Ridge regression and its applications in genetic studies

Arashi, Mohammad; Roozbeh, Mahdi; Hamzah, Nor Aishah; Gasparini, Mauro

doi:10.1371/journal.pone.0245376

Cited by 49 publications

(24 citation statements)

References 24 publications

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“…Ridge regression is an improved least-squares regression analysis and is more applicable to the case of collinearity between independent variables. [25][26][27] Adjusted for hypertension, the effects of the independent variables were determined by ridge regression analysis. What is the relationship between the increased V PAS and ATBAD?…”

Section: Discussionmentioning

confidence: 99%

Enlarged Lumen Volume of Proximal Aortic Segment and Acute Type B Aortic Dissection: A Computer Fluid Dynamics Study of Ideal Aortic Models

Peng¹,

Zhang²,

Li³

et al. 2022

IJGM

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Background: Recent study has revealed that enlarged diameters of the ascending aorta and proximal aortic arch enhance the probability of ATBAD. However, little is understood about the relation to ATBAD. Objective: This study explored the differences in proximal aortic segment (PAS) morphology in patients with acute type B aortic dissection (ATBAD), and performed hemodynamic simulations to provide proof of principle. Materials and Methods:The morphological characteristics of PAS in the ATBAD group (n = 163) and corresponding segment in the control group (n = 120) were retrospectively measured. The morphological parameters were analyzed using comprehensive statistical approaches. Ridge regression analysis was also performed to determine the association between independent variable and dependent variable. P < 0.01 was considered significant. Idealized aortic models were established based on variables of statistical significance, and hemodynamic simulations were performed to evaluate blood flow changes caused by morphology.Results: Diameters at landmarks of PAS were significantly larger in the ATBAD group. The lumen volume (V PAS ) of PAS in the ATBAD group was significantly enlarged than that of the control group (124,659.07 ± 34,089.27 mm 3 vs 89,796.65 ± 30,334.40 mm 3 ; P < 0.001). Furthermore, the V PAS was positively correlated to diameters. As the V PAS increased, the fluid kinetic energy in PAS enhanced linearly, and time-averaged wall shear stress and oscillatory shear index at the distal area of the left subclavian artery increased significantly. Conclusion:In the ATBAD group, the enlarged V PAS and increased diameters of PAS are positively correlated. Meanwhile, the enlarged V PAS leads to more aggressive hemodynamic parameters at the distal area of the left subclavian artery, which may create a contributory condition for ATBAD.

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Section: Discussionmentioning

confidence: 99%

Enlarged Lumen Volume of Proximal Aortic Segment and Acute Type B Aortic Dissection: A Computer Fluid Dynamics Study of Ideal Aortic Models

Peng¹,

Zhang²,

Li³

et al. 2022

IJGM

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“…Very recently, Dawoud and Kibria [5] proposed a new kind of two-parameter estimator called the Dawoud-Kibria (DK) estimator. There are other recent studies regarding the one parameter and two-parameter estimators in LR and GL models, such as Roozbeh et al [6], Lukman et al [7], Arashi et al [8], Farghali et al [9], Lukman et al [10,11], Algamal and Abonazel [12], Akram et al [13], and Abonazel et al [14]. In this article, we drive the Dawoud-Kibria estimator for the BR model in the presence of the multicollinearity problem.…”

Section: Introductionmentioning

confidence: 90%

“…Furthermore, in terms of the prediction, the R 2 value of the proposed estimator (BDK) is the greatest among all the used estimators. To further highlight the performance of the BDK estimator, generalized cross-validation (GCV) criterion is used in comparison [8,34,35]. Regarding GCV values, it can note that the BDK yielded the least value compared with other estimators.…”

Section: Real Data Applicationmentioning

confidence: 99%

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Abonazel

Dawoud

Awwad

et al. 2022

Front. Appl. Math. Stat.

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The linear regression model becomes unsuitable when the response variable is expressed as percentages, proportions, and rates. The beta regression (BR) model is more appropriate for the variable of this form. The BR model uses the conventional maximum likelihood estimator (BML), and this estimator may not be efficient when the regressors are linearly dependent. The beta ridge estimator was suggested as an alternative to BML in the literature. In this study, we developed the Dawoud–Kibria estimator to handle multicollinearity in the BR model. The properties of the new estimator are derived. We compared the performance of the estimator with the existing estimators theoretically using the mean squared error criterion. A Monte Carlo simulation and a real-life application were carried out to show the benefits of the proposed estimator. The theoretical comparison, simulation, and real-life application results revealed the superiority of the proposed estimator.

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“…Several authors have evaluated the different forms and various types of these biasing parameters. These include Hoerl et al, 25 Kibria, 26 Kibria and Banik, 27 Lukman and Ayinde, 28 Roozbeh et al, 29 Arashi et al, 30 Qasim et al, 31 Lukman et al 32,33 and others. For this new estimator, we introduce different methods for the estimation of k. The optimal value of the k can be considered to be that k that minimizes…”

Section: Determination Of Parameter Kmentioning

confidence: 99%

K‐L estimator for the linear mixed models: Computation and simulation

Lukman

Amin

Kibria

2021

Concurrency and Computation

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This study introduces a new biased estimator called the K-L estimator for the linear mixed model to overcome the effect of multicollinearity. We derived the mean squared error property of the proposed estimator and made a theoretical comparison with other methods. For the assessment of the K-L estimator, we use the mean squared error criterion as a performance evaluation criterion. Moreover, we defined some shrinkage parameters for the proposed estimator. For numerical evaluation, we use a Monte Carlo simulation study and a real example. The result shows the supremacy of the K-L estimator as compared to the available methods under certain conditions. K E Y W O R D SK-L estimator, linear mixed model, multicollinearity, shrinkage parameters 1 where y (n×1) is the vector of response variable and normally distributed with mean X𝛽 and variance 𝜎 2 H such that H = ZGZ ′ + W. The matrix H consists of two components that are used to model heteroscedasticity and correlation: a random effects component ZGZ ′ and a within-group component W. In some applications, the within-group component R is used to directly model the variance-covariance matrix of the data without the need to incorporate random effects in the model to account for dependence among observations. 4 X (n×p) is known design matrix of explanatory variables, Z (n×mq) is a known design matrix, 𝛽 p×1 is a vector of unknown regression parameters of the fixed effects, u (mq×1) is unobservable vector of random effects, and 𝜀 n×1 is the vector of errors. By assumption,

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Ridge regression and its applications in genetic studies

Cited by 49 publications

References 24 publications

Enlarged Lumen Volume of Proximal Aortic Segment and Acute Type B Aortic Dissection: A Computer Fluid Dynamics Study of Ideal Aortic Models

Enlarged Lumen Volume of Proximal Aortic Segment and Acute Type B Aortic Dissection: A Computer Fluid Dynamics Study of Ideal Aortic Models

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

K‐L estimator for the linear mixed models: Computation and simulation

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