Regularized Regression Research Articles

Comparative Analysis of Chemical Descriptors by Machine Learning Reveals Atomistic Insights into Solute-Lipid Interactions.

This study explores the research area of drug solubility in lipid excipients, an area persistently complex despite recent advancements in understanding and predicting solubility based on molecular structure. To this end, this research investigated novel descriptor sets, employing machine learning techniques to understand the determinants governing interactions between solutes and medium-chain triglycerides (MCTs). Quantitative structure-property relationships (QSPR) were constructed on an extended solubility data set comprising 182 experimental values of structurally diverse drug molecules, including both development and marketed drugs to extract meaningful property relationships. Four classes of molecular descriptors, ranging from traditional representations to complex geometrical descriptions, were assessed and compared in terms of their predictive accuracy and interpretability. These include two-dimensional (2D) and three-dimensional (3D) descriptors, Abraham solvation parameters, extended connectivity fingerprints (ECFPs), and the smooth overlap of atomic position (SOAP) descriptor. Through testing three distinct regularized regression algorithms alongside various preprocessing schemes, the SOAP descriptor enabled the construction of a superior performing model in terms of interpretability and accuracy. Its atom-centered characteristics allowed contributions to be estimated at the atomic level, thereby enabling the ranking of prevalent molecular motifs and their influence on drug solubility in MCTs. The performance on a separate test set demonstrated high predictive accuracy (RMSE = 0.50) for 2D and 3D, SOAP, and Abraham Solvation descriptors. The model trained on ECFP4 descriptors resulted in inferior predictive accuracy. Lastly, uncertainty estimations for each model were introduced to assess their applicability domains and provide information on where the models may extrapolate in chemical space and, thus, where more data may be necessary to refine a data-driven approach to predict solubility in MCTs. Overall, the presented approaches further enable computationally informed formulation development by introducing a novel in silico approach for rational drug development and prediction of dose loading in lipids.

Person-specific and pooled prediction models for binge eating, alcohol use and binge drinking in bulimia nervosa and alcohol use disorder.

Machine learning could predict binge behavior and help develop treatments for bulimia nervosa (BN) and alcohol use disorder (AUD). Therefore, this study evaluates person-specific and pooled prediction models for binge eating (BE), alcohol use, and binge drinking (BD) in daily life, and identifies the most important predictors. A total of 120 patients (BN: 50; AUD: 51; BN/AUD: 19) participated in an experience sampling study, where over a period of 12 months they reported on their eating and drinking behaviors as well as on several other emotional, behavioral, and contextual factors in daily life. The study had a burst-measurement design, where assessments occurred eight times a day on Thursdays, Fridays, and Saturdays in seven bursts of three weeks. Afterwards, person-specific and pooled models were fit with elastic net regularized regression and evaluated with cross-validation. From these models, the variables with the 10% highest estimates were identified. The person-specific models had a median AUC of 0.61, 0.80, and 0.85 for BE, alcohol use, and BD respectively, while the pooled models had a median AUC of 0.70, 0.90, and 0.93. The most important predictors across the behaviors were craving and time of day. However, predictors concerning social context and affect differed among BE, alcohol use, and BD. Pooled models outperformed person-specific models and the models for alcohol use and BD outperformed those for BE. Future studies should explore how the performance of these models can be improved and how they can be used to deliver interventions in daily life.

Unraveling the Dynamic Relationship between Neighborhood Deprivation and Walkability over Time: A Machine Learning Approach

Unraveling the Dynamic Relationship between Neighborhood Deprivation and Walkability over Time: A Machine Learning Approach

Enhanced fracture risk prediction: a novel multi-trait genetic approach integrating polygenic scores of fracture-related traits

SummaryThe novel metaPGS, integrating multiple fracture–related genetic traits, surpasses traditional polygenic scores in predicting fracture risk. Demonstrating a robust association with incident fractures, this metaPGS offers significant potential for enhancing clinical fracture risk assessment and tailoring prevention strategies.IntroductionCurrent polygenic scores (PGS) have limited predictive power for fracture risk. To improve genetic prediction, we developed and evaluated a novel metaPGS combining genetic information from multiple fracture–related traits.MethodsWe derived individual PGS from genome-wide association studies of 16 fracture-related traits and employed an elastic-net logistic regression model to examine the association between the 16 PGSs and fractures. An optimal metaPGS was constructed by combining 11 significant individual PGSs selected by the elastic regularized regression model. We evaluated the predictive power of the metaPGS alone and in combination with clinical risk factors recommended by guidelines. The discrimination ability of metaPGS was assessed using the concordance index. Reclassification was assessed using net reclassification improvement (NRI) and integrated discrimination improvement (IDI).ResultsThe metaPGS had a significant association with incident fractures (HR 1.21, 95% CI 1.18–1.25 per standard deviation of metaPGS), which was stronger than previously developed bone mineral density (BMD)-related individual PGSs. Models with PGS_FNBMD, PGS_TBBMD, and metaPGS had slightly higher but statistically non-significant c-index than the base model (0.640, 0.644, 0.644 vs. 0.638). However, the reclassification analysis showed that compared to the base model, the model with metaPGS improves the reclassification of fracture.ConclusionsThe metaPGS is a promising approach for stratifying fracture risk in the European population, improving fracture risk prediction by combining genetic information from multiple fracture–related traits.

Abstract PS06-07: Liquid biopsy determination of HER2 status in breast cancer: results from a novel epigenomic platform

Abstract Background: Tumor HER2 status remains a critical predictive biomarker for patients with breast cancer given the availability of highly effective anti-HER2 therapies. However, determination of HER2 status relies on a complex, tissue-dependent algorithm optimized for extremes of the phenotype – HER2+ vs HER2- status. Given the challenges in reliably obtaining informative tissue biopsies as disease progresses, the new therapeutic relevance of HER2-low breast cancer (IHC 1+ and FISH-negative IHC 2+), and the undependability of biomarkers in this range, better approaches are needed. Epigenomic signatures detectable in cell-free tumor DNA (cfDNA) may provide a minimally invasive, reliable determination of HER2 status. Here, we present a multimodal epigenomic liquid biopsy platform that could offer a minimally invasive alternative to tissue-based determination of transcriptionally regulated targets such as HER2. Methods: We identified patients with metastatic breast cancer (n=20) that were HER2-positive with IHC 3+ (n=6) or HER2-negative with IHC 0 (n=14) based on ASCO/CAP guidelines who underwent research biopsies at the Dana-Farber Cancer Institute from 2012-2023. Study participants had undergone concurrent blood sampling collected in Streck Tubes, processed as plasma, and stored at -80ºC. We applied a novel, multimodal epigenomic assay to profile tumor-derived gene regulatory programs from 1mL plasma. This genome-wide approach analyzed histone modifications associated with active gene promoters and enhancers, and DNA methylation. Classifier feature selection was derived from epigenomically profiled breast cancer cell lines. Final classifier performance was cross validated using a standard Leave one Out (LoO) scheme. Results: Our cross-validated classifier yielded an area under the ROC curve (AUC) of 0.91 in the 20 samples tested. When including only samples with detectable ctDNA as assessed by low pass whole genome sequencing (ichorCNA algorithm) (N=13), our classifier had an AUC of 0.98. Using regularized regression approach, we identified 33 loci with the highest predictive value; 8 loci were within the ERBB2 amplicon on chromosome 17, while the remaining 25 loci were in other genomic regions. We will present results from this and an expanded cohort, including participants with HER2 IHC 1+ and 2+ disease. Conclusions: We present a novel, minimally invasive HER2 classifier leveraging epigenomic information from cell-free tumor DNA from 1 mL plasma. If this approach remains robust in accurately classifying additional HER2 states, it could address the limitations of current tissue-based testing. Integration of this epigenomic platform in prospective interventional studies could support the development of novel and improved predictive classifiers for response to HER2-directed therapy. Citation Format: Heather Parsons, Sylvan Baca, Anthony D'Ippolito, Hyun-Hwan Jeong, Kalie Smith, Paolo Tarantino, Melissa Hughes, Kerry Sendrick, Corrie Painter, Ji-Heui Seo, Elizabeth Grant, Jamey Guess, Matthew Davidsohn, Gitanjali Lakshminarayanan, Sarah Strauss, Hunter Savignano, John Canniff, Brad Fortunato, Matthew Eaton, Toni Choueiri, Sara Tolaney, Matthew Freedman, Nancy Lin. Liquid biopsy determination of HER2 status in breast cancer: results from a novel epigenomic platform [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PS06-07.

Tweedie regularization model and application

This article proposes a new regular model called the Tweedie regular regression model. The Tweedie distributions are parameterized by their mean, dispersion and power parameter ξ. For each ξ, we obtain a specific regular model. Tweedie Regression model includes several distributions. In particular, for ξ = 0, we obtain the Gaussian case; the estimation of the parameters through the classical point of view has been done using Least Absolute Shrinkage and Selection Operator (Lasso), Ridge and Elastic methods. Therefore, the proposed model is appropriate for modeling equiover and underdispersed data. The parameters estimation, through the classical point of view, has been performed using the methods of Lasso, Ridge and Elastic approaches. The Tweedie regular regression model will be calibrated by choosing one of the Lasso, Ridge and Elastic approaches. To evaluate our suggested method, a detailed comparison study through a simulation and real data was conducted to verify the proposed models. It was carried out to examine the fitness of the estimated parameters. Compared with counterparts, the results demonstrate the superiority of models Ridge Tweedie Regression (RTR), Lasso Tweedie Regression (LTR), and Elastic Tweedie Regression (ETR) using MAE (Mean absolute error), RMSE (Root Mean Squared Error) and R-squared (Coefficient of determination)

Mahalanobis balancing: A multivariate perspective on approximate covariate balancing

AbstractIn the past decade, various exact balancing‐based weighting methods were introduced to the causal inference literature. It eliminates covariate imbalance by imposing balancing constraints in a certain optimization problem, which can nevertheless be infeasible when there is bad overlap between the covariate distributions in the treated and control groups or when the covariates are high dimensional. Recently, approximate balancing was proposed as an alternative balancing framework. It resolves the feasibility issue by using inequality moment constraints instead. However, it can be difficult to select the threshold parameters. Moreover, moment constraints may not fully capture the discrepancy of covariate distributions. In this paper, we propose Mahalanobis balancing to approximately balance covariate distributions from a multivariate perspective. We use a quadratic constraint to control overall imbalance with a single threshold parameter, which can be tuned by a simple selection procedure. We show that the dual problem of Mahalanobis balancing is an norm‐based regularized regression problem, and establish interesting connection to propensity score models. We derive asymptotic properties, discuss the high‐dimensional scenario, and make extensive numerical comparisons with existing balancing methods.

Combining regularization and logistic regression model to validate the Q-matrix for cognitive diagnosis model.

Q-matrix is an important component of most cognitive diagnosis models (CDMs); however, it mainly relies on subject matter experts' judgements in empirical studies, which introduces the possibility of misspecified q-entries. To address this, statistical Q-matrix validation methods have been proposed to aid experts' judgement. A few of these methods, including the multiple logistic regression-based (MLR-B) method and the Hull method, can be applied to general CDMs, but they are either time-consuming or lack accuracy under certain conditions. In this study, we combine the L1 regularization and MLR model to validate the Q-matrix. Specifically, an L1 penalty term is imposed on the log-likelihood of the MLR model to select the necessary attributes for each item. A simulation study with various factors was conducted to examine the performance of the new method against the two existing methods. The results show that the regularized MLR-B method (a) produces the highest Q-matrix recovery rate (QRR) and true positive rate (TPR) for most conditions, especially with a small sample size; (b) yields a slightly higher true negative rate (TNR) than either the MLR-B or the Hull method for most conditions; and (c) requires less computation time than the MLR-B method and similar computation time as the Hull method. A real data set is analysed for illustration purposes.

Weight gained during treatment predicts 6-month body mass index in a large sample of patients with anorexia nervosa using ensemble machine learning.

This study used machine learning methods to analyze data on treatment outcomes from individuals with anorexia nervosa admitted to a specialized eating disorders treatment program. Of 368 individuals with anorexia nervosa (209 adolescents and 159 adults), 160 individuals had data available for a 6-month follow-up analysis. Participants were treated in a 6-day-per-week partial-hospital program. Participants were assessed for eating disorder-specific and non-specific psychopathology. The analyses used established machine learning procedures combined in an ensemble model from support vector machine learning, random forest prediction, and the elastic net regularized regression with an exploration (training; 75%) and confirmation (test; 25%) split of the data. The models predicting body mass index (BMI) at 6-month follow-up explained a 28.6% variance in the training set (n = 120). The model had good performance in predicting 6-month BMI in the test dataset (n = 40), with predicted BMI significantly correlating with actual BMI (r = .51, p = 0.01). The change in BMI from admission to discharge was the most important predictor, strongly correlating with reported BMI at 6-month follow-up (r = .55). Behavioral variables were much less predictive of BMI outcome. Results were similar for z-transformed BMI in the adolescent-only group. Length of stay was most predictive of weight gain in treatment (r = .56) but did not predict longer-term BMI. This study, using an agnostic ensemble machine learning approach in the largest to-date sample of individuals with anorexia nervosa, suggests that achieving weight gain goals in treatment predicts longer-term weight-related outcomes. Other potential predictors, personality, mood, or eating disorder-specific symptoms were relatively much less predictive. The results from this study indicate that the amount of weight gained during treatment predicts BMI 6 months after discharge from a high level of care. This suggests that patients require sufficient time in a higher level of care treatment to meet their specific weight goals and be able to maintain normal weight.

Identifying tripartite relationship among cortical thickness, neuroticism, and mood and anxiety disorders

The number of young adults seeking help for emotional distress, subsyndromal-syndromal mood/anxiety symptoms, including those associated with neuroticism, is rising and can be an early manifestation of mood/anxiety disorders. Identification of gray matter (GM) thickness alterations and their relationship with neuroticism and mood/anxiety symptoms can aid in earlier diagnosis and prevention of risk for future mood and anxiety disorders. In a transdiagnostic sample of young adults (n = 252;177 females; age 21.7 ± 2), Hypothesis (H) 1:regularized regression followed by multiple regression examined relationships among GM cortical thickness and clinician-rated depression, anxiety, and mania/hypomania; H2:the neuroticism factor and its subfactors as measured by NEO Personality Inventory (NEO-PI-R) were tested as mediators. Analyses revealed positive relationships between left parsopercularis thickness and depression (B = 4.87, p = 0.002), anxiety (B = 4.68, p = 0.002), mania/hypomania (B = 6.08, p ≤ 0.001); negative relationships between left inferior temporal gyrus (ITG) thickness and depression (B = − 5.64, p ≤ 0.001), anxiety (B = − 6.77, p ≤ 0.001), mania/hypomania (B = − 6.47, p ≤ 0.001); and positive relationships between left isthmus cingulate thickness (B = 2.84, p = 0.011), and anxiety. NEO anger/hostility mediated the relationship between left ITG thickness and mania/hypomania; NEO vulnerability mediated the relationship between left ITG thickness and depression. Examining the interrelationships among cortical thickness, neuroticism and mood and anxiety symptoms enriches the potential for identifying markers conferring risk for mood and anxiety disorders and can provide targets for personalized intervention strategies for these disorders.

On sparse regression, Lp‐regularization, and automated model discovery

AbstractSparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem‐specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias that may aggressively change the results; only L0 regularization allows us to transparently fine‐tune the trade‐off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user‐defined properties.

Orthogonal systems based stable estimator for non parametric regression problems

. In this work, we study a univariate as well as a multivariate Jacobi polynomial-based estimator for solving the fundamental problem of non parametric (NP) regression. The proposed NP regression estimator aims to approximate a possibly very low regular regression function from the knowledge of its noised values given at some n random sampling points. We first study the univariate version of the proposed estimator, then extend this study to the general multivariate case with random sampling vectors drawn according to an unknown distribution. Our proposed estimator has the advantage of being stable with reasonable time complexity. Moreover, it has an optimal convergence rate under the weak condition that the regression function has a certain low Sobolev smoothness property. Although the proposed estimators are studied under the hypothesis that the random sampling vectors are supported on the d dimensional unit hypercube, by applying trivial transformations, the results of this work are still valid in the more general setting of any d dimensional hyperrectangle. Finally, the theoretical results of this work are illustrated by some numerical simulations on synthetic as well as real datasets.

Towards healthy cities: Modeling restorative potential of urban environments by coupling LiDAR-derived 3D metrics with panorama-based online survey

With the growing concern for the psychological well-being of urban dwellers, there has been a recognized need to explore the role of green environments in facilitating mental restorative benefits from the demands of city life. However, a significant gap exists in quantitatively modeling the restorative potential of urban environments, especially in terms of comprehensive 3D characteristics beyond mere greenery. This research gap has hindered our understanding of how to plan and design urban spaces that promote mental health. To bridge this gap, we conducted a study using Singapore as a case study to model the restorative potential for landscape planning and design by integrating LiDAR-derived 3D metrics, outcomes of an online survey, and a machine learning-based regularized regression model. We first collected data from 100 scenes, including both residential neighborhoods and urban parks, by extracting point cloud information from LiDAR scans for calculating a diverse set of 41 3D spatial metrics. Alongside these objective measurements, we conducted an online survey (N = 1500) using the Perceived Restorativeness Scale (PRS) where respondents evaluated the restorative potential of these scenes presented as interactive panoramic images. We subsequently utilized a regularized regression technique based on machine learning by conducting K-fold cross-validation (K = 10) with 1251 tests to identify the feature metrics significantly contributing to restorative potential. Our findings highlighted the importance of the green volumetric ratio as the most significant positive factor for restorative potential. Additionally, the results on the metrics of grey horizontal diversity and grey cluster number indicated a positive impact of unregulated and unaggregated grey components on restorative potential. The results on green horizontal diversity suggested that a uniform and concentrated spatial arrangement of greenery is a positive predictor, while other factors like front-background ratio, colorfulness, and slope variation also positively influenced restorative potential. In essence, our study not only provides novel insights but also introduces innovative methods for quantitatively assessing and characterizing the quality of urban environments that enhance psychological well-being. These findings inform the practical planning and design strategies aimed at fostering healthy and sustainable urban spaces.

What causes US equity market sector volatilities during the coronavirus pandemic?

ABSTRACT This paper seeks to identify key variables contributing to sectoral stock market volatilities in the US under the enduring pressure of the COVID-19 pandemic, using a broad array of candidate factors. We adopt a Beta-Skew-t-EGARCH model to capture the time-varying dynamics of the individual sectoral return volatilities. The empirical analysis is performed via an elastic-net regularized regression model. We find that trading volume, volatility of broad US dollar exchange rates, coronavirus infection rates, VIX, Google search trends, US economic policy uncertainty, and the initiation of vaccination programmes are the most common determinants of sectoral volatility.

Empirical Asset Pricing with Many Test Assets

Abstract We formulate the problem of estimating risk prices in a stochastic discount factor (SDF) model as an instrumental variables regression. The IV estimator allows efficient estimation for models with non-traded factors and many test assets. Optimal instruments are constructed using a regularized sparse first stage regression. In a simulation study, the IV estimator is close to the infeasible GMM estimator in a setting with many assets. In an empirical application, the tracking portfolio for consumption growth appears strongly correlated with consumption news. It implies that consumption is a priced factor for the cross-section of excess equity returns. A similar regularized regression, projecting the SDF on test assets, leads to an estimate of the Hansen–Jagannathan distance, and identifies portfolios that maximally violate the pricing implications of the model.

On building machine learning models for medical dataset with correlated features

Abstract This work builds machine learning models for the dataset generated using a numerical model developed on an idealized human artery. The model has been constructed accounting for varying blood characteristics as it flows through arteries with variable vascular properties, and it is applied to simulate blood flow in the femoral and its continued artery. For this purpose, we designed a pipeline model consisting of three components to include the major segments of the femoral artery: CFA, the common femoral artery and SFA, the superficial artery, and its continued one, the popliteal artery (PA). A notable point of this study is that the features and target variables of the former component pipe form the set of features of the latter, thus resulting in multicollinearity among the features in the third component pipe. Thus, we worked on understanding the effect of these correlated features on the target variables using regularized linear regression models, ensemble, and boosting algorithms. This study highlighted the blood velocity in CFA as the primary influential factor for wall shear stress in both CFA and SFA. Additionally, it established the blood rheology in PA as a significant factor for the same in it. Nevertheless, because the study relies on idealized conditions, these discoveries necessitate thorough clinical validation.

Overlapping yet dissociable contributions of superiority illusion features to Ponzo illusion strength and metacognitive performance

Humans are typically inept at evaluating their abilities and predispositions. People dismiss such a lack of metacognitive insight into their capacities while even enhancing (albeit illusorily) self-evaluation such that they should have more desirable traits than an average peer. This superiority illusion helps maintain a healthy mental state. However, the scope and range of its influence on broader human behavior, especially perceptual tasks, remain elusive. As belief shapes the way people perceive and recognize, the illusory self-superiority belief potentially regulates our perceptual and metacognitive performance. In this study, we used hierarchical Bayesian estimation and machine learning of signal detection theoretic measures to understand how the superiority illusion influences visual perception and metacognition for the Ponzo illusion. Our results demonstrated that the superiority illusion correlated with the Ponzo illusion magnitude and metacognitive performance. Next, we combined principal component analysis and cross-validated regularized regression (relaxed elastic net) to identify which superiority components contributed to the correlations. We revealed that the “extraversion” superiority dimension tapped into the Ponzo illusion magnitude and metacognitive ability. In contrast, the “honesty-humility” and “neuroticism” dimensions only predicted Ponzo illusion magnitude and metacognitive ability, respectively. These results suggest common and distinct influences of superiority features on perceptual sensitivity and metacognition. Our findings contribute to the accumulating body of evidence indicating that the leverage of superiority illusion is far-reaching, even to visual perception.

A Characterization of Simultaneous Optimization, Majorization, and (Bi-)Submodular Polyhedra

Motivated by resource allocation problems (RAPs) in power management applications, we investigate the existence of solutions to optimization problems that simultaneously minimize the class of Schur-convex functions, also called least-majorized elements. For this, we introduce a generalization of majorization and least-majorized elements, called (a, b)-majorization and least (a, b)-majorized elements, and characterize the feasible sets of problems that have such elements in terms of base and (bi-)submodular polyhedra. Hereby, we also obtain new characterizations of these polyhedra that extend classical characterizations in terms of optimal greedy algorithms from the 1970s. We discuss the implications of our results for RAPs in power management applications and derive a new characterization of convex cooperative games and new properties of optimal estimators of specific regularized regression problems. In general, our results highlight the combinatorial nature of simultaneously optimizing solutions and provide a theoretical explanation for why such solutions generally do not exist.

Predicting proximal tubule failed repair drivers through regularized regression analysis of single cell multiomic sequencing

Renal proximal tubule epithelial cells have considerable intrinsic repair capacity following injury. However, a fraction of injured proximal tubule cells fails to undergo normal repair and assumes a proinflammatory and profibrotic phenotype that may promote fibrosis and chronic kidney disease. The healthy to failed repair change is marked by cell state-specific transcriptomic and epigenomic changes. Single nucleus joint RNA- and ATAC-seq sequencing offers an opportunity to study the gene regulatory networks underpinning these changes in order to identify key regulatory drivers. We develop a regularized regression approach to construct genome-wide parametric gene regulatory networks using multiomic datasets. We generate a single nucleus multiomic dataset from seven adult human kidney samples and apply our method to study drivers of a failed injury response associated with kidney disease. We demonstrate that our approach is a highly effective tool for predicting key cis- and trans-regulatory elements underpinning the healthy to failed repair transition and use it to identify NFAT5 as a driver of the maladaptive proximal tubule state.

Using a centered general linear model for detection of interactions among biomarkers.

The dummy variable based general linear model (gLM) is commonly used to model categorical factors and their interactions. However, the main factors and their interactions in a general linear model are often correlated even when the factors are independently distributed. Alternatively, the classical two-way factorial analysis of variance (ANOVA) model can avoid the correlation between the main factors and their interactions when the main factors are independent. But the ANOVA model is hardly applicable to a regular linear regression model especially in the presence of other covariates due to constraints on its model parameters. In this study, a centered general linear model (cgLM) is proposed for modeling interactions between categorical factors based on their centered dummy variables. We show that the cgLM can avoid the correlation between the main factors and their interactions as the ANOVA model when the main factors are independent. Meanwhile, similar to gLM, it can be used in regular regression and fitted conveniently using the standard least square approach by choosing appropriate baselines to avoid constraints on its model parameters. The potential advantage of cgLM over gLM for detection of interactions in model building procedures is also illustrated and compared via a simulation study. Finally, the cgLM is applied to a postmortem brain gene expression data set.