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Sun N, Chu J, Hu W, Chen X, Yi N, Shen Y. A novel 14-gene signature for overall survival in lung adenocarcinoma based on the Bayesian hierarchical Cox proportional hazards model. Sci Rep 2022; 12:27. [PMID: 34996932 PMCID: PMC8741994 DOI: 10.1038/s41598-021-03645-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 12/06/2021] [Indexed: 12/14/2022] Open
Abstract
There have been few investigations of cancer prognosis models based on Bayesian hierarchical models. In this study, we used a novel Bayesian method to screen mRNAs and estimate the effects of mRNAs on the prognosis of patients with lung adenocarcinoma. Based on the identified mRNAs, we can build a prognostic model combining mRNAs and clinical features, allowing us to explore new molecules with the potential to predict the prognosis of lung adenocarcinoma. The mRNA data (n = 594) and clinical data (n = 470) for lung adenocarcinoma were obtained from the TCGA database. Gene set enrichment analysis (GSEA), univariate Cox proportional hazards regression, and the Bayesian hierarchical Cox proportional hazards model were used to explore the mRNAs related to the prognosis of lung adenocarcinoma. Multivariate Cox proportional hazard regression was used to identify independent markers. The prediction performance of the prognostic model was evaluated not only by the internal cross-validation but also by the external validation based on the GEO dataset (n = 437). With the Bayesian hierarchical Cox proportional hazards model, a 14-gene signature that included CPS1, CTPS2, DARS2, IGFBP3, MCM5, MCM7, NME4, NT5E, PLK1, POLR3G, PTTG1, SERPINB5, TXNRD1, and TYMS was established to predict overall survival in lung adenocarcinoma. Multivariate analysis demonstrated that the 14-gene signature (HR 3.960, 95% CI 2.710–5.786), T classification (T1, reference; T3, HR 1.925, 95% CI 1.104–3.355) and N classification (N0, reference; N1, HR 2.212, 95% CI 1.520–3.220; N2, HR 2.260, 95% CI 1.499–3.409) were independent predictors. The C-index of the model was 0.733 and 0.735, respectively, after performing cross-validation and external validation, a nomogram was provided for better prediction in clinical application. Bayesian hierarchical Cox proportional hazards models can be used to integrate high-dimensional omics information into a prediction model for lung adenocarcinoma to improve the prognostic prediction and discover potential targets. This approach may be a powerful predictive tool for clinicians treating malignant tumours.
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Affiliation(s)
- Na Sun
- Department of Epidemiology and Biostatistics, School of Public Health, Medical College of Soochow University, Suzhou, 215123, China
| | - Jiadong Chu
- Department of Epidemiology and Biostatistics, School of Public Health, Medical College of Soochow University, Suzhou, 215123, China
| | - Wei Hu
- Department of Epidemiology and Biostatistics, School of Public Health, Medical College of Soochow University, Suzhou, 215123, China
| | - Xuanli Chen
- Department of Epidemiology and Biostatistics, School of Public Health, Medical College of Soochow University, Suzhou, 215123, China
| | - Nengjun Yi
- Department of Biostatistics, School of Public Health, University of Alabama at Birmingham, Birmingham, AL, 35294, USA
| | - Yueping Shen
- Department of Epidemiology and Biostatistics, School of Public Health, Medical College of Soochow University, Suzhou, 215123, China.
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Ramzan Q, Akram MN, Amin M. Ridge parameter estimation for the linear regression model under different loss functions using T-K approximation. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1962345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Qasim Ramzan
- Department of Statistics, University of Sargodha, Sagodha, Pakistan
| | | | - Muhammad Amin
- Department of Statistics, University of Sargodha, Sagodha, Pakistan
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3
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Jhuang AT, Fuentes M, Jones JL, Esteves G, Fancher CM, Furman M, Reich BJ. Spatial Signal Detection Using Continuous Shrinkage Priors. Technometrics 2019; 61:494-506. [PMID: 31723308 PMCID: PMC6853616 DOI: 10.1080/00401706.2018.1546622] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Revised: 11/01/2018] [Accepted: 11/06/2018] [Indexed: 10/27/2022]
Abstract
Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. We apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.
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Affiliation(s)
- An-Ting Jhuang
- Department of Statistics, North Carolina State University, Raleigh, NC 27695
| | - Montserrat Fuentes
- College of Humanities and Sciences, Virginia Commonwealth University, Richmond, VA 23284
| | - Jacob L Jones
- Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695
| | - Giovanni Esteves
- Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695
| | - Chris M Fancher
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
| | - Marschall Furman
- Department of Statistics, North Carolina State University, Raleigh, NC 27695
| | - Brian J Reich
- Department of Statistics, North Carolina State University, Raleigh, NC 27695
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Abstract
Bayesian variable selection often assumes normality, but the effects of model misspecification are not sufficiently understood. There are sound reasons behind this assumption, particularly for large p: ease of interpretation, analytical and computational convenience. More flexible frameworks exist, including semi- or non-parametric models, often at the cost of some tractability. We propose a simple extension that allows for skewness and thicker-than-normal tails but preserves tractability. It leads to easy interpretation and a log-concave likelihood that facilitates optimization and integration. We characterize asymptotically parameter estimation and Bayes factor rates, under certain model misspecification. Under suitable conditions misspecified Bayes factors induce sparsity at the same rates than under the correct model. However, the rates to detect signal change by an exponential factor, often reducing sensitivity. These deficiencies can be ameliorated by inferring the error distribution, a simple strategy that can improve inference substantially. Our work focuses on the likelihood and can be combined with any likelihood penalty or prior, but here we focus on non-local priors to induce extra sparsity and ameliorate finite-sample effects caused by misspecification. We show the importance of considering the likelihood rather than solely the prior, for Bayesian variable selection. The methodology is in R package 'mombf'.
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Affiliation(s)
- David Rossell
- Universitat Pompeu Fabra, Department of Business and Economics, Barcelona (Spain)
| | - Francisco J Rubio
- London School of Hygiene & Tropical Medicine, London (United Kingdom)
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Schwager E, Mallick H, Ventz S, Huttenhower C. A Bayesian method for detecting pairwise associations in compositional data. PLoS Comput Biol 2017; 13:e1005852. [PMID: 29140991 PMCID: PMC5706738 DOI: 10.1371/journal.pcbi.1005852] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Revised: 11/29/2017] [Accepted: 10/25/2017] [Indexed: 12/12/2022] Open
Abstract
Compositional data consist of vectors of proportions normalized to a constant sum from a basis of unobserved counts. The sum constraint makes inference on correlations between unconstrained features challenging due to the information loss from normalization. However, such correlations are of long-standing interest in fields including ecology. We propose a novel Bayesian framework (BAnOCC: Bayesian Analysis of Compositional Covariance) to estimate a sparse precision matrix through a LASSO prior. The resulting posterior, generated by MCMC sampling, allows uncertainty quantification of any function of the precision matrix, including the correlation matrix. We also use a first-order Taylor expansion to approximate the transformation from the unobserved counts to the composition in order to investigate what characteristics of the unobserved counts can make the correlations more or less difficult to infer. On simulated datasets, we show that BAnOCC infers the true network as well as previous methods while offering the advantage of posterior inference. Larger and more realistic simulated datasets further showed that BAnOCC performs well as measured by type I and type II error rates. Finally, we apply BAnOCC to a microbial ecology dataset from the Human Microbiome Project, which in addition to reproducing established ecological results revealed unique, competition-based roles for Proteobacteria in multiple distinct habitats.
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Affiliation(s)
- Emma Schwager
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, United States of America
- Broad Institute of MIT and Harvard, Cambridge, Massachusetts, United States of America
| | - Himel Mallick
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, United States of America
- Broad Institute of MIT and Harvard, Cambridge, Massachusetts, United States of America
| | - Steffen Ventz
- Department of Computer Science and Statistics, University of Rhode Island, Kingstown, Rhode Island, United States of America
- Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, Massachusetts, United States of America
| | - Curtis Huttenhower
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, United States of America
- Broad Institute of MIT and Harvard, Cambridge, Massachusetts, United States of America
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Erler NS, Rizopoulos D, Jaddoe VW, Franco OH, Lesaffre EM. Bayesian imputation of time-varying covariates in linear mixed models. Stat Methods Med Res 2017; 28:555-568. [PMID: 29069967 PMCID: PMC6344996 DOI: 10.1177/0962280217730851] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Studies involving large observational datasets commonly face the challenge of
dealing with multiple missing values. The most popular approach to overcome this
challenge, multiple imputation using chained equations, however, has been shown
to be sub-optimal in complex settings, specifically in settings with
longitudinal outcomes, which cannot be easily and adequately included in the
imputation models. Bayesian methods avoid this difficulty by specification of a
joint distribution and thus offer an alternative. A popular choice for that
joint distribution is the multivariate normal distribution. In more complicated
settings, as in our two motivating examples that involve time-varying
covariates, additional issues require consideration: the endo- or exogeneity of
the covariate and its functional relation with the outcome. In such situations,
the implied assumptions of standard methods may be violated, resulting in bias.
In this work, we extend and study a more flexible, Bayesian alternative to the
multivariate normal approach, to better handle complex incomplete longitudinal
data. We discuss and compare assumptions of the two Bayesian approaches about
the endo- or exogeneity of the covariates and the functional form of the
association with the outcome, and illustrate and evaluate consequences of
violations of those assumptions using simulation studies and two real data
examples.
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Affiliation(s)
- Nicole S Erler
- 1 Department of Biostatistics, Erasmus MC, Rotterdam, The Netherlands.,2 Department of Epidemiology, Erasmus MC, Rotterdam, The Netherlands
| | | | - Vincent Wv Jaddoe
- 2 Department of Epidemiology, Erasmus MC, Rotterdam, The Netherlands.,3 Department of Pediatrics, Erasmus MC, Rotterdam, The Netherlands.,4 Generation R Study Group, Erasmus MC, University Medical Center, Rotterdam, The Netherlands
| | - Oscar H Franco
- 2 Department of Epidemiology, Erasmus MC, Rotterdam, The Netherlands
| | - Emmanuel Meh Lesaffre
- 1 Department of Biostatistics, Erasmus MC, Rotterdam, The Netherlands.,5 L-Biostat, KU Leuven, Leuven, Belgium
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Andrinopoulou ER, Rizopoulos D. Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures. Stat Med 2016; 35:4813-4823. [PMID: 27383428 DOI: 10.1002/sim.7027] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2016] [Revised: 05/25/2016] [Accepted: 06/09/2016] [Indexed: 11/05/2022]
Abstract
The joint modeling of longitudinal and survival data has recently received much attention. Several extensions of the standard joint model that consists of one longitudinal and one survival outcome have been proposed including the use of different association structures between the longitudinal and the survival outcomes. However, in general, relatively little attention has been given to the selection of the most appropriate functional form to link the two outcomes. In common practice, it is assumed that the underlying value of the longitudinal outcome is associated with the survival outcome. However, it could be that different characteristics of the patients' longitudinal profiles influence the hazard. For example, not only the current value but also the slope or the area under the curve of the longitudinal outcome. The choice of which functional form to use is an important decision that needs to be investigated because it could influence the results. In this paper, we use a Bayesian shrinkage approach in order to determine the most appropriate functional forms. We propose a joint model that includes different association structures of different biomarkers and assume informative priors for the regression coefficients that correspond to the terms of the longitudinal process. Specifically, we assume Bayesian lasso, Bayesian ridge, Bayesian elastic net, and horseshoe. These methods are applied to a dataset consisting of patients with a chronic liver disease, where it is important to investigate which characteristics of the biomarkers have an influence on survival. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
| | - Dimitris Rizopoulos
- Department of Biostatistics, Erasmus MC, PO Box 2040, Rotterdam, 3000, CA, The Netherlands
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Digre KB, Bruce BB, McDermott MP, Galetta KM, Balcer LJ, Wall M. Quality of life in idiopathic intracranial hypertension at diagnosis: IIH Treatment Trial results. Neurology 2015; 84:2449-56. [PMID: 25995055 PMCID: PMC4478032 DOI: 10.1212/wnl.0000000000001687] [Citation(s) in RCA: 65] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2014] [Accepted: 03/09/2015] [Indexed: 12/23/2022] Open
Abstract
OBJECTIVE The study purpose was to examine vision-specific and overall health-related quality of life (QOL) at baseline in Idiopathic Intracranial Hypertension Treatment Trial patients who were newly diagnosed and had mild visual loss. We also sought to determine the associations between vision-specific QOL scores and visual symptoms, visual function, pain, headache-related disability, and obesity. METHODS We assessed QOL using the 36-Item Short Form Health Survey, National Eye Institute Visual Function Questionnaire-25 (NEI-VFQ-25), and 10-Item NEI-VFQ-25 Neuro-Ophthalmic Supplement. We compared these results with those of previously reported idiopathic intracranial hypertension (IIH) QOL studies. We assessed relationships between QOL and other clinical characteristics. RESULTS Among 165 participants with IIH (161 women and 4 men with a mean age ± SD of 29.2 ± 7.5 years), vision-specific QOL scores were reduced compared with published values for disease-free controls. Scores of participants were comparable to published results for patients with multiple sclerosis and a history of optic neuritis. A multiple linear regression model for the NEI-VFQ-25 composite score found that perimetric mean deviation in the best eye, visual acuity in the worst eye, visual symptoms, and pain symptoms (headache, neck pain), but not obesity, were independently associated with QOL. CONCLUSIONS IIH affects QOL at time of diagnosis even in patients with mild visual impairment. Vision-specific QOL in patients with newly diagnosed IIH may be as decreased as that for patients with other neuro-ophthalmic disorders. IIH treatment should target visual loss and other symptoms of increased intracranial pressure associated with reduced QOL. Reduced QOL does not simply reflect obesity, an underlying IIH risk factor.
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Affiliation(s)
- Kathleen B Digre
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City.
| | - Beau B Bruce
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City
| | - Michael P McDermott
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City
| | - Kristin M Galetta
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City
| | - Laura J Balcer
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City
| | - Michael Wall
- From the Moran Eye Center (K.B.D.), University of Utah, Salt Lake City; Departments of Ophthalmology, Neurology, and Epidemiology (B.B.B.), Emory University, Atlanta, GA; Departments of Biostatistics and Computational Biology and Neurology (M.P.M.), and Center for Human Experimental Therapeutics, University of Rochester Medical Center, NY; Department of Neurology (K.M.G.), University of Pennsylvania School of Medicine, Philadelphia; Departments of Neurology and Ophthalmology (L.J.B.), New York University; and Department of Ophthalmology and Visual Sciences (M.W.), University of Iowa Carver College of Medicine, Iowa City
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