1
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He X, Pan X, Tan KM, Zhou WX. Scalable estimation and inference for censored quantile regression process. Ann Stat 2022. [DOI: 10.1214/22-aos2214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Xuming He
- Department of Statistics, University of Michigan
| | - Xiaoou Pan
- Department of Mathematical Sciences, University of California, San Diego
| | | | - Wen-Xin Zhou
- Department of Mathematical Sciences, University of California, San Diego
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2
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Li J, Liu J, Pei Y, Zhang R. Estimating restricted mean treatment effects with additive-multiplicative hazards models. J Nonparametr Stat 2022. [DOI: 10.1080/10485252.2022.2108810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Jinhong Li
- Department of Statistics, East China Normal University, Shanghai, People's Republic of China
- KLATASDS-MOE, East China Normal University, Shanghai, People's Republic of China
| | - Jicai Liu
- School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
| | - Yanbo Pei
- School of Statistics, Capital University of Economics and Business, Beijing, People's Republic of China
| | - Riquan Zhang
- KLATASDS-MOE, East China Normal University, Shanghai, People's Republic of China
- School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China
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3
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Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models. MATHEMATICS 2022. [DOI: 10.3390/math10122000] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The single-index model is an intuitive extension of the linear regression model. It has been increasingly popular due to its flexibility in modeling. In this work, we focus on the estimators of the parameters and the unknown link function for the single-index model in a high-dimensional situation. The SCAD and Laplace error penalty (LEP)-based penalized composite quantile regression estimators, which could realize variable selection and estimation simultaneously, are proposed; a practical iterative algorithm is introduced to obtain the efficient and robust estimators. The choices of the tuning parameters, the bandwidth, and the initial values are also discussed. Furthermore, under some mild conditions, we show the large sample properties and oracle property of the SCAD and Laplace penalized composite quantile regression estimators. Finally, we evaluated the performances of the proposed estimators by two numerical simulations and a real data application.
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Qin X, Yin D, Dong X, Chen D, Zhang S. Survival prediction model for right-censored data based on improved composite quantile regression neural network. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:7521-7542. [PMID: 35801434 DOI: 10.3934/mbe.2022354] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
With the development of the field of survival analysis, statistical inference of right-censored data is of great importance for the study of medical diagnosis. In this study, a right-censored data survival prediction model based on an improved composite quantile regression neural network framework, called rcICQRNN, is proposed. It incorporates composite quantile regression with the loss function of a multi-hidden layer feedforward neural network, combined with an inverse probability weighting method for survival prediction. Meanwhile, the hyperparameters involved in the neural network are adjusted using the WOA algorithm, integer encoding and One-Hot encoding are implemented to encode the classification features, and the BWOA variable selection method for high-dimensional data is proposed. The rcICQRNN algorithm was tested on a simulated dataset and two real breast cancer datasets, and the performance of the model was evaluated by three evaluation metrics. The results show that the rcICQRNN-5 model is more suitable for analyzing simulated datasets. The One-Hot encoding of the WOA-rcICQRNN-30 model is more applicable to the NKI70 data. The model results are optimal for k=15 after feature selection for the METABRIC dataset. Finally, we implemented the method for cross-dataset validation. On the whole, the Cindex results using One-Hot encoding data are more stable, making the proposed rcICQRNN prediction model flexible enough to assist in medical decision making. It has practical applications in areas such as biomedicine, insurance actuarial and financial economics.
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Affiliation(s)
- Xiwen Qin
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
| | - Dongmei Yin
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
| | - Xiaogang Dong
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
| | - Dongxue Chen
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
| | - Shuang Zhang
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
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5
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Feng H, Luo Q. A weighted quantile regression for nonlinear models with randomly censored data. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2020.1713364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Hailin Feng
- School of Mathematics and Statistics, Xidian University, Xian, China
| | - Qianqian Luo
- School of Mathematics and Statistics, Xidian University, Xian, China
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6
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Fei Z, Zheng Q, Hong HG, Li Y. Inference for High-Dimensional Censored Quantile Regression. J Am Stat Assoc 2021; 118:898-912. [PMID: 37309513 PMCID: PMC10259833 DOI: 10.1080/01621459.2021.1957900] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2019] [Revised: 04/12/2021] [Accepted: 07/13/2021] [Indexed: 10/20/2022]
Abstract
With the availability of high dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients' survival, along with proper statistical inference. Censored quantile regression has emerged as a powerful tool for detecting heterogeneous effects of covariates on survival outcomes. To our knowledge, there is little work available to draw inference on the effects of high dimensional predictors for censored quantile regression. This paper proposes a novel procedure to draw inference on all predictors within the framework of global censored quantile regression, which investigates covariate-response associations over an interval of quantile levels, instead of a few discrete values. The proposed estimator combines a sequence of low dimensional model estimates that are based on multi-sample splittings and variable selection. We show that, under some regularity conditions, the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure can properly quantify the uncertainty of the estimates in high dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in lung cancer pathways on patients' survival, using the Boston Lung Cancer Survivor Cohort, a cancer epidemiology study on the molecular mechanism of lung cancer.
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Affiliation(s)
- Zhe Fei
- Department of Biostatistics, University of California, Los Angeles
| | - Qi Zheng
- Department of Bioinformatics and Biostatistics, University of Louisville
| | - Hyokyoung G Hong
- Department of Statistics and Probability, Michigan State University
| | - Yi Li
- Department of Biostatistics, University of Michigan
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7
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Conde‐Amboage M, Van Keilegom I, González‐Manteiga W. A new lack‐of‐fit test for quantile regression with censored data. Scand Stat Theory Appl 2021. [DOI: 10.1111/sjos.12512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Mercedes Conde‐Amboage
- Models of Optimization, Decision, Statistics and Applications Research Group (MODESTYA), Department of Statistics, Mathematical Analysis and Optimization Universidade de Santiago de Compostela Santiago de Compostela Spain
- Research Centre for Operations Research and Statistics (ORSTAT) KU Leuven Leuven Belgium
| | - Ingrid Van Keilegom
- Research Centre for Operations Research and Statistics (ORSTAT) KU Leuven Leuven Belgium
| | - Wenceslao González‐Manteiga
- Models of Optimization, Decision, Statistics and Applications Research Group (MODESTYA), Department of Statistics, Mathematical Analysis and Optimization Universidade de Santiago de Compostela Santiago de Compostela Spain
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8
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Kim H, Shin SJ. A quantile-slicing approach for sufficient dimension reduction with censored responses. Biom J 2020; 63:201-212. [PMID: 32909280 DOI: 10.1002/bimj.201900250] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2019] [Revised: 03/24/2020] [Accepted: 07/23/2020] [Indexed: 11/06/2022]
Abstract
Sufficient dimension reduction (SDR) that effectively reduces the predictor dimension in regression has been popular in high-dimensional data analysis. Under the presence of censoring, however, most existing SDR methods suffer. In this article, we propose a new algorithm to perform SDR with censored responses based on the quantile-slicing scheme recently proposed by Kim et al. First, we estimate the conditional quantile function of the true survival time via the censored kernel quantile regression (Shin et al.) and then slice the data based on the estimated censored regression quantiles instead of the responses. Both simulated and real data analysis demonstrate promising performance of the proposed method.
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Affiliation(s)
- Hyungwoo Kim
- Department of Statistics, Korea University, Seongbuk-gu, Seoul, South Korea
| | - Seung Jun Shin
- Department of Statistics, Korea University, Seongbuk-gu, Seoul, South Korea
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9
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De Backer M, El Ghouch A, Van Keilegom I. Linear censored quantile regression: A novel minimum‐distance approach. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12475] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Affiliation(s)
- Mickaël De Backer
- Université Catholique de Louvain, Institut de Statistique, Biostatistique et Sciences Actuarielles
| | - Anouar El Ghouch
- Université Catholique de Louvain, Institut de Statistique, Biostatistique et Sciences Actuarielles
| | - Ingrid Van Keilegom
- Université Catholique de Louvain, Institut de Statistique, Biostatistique et Sciences Actuarielles
- Research Centre for Operations Research Business Statistics KU Leuven
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10
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De Backer M, Ghouch AE, Van Keilegom I. An Adapted Loss Function for Censored Quantile Regression. J Am Stat Assoc 2019. [DOI: 10.1080/01621459.2018.1469996] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Mickaël De Backer
- Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Anouar El Ghouch
- Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Ingrid Van Keilegom
- Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
- Research Centre for Operations Research and Business Statistics, KU Leuven, Leuven, Belgium
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11
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Soret P, Avalos M, Wittkop L, Commenges D, Thiébaut R. Lasso regularization for left-censored Gaussian outcome and high-dimensional predictors. BMC Med Res Methodol 2018; 18:159. [PMID: 30514234 PMCID: PMC6280495 DOI: 10.1186/s12874-018-0609-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Accepted: 11/02/2018] [Indexed: 12/14/2022] Open
Abstract
Background Biological assays for the quantification of markers may suffer from a lack of sensitivity and thus from an analytical detection limit. This is the case of human immunodeficiency virus (HIV) viral load. Below this threshold the exact value is unknown and values are consequently left-censored. Statistical methods have been proposed to deal with left-censoring but few are adapted in the context of high-dimensional data. Methods We propose to reverse the Buckley-James least squares algorithm to handle left-censored data enhanced with a Lasso regularization to accommodate high-dimensional predictors. We present a Lasso-regularized Buckley-James least squares method with both non-parametric imputation using Kaplan-Meier and parametric imputation based on the Gaussian distribution, which is typically assumed for HIV viral load data after logarithmic transformation. Cross-validation for parameter-tuning is based on an appropriate loss function that takes into account the different contributions of censored and uncensored observations. We specify how these techniques can be easily implemented using available R packages. The Lasso-regularized Buckley-James least square method was compared to simple imputation strategies to predict the response to antiretroviral therapy measured by HIV viral load according to the HIV genotypic mutations. We used a dataset composed of several clinical trials and cohorts from the Forum for Collaborative HIV Research (HIV Med. 2008;7:27-40). The proposed methods were also assessed on simulated data mimicking the observed data. Results Approaches accounting for left-censoring outperformed simple imputation methods in a high-dimensional setting. The Gaussian Buckley-James method with cross-validation based on the appropriate loss function showed the lowest prediction error on simulated data and, using real data, the most valid results according to the current literature on HIV mutations. Conclusions The proposed approach deals with high-dimensional predictors and left-censored outcomes and has shown its interest for predicting HIV viral load according to HIV mutations.
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Affiliation(s)
- Perrine Soret
- Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, F-33000, France.,Inria SISTM Team, Talence, F-33405, France.,Vaccine Research Institute (VRI), Créteil, F-94000, France
| | - Marta Avalos
- Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, F-33000, France. .,Inria SISTM Team, Talence, F-33405, France.
| | - Linda Wittkop
- Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, F-33000, France.,Inria SISTM Team, Talence, F-33405, France.,CHU Bordeaux, Department of Public Health, Bordeaux, F-33000, France
| | - Daniel Commenges
- Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, F-33000, France.,Inria SISTM Team, Talence, F-33405, France
| | - Rodolphe Thiébaut
- Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, F-33000, France.,Inria SISTM Team, Talence, F-33405, France.,Vaccine Research Institute (VRI), Créteil, F-94000, France.,CHU Bordeaux, Department of Public Health, Bordeaux, F-33000, France
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Yao M, Wang JF, Lin L, Wang YX. Variable selection and weighted composite quantile estimation of regression parameters with left-truncated data. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2017.1376089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Mei Yao
- School of Mathematics, Hefei University of Technology, Hefei, China
- Shandong University Qilu Securities Institute for Financial Studies, Shandong University, Jinan, China
| | - Jiang-Feng Wang
- Department of Statistics, Zhejiang Gongshang University, Hongzhou, China
| | - Lu Lin
- Shandong University Qilu Securities Institute for Financial Studies, Shandong University, Jinan, China
| | - Yu-Xin Wang
- School of Economics, Hefei University of Technology, Hefei, China
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Tian Y, Tang M, Tian M. Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies. Comput Stat 2018. [DOI: 10.1007/s00180-018-0812-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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14
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Ahn KW, Kim S. Variable selection with group structure in competing risks quantile regression. Stat Med 2018; 37:1577-1586. [PMID: 29468710 DOI: 10.1002/sim.7619] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 12/05/2017] [Accepted: 01/03/2018] [Indexed: 11/11/2022]
Abstract
We study the group bridge and the adaptive group bridge penalties for competing risks quantile regression with group variables. While the group bridge consistently identifies nonzero group variables, the adaptive group bridge consistently selects variables not only at group level but also at within-group level. We allow the number of covariates to diverge as the sample size increases. The oracle property for both methods is also studied. The performance of the group bridge and the adaptive group bridge is compared in simulation and in a real data analysis. The simulation study shows that the adaptive group bridge selects nonzero within-group variables more consistently than the group bridge. A bone marrow transplant study is provided as an example.
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Affiliation(s)
- Kwang Woo Ahn
- Division of Biostatistics, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
| | - Soyoung Kim
- Division of Biostatistics, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
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Abstract
Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equations and address the challenges due to the recursive nature of the procedure. We establish the uniform convergence rates for the proposed estimators, and investigate the properties on weak convergence and variable selection. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.
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Affiliation(s)
- Qi Zheng
- Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40242, USA
| | - Limin Peng
- Department of Biostatistics and Bioinformatics, Emory University, 1518 Clifton Rd, NE, Atlanta, GA 30322, USA
| | - Xuming He
- Department of Statistics University of Michigan, Ann Arbor, MI 48109, USA
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16
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Frequentist model averaging estimation for the censored partial linear quantile regression model. J Stat Plan Inference 2017. [DOI: 10.1016/j.jspi.2017.04.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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17
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Liu H, Yang H. Penalized composite quantile estimation for censored regression model with a diverging number of parameters. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1130840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Huilan Liu
- College of Mathematics and Statistics, Chongqing University, Chongqing, P. R. China
- School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, P. R. China
| | - Hu Yang
- College of Mathematics and Statistics, Chongqing University, Chongqing, P. R. China
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Du J, Zhang Z, Xie T. Focused information criterion and model averaging in censored quantile regression. METRIKA 2017. [DOI: 10.1007/s00184-017-0616-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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19
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Liu H, Yang H, Xia X. Robust estimation and variable selection in censored partially linear additive models. J Korean Stat Soc 2017. [DOI: 10.1016/j.jkss.2016.07.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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21
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Volgushev S, Wagener J, Dette H. Censored quantile regression processes under dependence and penalization. Electron J Stat 2014. [DOI: 10.1214/14-ejs54] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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22
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Tian GL, Wang M, Song L. Variable selection in the high-dimensional continuous generalized linear model with current status data. J Appl Stat 2013. [DOI: 10.1080/02664763.2013.840271] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Abstract
Quantile regression has emerged as a powerful tool in survival analysis as it directly links the quantiles of patients' survival times to their demographic and genomic profiles, facilitating the identification of important prognostic factors. In view of limited work on variable selection in the context, we develop a new adaptive-lasso-based variable selection procedure for quantile regression with censored outcomes. To account for random censoring for data with multivariate covariates, we employ the ideas of redistribution-of-mass and e ective dimension reduction. Asymptotically our procedure enjoys the model selection consistency, that is, identifying the true model with probability tending to one. Moreover, as opposed to the existing methods, our new proposal requires fewer assumptions, leading to more accurate variable selection. The analysis of a real cancer clinical trial demonstrates that our procedure can identify and distinguish important factors associated with patient sub-populations characterized by short or long survivals, which is of particular interest to oncologists.
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Wagener J, Volgushev S, Dette H. The quantile process under random censoring. MATHEMATICAL METHODS OF STATISTICS 2012. [DOI: 10.3103/s1066530712020044] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Tang L, Zhou Z, Wu C. Weighted composite quantile estimation and variable selection method for censored regression model. Stat Probab Lett 2012. [DOI: 10.1016/j.spl.2011.11.021] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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