end, there is an increasing store of RNA expression level data incorporating both miRNA and mRNA, and in this chapter, we describe how to use machine learning and gene-sets to translate the knowledge of phenotype defined by mRNA to putative roles for miRNA. We outline our approach to this process and highlight how it was done for our miRNA annotation of the hallmarks of cancer using the Cancer Genome Atlas (TCGA) dataset. The concepts we present are applicable across datasets and phenotypes, and we highlight potential pitfalls and challenges that may be faced as they are used.

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Encoding models provide a powerful framework to identify the information represented in brain recordings. In this framework, a stimulus representation is expressed within a feature space and is used in a regularized linear regression to predict brain activity. To account for a potential complementarity of different feature spaces, a joint model is fit on multiple feature spaces simultaneously. To adapt regularization strength to each feature space, ridge regression is extended to banded ridge regression, which optimizes a different regularization hyperparameter per feature space. The present paper proposes a method to decompose over feature spaces the variance explained by a banded ridge regression model. It also describes how banded ridge regression performs a feature-space selection, effectively ignoring non-predictive and redundant feature spaces. This feature-space selection leads to better prediction accuracy and to better interpretability. Banded ridge regression is then mathematically linked to a number of other regression methods with similar feature-space selection mechanisms. Finally, several methods are proposed to address the computational challenge of fitting banded ridge regressions on large numbers of voxels and feature spaces. All implementations are released in an open-source Python package called Himalaya.

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The L1-regularized regression with Kullback-Leibler divergence (KL-L1R) is a popular regression technique. Although many efforts have been devoted to its efficient implementation, it remains challenging when the number of features is extremely large. In this paper, to accelerate KL-L1R, we introduce a novel and fast sequential safe feature elimination rule (FER) based on its sparsity, local regularity properties, and duality theory. It takes negligible time to select and delete most redundant features before and during the training process. Only one reduced model needs to be solved, which makes the computational time shortened. To further speed up the reduced model, the Newton coordinate descent method (Newton-CDM) is chosen as a solver. The superiority of FER is safety, i.e., its solution is exactly the same as the original KL-L1R. Numerical experiments on three artificial datasets, five real-world datasets, and one handwritten digit dataset demonstrate the feasibility and validity of our FER.

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We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regularizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in practical contexts, by dealing with neuroimaging and hemodynamic data.

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A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees handle more complex relationships among random variables and appear in many disciplines, such as brain imaging, genomics and finance. We consider the problem of sparse regression on data that are associated with a compositional tree and propose a transformation-free tree-based regularized regression method for component selection. The regularization penalty is designed based on the tree structure and encourages a sparse tree representation. We prove that our proposed estimator for regression coefficients is both consistent and model selection consistent. In the simulation study, our method shows higher accuracy than competing methods under different scenarios. By analyzing a brain imaging data set from studies of Alzheimer's disease, our method identifies meaningful associations between memory decline and volume of brain regions that are consistent with current understanding.

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Early detection of lung cancer has a higher likelihood of curative treatment and thus improves survival rate. Low-dose computed tomography (LDCT) screening has been shown to be effective for high-risk individuals in several clinical trials, but has high false positive rates. To evaluate the risk of stage I lung cancer in the general population not limited to smokers, a retrospective study of 133 subjects was conducted in a medical center in Taiwan. Regularized regression was used to build the risk prediction model by using LDCT and health examinations. The proposed model selected seven variables related to nodule morphology, counts and location, and ten variables related to blood tests and medical history, achieving an area under the curve (AUC) value of 0.93. The higher the age, white blood cell count (WBC), blood urea nitrogen (BUN), diabetes, gout, chronic obstructive pulmonary disease (COPD), other cancers, and the presence of spiculation, ground-glass opacity (GGO), and part solid nodules, the higher the risk of lung cancer. Subjects with calcification, solid nodules, nodules in the middle lobes, more nodules, and diseases related to thyroid, liver, and digestive systems were at a lower risk. The selected variables did not indicate causation.

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Single-cell technologies provide us new ways to profile transcriptomic landscape, chromatin accessibility, spatial expression patterns in heterogeneous tissues at the resolution of single cell. With enormous generated single-cell datasets, a key analytic challenge is to integrate these datasets to gain biological insights into cellular compositions. Here, we developed a domain-adversarial and variational approximation, DAVAE, which can integrate multiple single-cell datasets across samples, technologies and modalities with a single strategy. Besides, DAVAE can also integrate paired data of ATAC profile and transcriptome profile that are simultaneously measured from a same cell. With a mini-batch stochastic gradient descent strategy, it is scalable for large-scale data and can be accelerated by GPUs. Results on seven real data integration applications demonstrated the effectiveness and scalability of DAVAE in batch-effect removing, transfer learning and cell-type predictions for multiple single-cell datasets across samples, technologies and modalities. Availability: DAVAE has been implemented in a toolkit package "scbean" in the pypi repository, and the source code can be also freely accessible at https://github.com/jhu99/scbean. All our data and source code for reproducing the results of this paper can be accessible at https://github.com/jhu99/davae_paper.

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Trout-perch are sampled from the Athabasca River in Alberta, Canada, as a sentinel species for environmental health. The performance of trout-perch populations is known to be influenced by the quality of the water in which they reside. Using climate, environmental, and water quality variables measured in the Athabasca River near trout-perch sampling locations is found to improve model fitting and the predictability of models for the adjusted body weight, adjusted gonad weight, and adjusted liver weight of trout-perch. Given a large number of covariables, three variable selection techniques: stepwise regression, the lasso, and the elastic net (EN) are considered for selecting a subset of relevant variables. The models selected by the lasso and EN are found to outperform the models selected by stepwise regression in general, and little difference is observed between the models selected by the lasso and EN. Uranium, tungsten, tellurium, pH, molybdenum, and antimony are selected for at least one fish response.

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With recent advances in machine learning, we demonstrated the use of supervised machine learning to optimize the prediction of treatment outcomes of vedolizumab through iterative optimization using VARSITY and VISIBLE 1 data in patients with moderate-to-severe ulcerative colitis. The analysis was carried out using elastic net regularized regression following a 2-stage training process. The model performance was assessed through AUROC, specificity, sensitivity, and accuracy. The generalizable predictive patterns suggest that easily obtained baseline and medical history variables may be able to predict therapeutic response to vedolizumab with clinically meaningful accuracy, implying a potential for individualized prescription of vedolizumab.

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One of the prominent reasons behind the deterioration of cardiovascular conditions is hypertension. Due to lack of specific symptoms, sometimes existing hypertension goes unnoticed until significant damage happens to the heart or any other body organ. Monitoring of BP at a higher frequency is necessary so that we can take early preventive measures to control and keep it within the normal range. The cuff-based method of measuring BP is inconvenient for frequent daily measurements. The cuffless BP measurement method proposed in this paper uses features extracted from the electrocardiogram (ECG) and photoplethysmography (PPG). ECG and PPG both have distinct characteristics, which change with the change of blood pressure levels. Feature extraction and hybrid feature selection algorithms are followed by a generalized penalty-based regression technique led to a new BP measurement process that uses the minimum number of features. The performance of the proposed technique to measure blood pressure was compared to an approach using an ordinary linear regression method with no feature selection and to other contemporary techniques. MIMIC-II database was used to train and test our proposed method. The root mean square error (RMSE) for systolic blood pressure (SBP) improved from 11.2 mmHg to 5.6 mmHg when the proposed technique was implemented and for diastolic blood pressure (DBP) improved from 12.7 mmHg to 6.69 mmHg. The mean absolute error (MAE) was found to be 4.91 mmHg for SBP and 5.77 mmHg for DBP, which have shown improvement over other existing cuffless techniques where the substantial number of patients, as well as feature selection algorithm, were implemented. In addition, according to the British Hypertension Society standard (BHS) standard for cuff-based BP measurement, the criteria for acceptable measurement are to achieve at least grade B; our proposed method also satisfies this criterion.

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Wastewater reclamation and reuse have been practically applied to water-stressed regions, but waterborne pathogens remaining in insufficiently treated wastewater are of concern. Sanitation Safety Planning adopts the hazard analysis and critical control point (HACCP) approach to manage human health risks upon exposure to reclaimed wastewater. HACCP requires a predetermined reference value (critical limit: CL) at critical control points (CCPs), in which specific parameters are monitored and recorded in real time. A disinfection reactor of a wastewater treatment plant (WWTP) is regarded as a CCP, and one of the CCP parameters is the disinfection intensity (e.g., initial disinfectant concentration and contact time), which is proportional to the log reduction value (LRV) of waterborne pathogens. However, the achievable LRVs are not always stable because the disinfection intensity is affected by water quality parameters, which vary among WWTPs. In this study, we established models for projecting virus LRVs using ozone, in which water quality and operational parameters were used as explanatory variables. For the model construction, we used five machine learning algorithms and found that automatic relevance determination with interaction terms resulted in better prediction performances for norovirus and rotavirus LRVs. Poliovirus and coxsackievirus LRVs were predicted well by a Bayesian ridge with interaction terms and lasso with quadratic terms, respectively. The established models were relatively robust to predict LRV using new datasets that were out of the range of the training data used here, but it is important to collect LRV datasets further to make the models more predictable and flexible for newly obtained datasets. The modeling framework proposed here can help WWTP operators and risk assessors determine the appropriate CL to protect human health in wastewater reclamation and reuse.