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Lu Y, Linderman GC, Mahajan S, Liu Y, Huang C, Khera R, Mortazavi BJ, Spatz ES, Krumholz HM. Quantifying Blood Pressure Visit-to-Visit Variability in the Real-World Setting: A Retrospective Cohort Study. Circ Cardiovasc Qual Outcomes 2023; 16:e009258. [PMID: 36883456 DOI: 10.1161/circoutcomes.122.009258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 01/09/2023] [Indexed: 03/09/2023]
Abstract
BACKGROUND Visit-to-visit variability (VVV) in blood pressure values has been reported in clinical studies. However, little is known about VVV in clinical practice and whether it is associated with patient characteristics in real-world setting. METHODS We conducted a retrospective cohort study to quantify VVV in systolic blood pressure (SBP) values in a real-world setting. We included adults (age ≥18 years) with at least 2 outpatient visits between January 1, 2014 and October 31, 2018 from Yale New Haven Health System. Patient-level measures of VVV included SD and coefficient of variation of a given patient's SBP across visits. We calculated patient-level VVV overall and by patient subgroups. We further developed a multilevel regression model to assess the extent to which VVV in SBP was explained by patient characteristics. RESULTS The study population included 537 218 adults, with a total of 7 721 864 SBP measurements. The mean age was 53.4 (SD 19.0) years, 60.4% were women, 69.4% were non-Hispanic White, and 18.1% were on antihypertensive medications. Patients had a mean body mass index of 28.4 (5.9) kg/m2 and 22.6%, 8.0%, 9.7%, and 5.6% had a history of hypertension, diabetes, hyperlipidemia, and coronary artery disease, respectively. The mean number of visits per patient was 13.3, over an average period of 2.4 years. The mean (SD) intraindividual SD and coefficient of variation of SBP across visits were 10.6 (5.1) mm Hg and 0.08 (0.04). These measures of blood pressure variation were consistent across patient subgroups defined by demographic characteristics and medical history. In the multivariable linear regression model, only 4% of the variance in absolute standardized difference was attributable to patient characteristics. CONCLUSIONS The VVV in real-world practice poses challenges for management of patients with hypertension based on blood pressure readings in outpatient settings and suggest the need to go beyond episodic clinic evaluation.
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Affiliation(s)
- Yuan Lu
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine, CT (Y.L., S.M., R.K., E.S.S., H.M.K.)
| | - George C Linderman
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Department of Applied Mathematics, Yale University, New Haven, CT (G.C.L.)
| | - Shiwani Mahajan
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine, CT (Y.L., S.M., R.K., E.S.S., H.M.K.)
| | - Yuntian Liu
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
| | - Chenxi Huang
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
| | - Rohan Khera
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine, CT (Y.L., S.M., R.K., E.S.S., H.M.K.)
| | - Bobak J Mortazavi
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Department of Computer Science and Engineering, Texas A&M University, College Station, TX (B.M.)
- Center for Remote Health Technologies and Systems, Texas A&M University, College Station, TX (B.M.)
| | - Erica S Spatz
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine, CT (Y.L., S.M., R.K., E.S.S., H.M.K.)
| | - Harlan M Krumholz
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, CT (Y.L., G.C.L., S.M., Y.L., C.H., R.K., B.M., E.S.S., H.M.K.)
- Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine, CT (Y.L., S.M., R.K., E.S.S., H.M.K.)
- Department of Health Policy and Management, Yale School of Public Health, New Haven, CT (H.M.K.)
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Linderman GC, Zhao J, Roulis M, Bielecki P, Flavell RA, Nadler B, Kluger Y. Zero-preserving imputation of single-cell RNA-seq data. Nat Commun 2022; 13:192. [PMID: 35017482 PMCID: PMC8752663 DOI: 10.1038/s41467-021-27729-z] [Citation(s) in RCA: 79] [Impact Index Per Article: 39.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Accepted: 11/30/2021] [Indexed: 01/14/2023] Open
Abstract
A key challenge in analyzing single cell RNA-sequencing data is the large number of false zeros, where genes actually expressed in a given cell are incorrectly measured as unexpressed. We present a method based on low-rank matrix approximation which imputes these values while preserving biologically non-expressed genes (true biological zeros) at zero expression levels. We provide theoretical justification for this denoising approach and demonstrate its advantages relative to other methods on simulated and biological datasets.
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Affiliation(s)
- George C Linderman
- Program in Applied Mathematics, Yale University, New Haven, CT, 06511, USA
| | - Jun Zhao
- Interdepartmental Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, 06511, USA
| | - Manolis Roulis
- Department of Immunobiology, Yale University, New Haven, CT, 06511, USA
| | - Piotr Bielecki
- Department of Immunobiology, Yale University, New Haven, CT, 06511, USA.,Celsius Therapeutics, Cambridge, USA
| | - Richard A Flavell
- Department of Immunobiology, Yale University, New Haven, CT, 06511, USA.,Howard Hughes Medical Institute, Yale University School of Medicine, New Haven, CT, USA
| | - Boaz Nadler
- Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
| | - Yuval Kluger
- Program in Applied Mathematics, Yale University, New Haven, CT, 06511, USA. .,Interdepartmental Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, 06511, USA. .,Department of Pathology, Yale University, New Haven, CT, 06511, USA.
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Linderman GC, Lin W, Becher RD, Maung AA, Bhattacharya B, Davis KA, Schuster KM. Increased mortality with resuscitative endovascular balloon occlusion of the aorta only mitigated by strong unmeasured confounding: An expanded analysis using the National Trauma Data Bank. J Trauma Acute Care Surg 2021; 91:790-797. [PMID: 33951027 PMCID: PMC8547242 DOI: 10.1097/ta.0000000000003265] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
BACKGROUND Resuscitative endovascular balloon occlusion of the aorta (REBOA) is being increasingly adopted to manage noncompressible torso hemorrhage, but a recent analysis of the 2015 to 2016 Trauma Quality Improvement Project (TQIP) data set showed that placement of REBOA was associated with higher rates of death, lower extremity amputation, and acute kidney injury (AKI). We expand this analysis by including the 2017 data set, quantifying the potential role of residual confounding, and distinguishing between traumatic and ischemic lower extremity amputation. METHODS This retrospective study used the 2015 to 2017 TQIP database and included patients older than 18 years, with signs of life on arrival, who had no aortic injury and were not transferred. Resuscitative endovascular balloon occlusions of the aorta placed after 2 hours were excluded. We adjusted for baseline variables using propensity scores with inverse probability of treatment weighting. A sensitivity analysis was then conducted to determine the strength of an unmeasured confounder (e.g., unmeasured shock severity/response to resuscitation) that could explain the effect on mortality. Finally, lower extremity injury patterns of patients undergoing REBOA were inspected to distinguish amputation indicated for traumatic injury from complications of REBOA placement. RESULTS Of 1,392,482 patients meeting the inclusion criteria, 187 underwent REBOA. After inverse probability of treatment weighting, all covariates were balanced. The risk difference for mortality was 0.21 (0.14-0.29) and for AKI was 0.041 (-0.007 to 0.089). For the mortality effect to be explained by an unmeasured confounder, it would need to be stronger than any observed in terms of its relationship with mortality and with REBOA placement. Eleven REBOA patients underwent lower extremity amputation; however, they all suffered severe traumatic injury to the lower extremity. CONCLUSION There is no evidence in the TQIP data set to suggest that REBOA causes amputation, and the evidence for its effect on AKI is considerably weaker than previously reported. The increased mortality effect of REBOA is confirmed and could only be nullified by a potent confounder. LEVEL OF EVIDENCE Therapeutic/care management, level IV.
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Affiliation(s)
- George C. Linderman
- Department of Surgery, Yale School of Medicine
- Applied Mathematics Program, Department of Mathematics, Yale University
| | - Winston Lin
- Department of Statistics and Data Science, Yale University
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Linderman GC, Schuster KM. Authors' response to the letter to the editor by McDonough and Dimitrakoff. J Trauma Acute Care Surg 2021; 91:e128. [PMID: 34254957 DOI: 10.1097/ta.0000000000003355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Linderman GC, Lin W, Sanghvi MR, Becher RD, Maung AA, Bhattacharya B, Davis KA, Schuster KM. Improved outcomes using laparoscopy for emergency colectomy after mitigating bias by negative control exposure analysis. Surgery 2021; 171:305-311. [PMID: 34332782 DOI: 10.1016/j.surg.2021.06.048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 06/11/2021] [Accepted: 06/29/2021] [Indexed: 02/07/2023]
Abstract
BACKGROUND Laparoscopy is superior to open surgery for elective colectomy, but its role in emergency colectomy remains unclear. Previous studies were small and limited by confounding because surgeons may have selected lower-risk patients for laparoscopy. We therefore studied the effect of attempting laparoscopy for emergency colectomies while adjusting for confounding using multiple techniques in a large, nationwide registry. METHODS Using National Surgical Quality Improvement Program data, we identified emergency colectomy cases from 2014 to 2018. We first compared outcomes between patients who underwent laparoscopic versus open surgery, while adjusting for baseline variables using both propensity scores and regression. Next, we performed a negative control exposure analysis. By assuming that the group that converted to open did not benefit from the attempt at laparoscopy, we used the observed benefit to bound the effect of unmeasured confounding. RESULTS Of 21,453 patients meeting criteria, 3,867 underwent laparoscopy, of which 1,375 converted to open. In both inverse probability of treatment weighting and regression analyses, attempting laparoscopy was associated with improved 30-day mortality, overall morbidity, anastomotic leak, surgical site infection, postoperative septic shock, and length of hospital stay compared with open surgery. These effects were consistent with the lower bounds computed from the converted group. CONCLUSION Laparoscopic surgery for colorectal emergencies appears to improve outcomes compared with open surgery. The benefit is observed even after adjusting for both measured and unmeasured confounding using multiple statistical approaches, thus suggesting a benefit not attributable to patient selection.
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Affiliation(s)
- George C Linderman
- Department of Surgery, Yale School of Medicine, New Haven, CT; Applied Mathematics Program, Department of Mathematics, Yale University, New Haven, CT. https://twitter.com/GCLinderman
| | - Winston Lin
- Department of Statistics and Data Science, Yale University, New Haven, CT
| | - Mansi R Sanghvi
- Department of Surgery, Yale School of Medicine, New Haven, CT
| | - Robert D Becher
- Department of Surgery, Yale School of Medicine, New Haven, CT
| | - Adrian A Maung
- Department of Surgery, Yale School of Medicine, New Haven, CT
| | | | - Kimberly A Davis
- Department of Surgery, Yale School of Medicine, New Haven, CT. https://twitter.com/kadtraumamd
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Kobak D, Linderman GC. Initialization is critical for preserving global data structure in both t-SNE and UMAP. Nat Biotechnol 2021; 39:156-157. [PMID: 33526945 DOI: 10.1038/s41587-020-00809-z] [Citation(s) in RCA: 69] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Accepted: 12/23/2020] [Indexed: 01/07/2023]
Affiliation(s)
- Dmitry Kobak
- Institute for Ophthalmic Research, University of Tübingen, Tübingen, Germany.
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Abstract
Dimensionality reduction is a crucial step in essentially every single-cell RNA-sequencing (scRNA-seq) analysis. In this chapter, we describe the typical dimensionality reduction workflow that is used for scRNA-seq datasets, specifically highlighting the roles of principal component analysis, t-distributed stochastic neighborhood embedding, and uniform manifold approximation and projection in this setting. We particularly emphasize efficient computation; the software implementations used in this chapter can scale to datasets with millions of cells.
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Mori M, Brooks C, Spatz E, Mortazavi BJ, Dhruva SS, Linderman GC, Grab LA, Zhang Y, Geirsson A, Chaudhry SI, Krumholz HM. Protocol for project recovery after cardiac surgery: a single-center cohort study leveraging digital platform to characterise longitudinal patient-reported postoperative recovery patterns. BMJ Open 2020; 10:e036959. [PMID: 32873671 PMCID: PMC7467526 DOI: 10.1136/bmjopen-2020-036959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/05/2022] Open
Abstract
INTRODUCTION Improving postoperative patient recovery after cardiac surgery is a priority, but our current understanding of individual variations in recovery and factors associated with poor recovery is limited. We are using a health-information exchange platform to collect patient-reported outcome measures (PROMs) and wearable device data to phenotype recovery patterns in the 30-day period after cardiac surgery hospital discharge, to identify factors associated with these phenotypes and to investigate phenotype associations with clinical outcomes. METHODS AND ANALYSIS We designed a prospective cohort study to enrol 200 patients undergoing valve, coronary artery bypass graft or aortic surgery at a tertiary centre in the USA. We are enrolling patients postoperatively after the intensive care unit discharge and delivering electronic surveys directly to patients every 3 days for 30 days after hospital discharge. We will conduct medical record reviews to collect patient demographics, comorbidity, operative details and hospital course using the Society of Thoracic Surgeons data definitions. We will use phone interview and medical record review data for adjudication of survival, readmission and complications. We will apply group-based trajectory modelling to the time-series PROM and device data to classify patients into distinct categories of recovery trajectories. We will evaluate whether certain recovery pattern predicts death or hospital readmissions, as well as whether clinical factors predict a patient having poor recovery trajectories. We will evaluate whether early recovery patterns predict the overall trajectory at the patient-level. ETHICS AND DISSEMINATION The Yale Institutional Review Board approved this study. Following the description of the study procedure, we obtain written informed consent from all study participants. The consent form states that all personal information, survey response and any medical records are confidential, will not be shared and are stored in an encrypted database. We plan to publish our study findings in peer-reviewed journals.
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Affiliation(s)
- Makoto Mori
- Division of Cardiac Surgery, Yale School of Medicine, New Haven, Connecticut, USA
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, New Haven, Connecticut, USA
| | - Cornell Brooks
- Division of Cardiac Surgery, Yale School of Medicine, New Haven, Connecticut, USA
| | - Erica Spatz
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, New Haven, Connecticut, USA
- Section of Cardiovascular Medicine, Yale School of Medicine, New Haven, Connecticut, USA
| | - Bobak J Mortazavi
- Department of Computer Science and Engineering, Texas A&M University System, College Station, Texas, USA
| | - Sanket S Dhruva
- Department of Medicine, University of California San Francisco, San Francisco, California, USA
| | - George C Linderman
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, New Haven, Connecticut, USA
| | - Lawrence A Grab
- Division of Cardiac Surgery, Yale School of Medicine, New Haven, Connecticut, USA
| | - Yawei Zhang
- Department of Environmental Science, Yale School of Public Health, New Haven, Connecticut, USA
| | - Arnar Geirsson
- Division of Cardiac Surgery, Yale School of Medicine, New Haven, Connecticut, USA
| | - Sarwat I Chaudhry
- Section of General Internal Medicine, Department of Internal Medicine, Yale School of Medicine, New Haven, Connecticut, USA
| | - Harlan M Krumholz
- Center for Outcomes Research and Evaluation, Yale New Haven Hospital, New Haven, Connecticut, USA
- Section of Cardiovascular Medicine, Yale School of Medicine, New Haven, Connecticut, USA
- Department of Health Policy and Management, Yale School of Public Health, New Haven, Connecticut, USA
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Linderman GC, Mishne G, Jaffe A, Kluger Y, Steinerberger S. Randomized near-neighbor graphs, giant components and applications in data science. J Appl Probab 2020; 57:458-476. [PMID: 32913373 PMCID: PMC7480951 DOI: 10.1017/jpr.2020.21] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
If we pick n random points uniformly in [0, 1] d and connect each point to its c d log n-nearest neighbors, where d ≥ 2 is the dimension and c d is a constant depending on the dimension, then it is well known that the graph is connected with high probability. We prove that it suffices to connect every point to c d,1 log log n points chosen randomly among its c d,2 log n-nearest neighbors to ensure a giant component of size n - o(n) with high probability. This construction yields a much sparser random graph with ~ n log log n instead of ~ n log n edges that has comparable connectivity properties. This result has nontrivial implications for problems in data science where an affinity matrix is constructed: instead of connecting each point to its k nearest neighbors, one can often pick k' ≪ k random points out of the k nearest neighbors and only connect to those without sacrificing quality of results. This approach can simplify and accelerate computation; we illustrate this with experimental results in spectral clustering of large-scale datasets.
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Affiliation(s)
- George C Linderman
- Postal address: Applied Mathematics, Yale University, New Haven, CT 06511
| | - Gal Mishne
- Postal address: Applied Mathematics, Yale University, New Haven, CT 06511
| | - Ariel Jaffe
- Postal address: Applied Mathematics, Yale University, New Haven, CT 06511
| | - Yuval Kluger
- Dept. of Pathology & Applied Mathematics, Yale University, New Haven, CT 06511
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Linderman GC, Steinerberger S. NUMERICAL INTEGRATION ON GRAPHS: WHERE TO SAMPLE AND HOW TO WEIGH. Math Comput 2020; 89:1933-1952. [PMID: 33927452 PMCID: PMC8081285 DOI: 10.1090/mcom/3515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Let G = (V,E,w) be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset W ⊂ V of vertices and weights aw such that 1 | V | ∑ v ∈ V f ( v ) ∼ ∑ w ∈ W a w f ( w ) for functions f : V → ℝ that are 'smooth' with respect to the geometry of the graph; here ~ indicates that we want the right-hand side to be as close to the left-hand side as possible. The main application are problems where f is known to vary smoothly over the underlying graph but is expensive to evaluate on even a single vertex. We prove an inequality showing that the integration problem can be rewritten as a geometric problem ('the optimal packing of heat balls'). We discuss how one would construct approximate solutions of the heat ball packing problem; numerical examples demonstrate the efficiency of the method.
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Affiliation(s)
- George C Linderman
- Program in Applied Mathematics, Yale University, New Haven, CT 06511, USA
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Li DT, Linderman GC, Cui JJ, DeVries S, Nicholson AD, Li E, Petit L, Kahan JB, Talty R, Kluger Y, Cooperman DR, Smith BG. The Proximal Humeral Ossification System Improves Assessment of Maturity in Patients with Scoliosis. J Bone Joint Surg Am 2019; 101:1868-1874. [PMID: 31626012 PMCID: PMC7515481 DOI: 10.2106/jbjs.19.00296] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
BACKGROUND We recently developed a classification system to assess skeletal maturity by scoring proximal humeral ossification in a similar way to the canonical Risser sign. The purpose of the present study was to determine whether our system can be used to reliably assess radiographs of the spine for modern patients with idiopathic scoliosis, whether it can be used in combination with the Sanders hand system, and whether the consideration of patient factors such as age, sex, and standing height improves the accuracy of predictions. METHODS We retrospectively reviewed 414 randomized radiographs from 216 modern patients with scoliosis and measured reliability with use of the intraclass correlation coefficient (ICC). We then analyzed 606 proximal humeral radiographs for 70 children from a historical collection to determine the value of integrating multiple classification systems. The age of peak height velocity (PHV) was predicted with use of linear regression models, and performance was evaluated with use of tenfold cross-validation. RESULTS The proximal humeral ossification system demonstrated excellent reliability in modern patients with scoliosis, with an ICC of 0.97 and 0.92 for intraobserver and interobserver comparisons, respectively. The use of our system in combination with the Sanders hand system yielded 7 categories prior to PHV and demonstrated better results compared with either system alone. Linear regression algorithms showed that integration of the proximal part of the humerus, patient factors, and other classification systems outperformed models based on canonical Risser and triradiate-closure methods. CONCLUSIONS Humeral head ossification can be reliably assessed in modern patients with scoliosis. Furthermore, the system described here can be used in combination with other parameters such as the Sanders hand system, age, sex, and height to predict PHV and percent growth remaining with high accuracy. CLINICAL RELEVANCE The proximal humeral ossification system can improve the prediction of PHV in patients with scoliosis on the basis of a standard spine radiograph without a hand radiograph for the determination of bone age. This increased accuracy for predicting maturity will allow physicians to better assess patient maturity relative to PHV and therefore can help to guide treatment decision-making without increasing radiation exposure, time, or cost. The present study demonstrates that assessment of the proximal humeral physis is a viable and valuable aid in the determination of skeletal maturity as obtained from radiographs of the spine that happen to include the shoulder in adolescent patients with idiopathic scoliosis.
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Affiliation(s)
- Don T. Li
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - George C. Linderman
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Jonathan J. Cui
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Stephen DeVries
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Allen D. Nicholson
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Eric Li
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Logan Petit
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Joseph B. Kahan
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Ronan Talty
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Yuval Kluger
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Daniel R. Cooperman
- Departments of Orthopaedics and Rehabilitation (D.T.L., G.C.L., J.J.C., S.D., A.D.N., E.L., L.P., J.B.K., R.T., and D.R.C.), Cell Biology (D.T.L.), Applied Mathematics (G.C.L.), and Pathology (Y.K.), Yale School of Medicine, New Haven, Connecticut
| | - Brian G. Smith
- Division of Orthopaedics and Scoliosis, Texas Children’s Hospital, Houston, Texas
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Abstract
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters; more precisely, we prove that t-SNE in the 'early exaggeration' phase, an optimization technique proposed by van der Maaten & Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter α and step size h. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods.
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Affiliation(s)
- George C Linderman
- Program in Applied Mathematics, Yale University, New Haven, CT 06511, USA
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Linderman GC, Rachh M, Hoskins JG, Steinerberger S, Kluger Y. Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data. Nat Methods 2019; 16:243-245. [PMID: 30742040 PMCID: PMC6402590 DOI: 10.1038/s41592-018-0308-4] [Citation(s) in RCA: 217] [Impact Index Per Article: 43.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Accepted: 12/12/2018] [Indexed: 11/29/2022]
Abstract
t-distributed stochastic neighbor embedding (t-SNE) is widely used for visualizing single-cell RNA-sequencing (scRNA-seq) data, but it scales poorly to large datasets. We dramatically accelerate t-SNE, obviating the need for data downsampling, and hence allowing visualization of rare cell populations. Furthermore, we implement a heatmap-style visualization for scRNA-seq based on one-dimensional t-SNE for simultaneously visualizing the expression patterns of thousands of genes. Software is available at https://github.com/KlugerLab/FIt-SNE and https://github.com/KlugerLab/t-SNE-Heatmaps .
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Affiliation(s)
| | - Manas Rachh
- Applied Mathematics Program, Yale University, New Haven, CT, USA
| | - Jeremy G Hoskins
- Applied Mathematics Program, Yale University, New Haven, CT, USA
| | | | - Yuval Kluger
- Applied Mathematics Program, Yale University, New Haven, CT, USA.
- Department of Pathology, Yale University School of Medicine, New Haven, CT, USA.
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Abstract
IMPORTANCE Body mass index (BMI) is positively associated with blood pressure (BP); this association has critical implications for countries like China, where hypertension is highly prevalent and obesity is increasing. A greater understanding of the association between BMI and BP is required to determine its effect and develop strategies to mitigate it. OBJECTIVE To assess the heterogeneity in the association between BMI and BP across a wide variety of subgroups of the Chinese population. DESIGN, SETTING, AND PARTICIPANTS In this cross-sectional study, data were collected at 1 time point from 1.7 million adults (aged 35-80 years) from 141 primary health care sites (53 urban districts and 88 rural counties) from all 31 provinces in mainland China who were enrolled in the China PEACE (Patient-Centered Evaluative Assessment of Cardiac Events) Million Persons Project, conducted between September 15, 2014, and June 20, 2017. A comprehensive subgroup analysis was performed by defining more than 22 000 subgroups of individuals based on covariates, and within each subgroup, linearly regressing BMI to BP. MAIN OUTCOMES AND MEASURES Systolic BP was measured twice with the participant in a seated position, using an electronic BP monitor. RESULTS The study included 1 727 411 participants (1 027 711 women and 699 700 men; mean [SD] age, 55.7 [9.8] years). Among the study sample, the mean (SD) BMI was 24.7 (3.5), the mean (SD) systolic BP was 136.5 (20.4) mm Hg, and the mean (SD) diastolic BP was 81.1 (11.2) mm Hg. The increase of BP per unit BMI ranged from 0.8 to 1.7 mm Hg/(kg/m2) for 95% of the subgroups not taking antihypertensive medication. The association between BMI and BP was substantially weaker in subgroups of patients taking antihypertensive medication compared with those who were untreated. In untreated subgroups, 95% of the coefficients varied by less than 1 mm Hg/(kg/m2). CONCLUSIONS AND RELEVANCE The association between BMI and BP is positive across tens of thousands of individuals in population subgroups, and, if causal, given its magnitude, would have significant implications for public health.
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Affiliation(s)
- George C. Linderman
- Center for Outcomes Research and Evaluation, Yale–New Haven Hospital, Yale University, New Haven, Connecticut
| | - Jiapeng Lu
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, People’s Republic of China
| | - Yuan Lu
- Center for Outcomes Research and Evaluation, Yale–New Haven Hospital, Yale University, New Haven, Connecticut
| | - Xin Sun
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, People’s Republic of China
| | - Wei Xu
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, People’s Republic of China
| | - Khurram Nasir
- Center for Prevention and Wellness Research, Baptist Health Medical Group, Miami Beach, Florida
| | - Wade Schulz
- Center for Outcomes Research and Evaluation, Yale–New Haven Hospital, Yale University, New Haven, Connecticut
- Department of Laboratory Medicine, Yale School of Medicine, New Haven, Connecticut
| | - Lixin Jiang
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, People’s Republic of China
| | - Harlan M. Krumholz
- Center for Outcomes Research and Evaluation, Yale–New Haven Hospital, Yale University, New Haven, Connecticut
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Lu J, Lu Y, Wang X, Li X, Linderman GC, Wu C, Cheng X, Mu L, Zhang H, Liu J, Su M, Zhao H, Spatz ES, Spertus JA, Masoudi FA, Krumholz HM, Jiang L. Prevalence, awareness, treatment, and control of hypertension in China: data from 1·7 million adults in a population-based screening study (China PEACE Million Persons Project). Lancet 2017; 390:2549-2558. [PMID: 29102084 DOI: 10.1016/s0140-6736(17)32478-9] [Citation(s) in RCA: 673] [Impact Index Per Article: 96.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Revised: 09/11/2017] [Accepted: 09/12/2017] [Indexed: 12/18/2022]
Abstract
BACKGROUND Hypertension is common in China and its prevalence is rising, yet it remains inadequately controlled. Few studies have the capacity to characterise the epidemiology and management of hypertension across many heterogeneous subgroups. We did a study of the prevalence, awareness, treatment, and control of hypertension in China and assessed their variations across many subpopulations. METHODS We made use of data generated in the China Patient-Centered Evaluative Assessment of Cardiac Events (PEACE) Million Persons Project from Sept 15, 2014, to June 20, 2017, a population-based screening project that enrolled around 1·7 million community-dwelling adults aged 35-75 years from all 31 provinces in mainland China. In this population, we defined hypertension as systolic blood pressure of at least 140 mm Hg, or diastolic blood pressure of at least 90 mm Hg, or self-reported antihypertensive medication use in the previous 2 weeks. Hypertension awareness, treatment, and control were defined, respectively, among hypertensive adults as a self-reported diagnosis of hypertension, current use of antihypertensive medication, and blood pressure of less than 140/90 mm Hg. We assessed awareness, treatment, and control in 264 475 population subgroups-defined a priori by all possible combinations of 11 demographic and clinical factors (age [35-44, 45-54, 55-64, and 65-75 years], sex [men and women], geographical region [western, central, and eastern China], urbanity [urban vs rural], ethnic origin [Han and non-Han], occupation [farmer and non-farmer], annual household income [< ¥10 000, ¥10 000-50 000, and ≥¥50 000], education [primary school and below, middle school, high school, and college and above], previous cardiovascular events [yes or no], current smoker [yes or no], and diabetes [yes or no]), and their associations with individual and primary health-care site characteristics, using mixed models. FINDINGS The sample contained 1 738 886 participants with a mean age of 55·6 years (SD 9·7), 59·5% of whom were women. 44·7% (95% CI 44·6-44·8) of the sample had hypertension, of whom 44·7% (44·6-44·8) were aware of their diagnosis, 30·1% (30·0-30·2) were taking prescribed antihypertensive medications, and 7·2% (7·1-7·2) had achieved control. The age-standardised and sex-standardised rates of hypertension prevalence, awareness, treatment, and control were 37·2% (37·1-37·3), 36·0% (35·8-36·2), 22·9% (22·7-23·0), and 5·7% (5·6-5·7), respectively. The most commonly used medication class was calcium-channel blockers (55·2%, 55·0-55·4). Among individuals whose hypertension was treated but not controlled, 81·5% (81·3-81·6) were using only one medication. The proportion of participants who were aware of their hypertension and were receiving treatment varied significantly across subpopulations; lower likelihoods of awareness and treatment were associated with male sex, younger age, lower income, and an absence of previous cardiovascular events, diabetes, obesity, or alcohol use (all p<0·01). By contrast, control rate was universally low across all subgroups (<30·0%). INTERPRETATION Among Chinese adults aged 35-75 years, nearly half have hypertension, fewer than a third are being treated, and fewer than one in twelve are in control of their blood pressure. The low number of people in control is ubiquitous in all subgroups of the Chinese population and warrants broad-based, global strategy, such as greater efforts in prevention, as well as better screening and more effective and affordable treatment. FUNDING Ministry of Finance and National Health and Family Planning Commission, China.
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Affiliation(s)
- Jiapeng Lu
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | - Yuan Lu
- Center for Outcomes Research and Evaluation, Yale University/Yale-New Haven Hospital, New Haven, CT, USA
| | | | - Xinyue Li
- Department of Biostatistics, New Haven, CT, USA
| | - George C Linderman
- Center for Outcomes Research and Evaluation, Yale University/Yale-New Haven Hospital, New Haven, CT, USA
| | - Chaoqun Wu
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | | | - Lin Mu
- Center for Outcomes Research and Evaluation, Yale University/Yale-New Haven Hospital, New Haven, CT, USA
| | - Haibo Zhang
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | - Jiamin Liu
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | - Meng Su
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | - Hongyu Zhao
- Department of Biostatistics, New Haven, CT, USA
| | - Erica S Spatz
- Center for Outcomes Research and Evaluation, Yale University/Yale-New Haven Hospital, New Haven, CT, USA
| | - John A Spertus
- Health Outcomes Research, Saint Luke's Mid America Heart Institute/University of Missouri-Kansas City, Kansas City, MS, USA
| | - Frederick A Masoudi
- Division of Cardiology, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
| | - Harlan M Krumholz
- Center for Outcomes Research and Evaluation, Yale University/Yale-New Haven Hospital, New Haven, CT, USA
| | - Lixin Jiang
- National Clinical Research Center of Cardiovascular Diseases, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China.
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Li H, Linderman GC, Szlam A, Stanton KP, Kluger Y, Tygert M. Algorithm 971: An Implementation of a Randomized Algorithm for Principal Component Analysis. ACM Trans Math Softw 2017; 43:28. [PMID: 28983138 PMCID: PMC5625842 DOI: 10.1145/3004053] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Accepted: 09/01/2016] [Indexed: 06/07/2023]
Abstract
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks' MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).
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Affiliation(s)
- Huamin Li
- Program in Applied Mathematics, 51 Prospect St., Yale University, New Haven, CT 06510
| | - George C Linderman
- Program in Applied Mathematics, 51 Prospect St., Yale University, New Haven, CT 06510
| | - Arthur Szlam
- Facebook, 8th floor, 770 Broadway, New York, NY 10003
| | - Kelly P Stanton
- Yale University, School of Medicine, Department of Pathology, Suite 505L, 300 George St., New Haven, CT 06520
| | - Yuval Kluger
- Yale University, School of Medicine, Department of Pathology, Suite 505L, 300 George St., New Haven, CT 06520
| | - Mark Tygert
- Facebook, 1 Facebook Way, Menlo Park, CA 94025
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Jenkins MW, Linderman GC, Bezerra HG, Fujino Y, Costa MA, Wilson DL, Rollins AM. 3-D Stent Detection in Intravascular OCT Using a Bayesian Network and Graph Search. IEEE Trans Med Imaging 2015; 34:1549-1561. [PMID: 25751863 PMCID: PMC4547908 DOI: 10.1109/tmi.2015.2405341] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Worldwide, many hundreds of thousands of stents are implanted each year to revascularize occlusions in coronary arteries. Intravascular optical coherence tomography is an important emerging imaging technique, which has the resolution and contrast necessary to quantitatively analyze stent deployment and tissue coverage following stent implantation. Automation is needed, as current, it takes up to 16 h to manually analyze hundreds of images and thousands of stent struts from a single pullback. For automated strut detection, we used image formation physics and machine learning via a Bayesian network, and 3-D knowledge of stent structure via graph search. Graph search was done on en face projections using minimum spanning tree algorithms. Depths of all struts in a pullback were simultaneously determined using graph cut. To assess the method, we employed the largest validation data set used so far, involving more than 8000 clinical images from 103 pullbacks from 72 patients. Automated strut detection achieved a 0.91±0.04 recall, and 0.84±0.08 precision. Performance was robust in images of varying quality. This method can improve the workflow for analysis of stent clinical trial data, and can potentially be used in the clinic to facilitate real-time stent analysis and visualization, aiding stent implantation.
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18
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Abstract
MicroArray Gene expression and Network Evaluation Toolkit (MAGNET) is a web-based application that provides tools to generate and score both protein-protein interaction networks and coexpression networks. MAGNET integrates user-provided experimental measurements with high-throughput proteomic datasets, generating weighted gene-gene and protein-protein interaction networks. MAGNET allows users to weight edges of protein-protein interaction networks using a logistic regression model integrating tissue-specific gene expression data, sub-cellular localization data, co-clustering of interacting proteins and the number of observations of the interaction. This provides a way to quantitatively measure the plausibility of interactions in protein-protein interaction networks given protein/gene expression measurements. Secondly, MAGNET generates filtered coexpression networks, where genes are represented as nodes, and their correlations are represented with edges. Overall, MAGNET provides researchers with a new framework with which to analyze and generate gene-gene and protein-protein interaction networks, based on both the user's own data and publicly available -omics datasets. The freely available service and documentation can be accessed at http://gurkan.case.edu/software or http://magnet.case.edu.
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Affiliation(s)
- George C Linderman
- Department of Biomedical Engineering, Center for Proteomics and Bioinformatics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, USA
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Linderman GC, Patel VN, Chance MR, Bebek G. BiC: a web server for calculating bimodality of coexpression between gene and protein networks. Bioinformatics 2011; 27:1174-5. [PMID: 21345871 PMCID: PMC3072551 DOI: 10.1093/bioinformatics/btr086] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2010] [Revised: 02/01/2011] [Accepted: 02/09/2011] [Indexed: 11/13/2022] Open
Abstract
UNLABELLED Bimodal patterns of expression have recently been shown to be useful not only in prioritizing genes that distinguish phenotypes, but also in prioritizing network models that correlate with proteomic evidence. In particular, subgroups of strongly coexpressed gene pairs result in an increased variance of the correlation distribution. This variance, a measure of association between sets of genes (or proteins), can be summarized as the bimodality of coexpression (BiC). We developed an online tool to calculate the BiC for user-defined gene lists and associated mRNA expression data. BiC is a comprehensive application that provides researchers with the ability to analyze both publicly available and user-collected array data. AVAILABILITY The freely available web service and the documentation can be accessed at http://gurkan.case.edu/software. CONTACT gurkan@case.edu.
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Affiliation(s)
- George C Linderman
- Department of Biomedical Engineering, Case Center for Proteomics and Bioinformatics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
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