1
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Chen X, Ping Y, Sun J. Efficient estimation of Cox model with random change point. Stat Med 2024; 43:1213-1226. [PMID: 38247108 DOI: 10.1002/sim.9987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 11/27/2023] [Accepted: 11/29/2023] [Indexed: 01/23/2024]
Abstract
In clinical studies, the risk of a disease may dramatically change when some biological indexes of the human body exceed some thresholds. Furthermore, the differences in individual characteristics of patients such as physical and psychological experience may lead to subject-specific thresholds or change points. Although a large literature has been established for regression analysis of failure time data with change points, most of the existing methods assume the same, fixed change point for all study subjects. In this paper, we consider the situation where there exists a subject-specific change point and two Cox type models are presented. The proposed models also offer a framework for subgroup analysis. For inference, a sieve maximum likelihood estimation procedure is proposed and the asymptotic properties of the resulting estimators are established. An extensive simulation study is conducted to assess the empirical performance of the proposed method and indicates that it works well in practical situations. Finally the proposed approach is applied to a set of breast cancer data.
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Affiliation(s)
- Xuerong Chen
- Centre of Statistical Research, Southwestern University of Finance and Economics, Chengdu, China
| | - Yalu Ping
- Centre of Statistical Research, Southwestern University of Finance and Economics, Chengdu, China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, Missouri, USA
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2
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Wang Z, Li T, Xiao L, Tu D. A threshold longitudinal Tobit quantile regression model for identification of treatment-sensitive subgroups based on interval-bounded longitudinal measurements and a continuous covariate. Stat Med 2023; 42:4618-4631. [PMID: 37599222 DOI: 10.1002/sim.9879] [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: 12/14/2022] [Revised: 06/12/2023] [Accepted: 08/01/2023] [Indexed: 08/22/2023]
Abstract
Identification of a subgroup of patients who may be sensitive to a specific treatment is an important problem in precision medicine. This article considers the case where the treatment effect is assessed by longitudinal measurements, such as quality of life scores assessed over the duration of a clinical trial, and the subset is determined by a continuous baseline covariate, such as age and expression level of a biomarker. Recently, a linear mixed threshold regression model has been proposed but it assumes the longitudinal measurements are normally distributed. In many applications, longitudinal measurements, such as quality of life data obtained from answers to questions on a Likert scale, may be restricted in a fixed interval because of the floor and ceiling effects and, therefore, may be skewed. In this article, a threshold longitudinal Tobit quantile regression model is proposed and a computational approach based on alternating direction method of multipliers algorithm is developed for the estimation of parameters in the model. In addition, a random weighting method is employed to estimate the variances of the parameter estimators. The proposed procedures are evaluated through simulation studies and applications to the data from clinical trials.
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Affiliation(s)
- Zhanfeng Wang
- Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China
| | - Tao Li
- Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China
| | - Liqun Xiao
- School of Economics and Statistics, Guangzhou University, Guangzhou, China
| | - Dongsheng Tu
- Canadian Cancer Trials Group, Queen's University, Kingston, Ontario, Canada
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3
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Liu P, Li J, Kosorok MR. Change plane model averaging for subgroup identification. Stat Methods Med Res 2023; 32:773-788. [PMID: 36775991 DOI: 10.1177/09622802231154327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/14/2023]
Abstract
Central to personalized medicine and tailored therapies is discovering the subpopulations that account for treatment effect heterogeneity and are likely to benefit more from given interventions. In this article, we introduce a change plane model averaging method to identify subgroups characterized by linear combinations of predictive variables and multiple cut-offs. We first fit a sequence of statistical models, each incorporating the thresholding effect of one particular covariate. The estimation of submodels is accomplished through an iterative integration of a change point detection method and numerical optimization algorithms. A frequentist model averaging approach is then employed to linearly combine the submodels with optimal weights. Our approach can deal with high-dimensional settings involving enormous potential grouping variables by adopting the sparsity-inducing penalties. Simulation studies are conducted to investigate the prediction and subgrouping performance of the proposed method, with a comparison to various competing subgroup detection methods. Our method is applied to a dataset from a warfarin pharmacogenetics study, producing some new findings.
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Affiliation(s)
- Pan Liu
- Department of Statistics and Data Science, 37580National University of Singapore, Singapore, Singapore
| | - Jialiang Li
- Department of Statistics and Data Science, 37580National University of Singapore, Singapore, Singapore.,Duke University NUS Graduate Medical School, Singapore, Singapore
| | - Michael R Kosorok
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, USA
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4
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Ge X, Peng Y, Tu D. A generalized single‐index linear threshold model for identifying treatment‐sensitive subsets based on multiple covariates and longitudinal measurements. CAN J STAT 2022. [DOI: 10.1002/cjs.11737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Xinyi Ge
- Department of Mathematics and Statistics Queen's University Kingston Ontario Canada
| | - Yingwei Peng
- Departments of Mathematics and Statistics & Public Health Sciences Queen's University Kingston Ontario Canada
| | - Dongsheng Tu
- Departments of Mathematics and Statistics & Public Health Sciences and Canadian Cancer Trials Group Queen's University Kingston Ontario Canada
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5
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Zhang R, Qin G, Tu D. A robust threshold t linear mixed model for subgroup identification using multivariate T distributions. Comput Stat 2022. [DOI: 10.1007/s00180-022-01229-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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6
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Wei K, Zhu H, Qin G, Zhu Z, Tu D. Multiply robust subgroup analysis based on a single-index threshold linear marginal model for longitudinal data with dropouts. Stat Med 2022; 41:2822-2839. [PMID: 35347738 DOI: 10.1002/sim.9386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Revised: 02/21/2022] [Accepted: 03/02/2022] [Indexed: 11/08/2022]
Abstract
Identifying subpopulations that may be sensitive to the specific treatment is an important step toward precision medicine. On the other hand, longitudinal data with dropouts is common in medical research, and subgroup analysis for this data type is still limited. In this paper, we consider a single-index threshold linear marginal model, which can be used simultaneously to identify subgroups with differential treatment effects based on linear combination of the selected biomarkers, estimate the treatment effects in different subgroups based on regression coefficients, and test the significance of the difference in treatment effects based on treatment-subgroup interaction. The regression parameters are estimated by solving a penalized smoothed generalized estimating equation and the selection bias caused by missingness is corrected by a multiply robust weighting matrix, which allows multiple missingness models to be taken account into estimation. The proposed estimator remains consistent when any model for missingness is correctly specified. Under regularity conditions, the asymptotic normality of the estimator is established. Simulation studies confirm the desirable finite-sample performance of the proposed method. As an application, we analyze the data from a clinical trial on pancreatic cancer.
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Affiliation(s)
- Kecheng Wei
- Department of Biostatistics, School of Public Health, Fudan University, Shanghai, China
| | - Huichen Zhu
- Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
| | - Guoyou Qin
- Department of Biostatistics, School of Public Health, Fudan University, Shanghai, China
| | - Zhongyi Zhu
- Department of Statistics, School of Management, Fudan University, Shanghai, China
| | - Dongsheng Tu
- Canadian Cancer Trials Group, Queen's University, Kingston, Ontario, Canada
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7
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Zhang Y, Wang HJ, Zhu Z. Single-index Thresholding in Quantile Regression. J Am Stat Assoc 2021. [DOI: 10.1080/01621459.2021.1915319] [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)
- Yingying Zhang
- Academy of Statistics and Interdisciplinary Sciences, KLATASDS-MOE, East China Normal University, Shanghai, China
| | - Huixia Judy Wang
- Department of Statistics, The George Washington University, Washington, DC
| | - Zhongyi Zhu
- Department of Statistics, Fudan University, Shanghai, China
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8
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Shuo Liu S, Chen BE. Continuous threshold models with two‐way interactions in survival analysis. CAN J STAT 2020. [DOI: 10.1002/cjs.11561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Shuo Shuo Liu
- Department of Statistics The Pennsylvania State University University Park PA U.S.A
| | - Bingshu E. Chen
- Canadian Cancer Trials Group and Department of Public Health Sciences Queen's University Kingston Ontario Canada
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9
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Ge X, Peng Y, Tu D. A threshold linear mixed model for identification of treatment-sensitive subsets in a clinical trial based on longitudinal outcomes and a continuous covariate. Stat Methods Med Res 2020; 29:2919-2931. [PMID: 32193992 DOI: 10.1177/0962280220912772] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Identification of a subset of patients who may be sensitive to a specific treatment is an important problem in clinical trials. In this paper, we consider the case where the treatment effect is measured by longitudinal outcomes, such as quality of life scores assessed over the duration of a clinical trial, and the subset is determined by a continuous baseline covariate, such as age and expression level of a biomarker. A threshold linear mixed model is introduced, and a smoothing maximum likelihood method is proposed to obtain the estimation of the parameters in the model. Broyden-Fletcher-Goldfarb-Shanno algorithm is employed to maximize the proposed smoothing likelihood function. The proposed procedure is evaluated through simulation studies and application to the analysis of data from a randomized clinical trial on patients with advanced colorectal cancer.
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Affiliation(s)
- Xinyi Ge
- Department of Mathematics and Statistics, Queen's University, Kingston, Canada
| | - Yingwei Peng
- Department of Mathematics and Statistics, Queen's University, Kingston, Canada.,Departments of Public Health Sciences, Queen's University, Kingston, Canada
| | - Dongsheng Tu
- Department of Mathematics and Statistics, Queen's University, Kingston, Canada.,Departments of Public Health Sciences, Queen's University, Kingston, Canada.,Canadian Cancer Trials Group, Queen's University, Kingston, Canada
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