1
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Lou Y, Wang P, Sun J. Inference on semi-parametric transformation model with a pairwise likelihood based on left-truncated and interval-censored data. J Nonparametr Stat 2022. [DOI: 10.1080/10485252.2022.2138383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Affiliation(s)
- Yichen Lou
- School of Mathematics, Jilin University, Changchun, People's Republic of China
| | - Peijie Wang
- School of Mathematics, Jilin University, Changchun, People's Republic of China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MO, USA
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2
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Wang L, Wang L. An EM algorithm for analyzing right-censored survival data under the semiparametric proportional odds model. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1837879] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Lu Wang
- Department of Statistics, University of South Carolina, Columbia, South Carolina, USA
| | - Lianming Wang
- Department of Statistics, University of South Carolina, Columbia, South Carolina, USA
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3
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Liang L, Hou J, Uno H, Cho K, Ma Y, Cai T. Semi-supervised approach to event time annotation using longitudinal electronic health records. LIFETIME DATA ANALYSIS 2022; 28:428-491. [PMID: 35753014 PMCID: PMC10044535 DOI: 10.1007/s10985-022-09557-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 05/13/2022] [Indexed: 06/15/2023]
Abstract
Large clinical datasets derived from insurance claims and electronic health record (EHR) systems are valuable sources for precision medicine research. These datasets can be used to develop models for personalized prediction of risk or treatment response. Efficiently deriving prediction models using real world data, however, faces practical and methodological challenges. Precise information on important clinical outcomes such as time to cancer progression are not readily available in these databases. The true clinical event times typically cannot be approximated well based on simple extracts of billing or procedure codes. Whereas, annotating event times manually is time and resource prohibitive. In this paper, we propose a two-step semi-supervised multi-modal automated time annotation (MATA) method leveraging multi-dimensional longitudinal EHR encounter records. In step I, we employ a functional principal component analysis approach to estimate the underlying intensity functions based on observed point processes from the unlabeled patients. In step II, we fit a penalized proportional odds model to the event time outcomes with features derived in step I in the labeled data where the non-parametric baseline function is approximated using B-splines. Under regularity conditions, the resulting estimator of the feature effect vector is shown as root-n consistent. We demonstrate the superiority of our approach relative to existing approaches through simulations and a real data example on annotating lung cancer recurrence in an EHR cohort of lung cancer patients from Veteran Health Administration.
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Affiliation(s)
- Liang Liang
- Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA
| | - Jue Hou
- Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA
| | - Hajime Uno
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Kelly Cho
- Massachusetts Veterans Epidemiology Research and Information Center, US Department of Veteran Affairs, Boston, MA, USA
- Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Yanyuan Ma
- Department of Statistics, Penn State University, University Park, PA, Boston, USA
| | - Tianxi Cai
- Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA.
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA.
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4
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Tang W, He K, Xu G, Zhu J. Survival Analysis via Ordinary Differential Equations. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2051519] [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)
- Weijing Tang
- Department of Statistics, University of Michigan, Ann Arbor, Michigan
| | - Kevin He
- Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, Michigan
| | - Gongjun Xu
- Department of Statistics, University of Michigan, Ann Arbor, Michigan
| | - Ji Zhu
- Department of Statistics, University of Michigan, Ann Arbor, Michigan
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5
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Zhou J, Jiang X, Xia HA, Wei P, Hobbs BP. Predicting outcomes of phase III oncology trials with Bayesian mediation modeling of tumor response. Stat Med 2021; 41:751-768. [PMID: 34888892 DOI: 10.1002/sim.9268] [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: 03/25/2021] [Revised: 10/04/2021] [Accepted: 11/06/2021] [Indexed: 11/12/2022]
Abstract
Pivotal cancer trials often fail to yield evidence in support of new therapies thought to offer promising alternatives to standards-of-care. Conducting randomized controlled trials in oncology tends to be considerably more expensive than studies of other diseases with comparable sample size. Moreover, phase III trial design often takes place with a paucity of survival data for experimental therapies. Experts have explained the failures on the basis of design flaws which produce studies with unrealistic expectations. This article presents a framework for predicting outcomes of phase III oncology trials using Bayesian mediation models. Predictions, which arise from interim analyses, derive from multivariate modeling of the relationships among treatment, tumor response, and their conjoint effects on survival. Acting as a safeguard against inaccurate pre-trial design assumptions, the methodology may better facilitate rapid closure of negative studies. Additionally the models can be used to inform re-estimations of sample size for under-powered trials that demonstrate survival benefit via tumor response mediation. The methods are applied to predict the outcomes of two colorectal cancer studies. Simulation is used to evaluate and compare models in the absence versus presence of reliable surrogate markers of survival.
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Affiliation(s)
- Jie Zhou
- Quantitative Health Sciences, Cleveland Clinic, Cleveland, Ohio, USA
| | - Xun Jiang
- Center for Design and Analysis, Amgen, Thousand Oaks, California, USA
| | - Hong Amy Xia
- Center for Design and Analysis, Amgen, Thousand Oaks, California, USA
| | - Peng Wei
- Department of Biostatistics, Division of Basic Sciences, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
| | - Brian P Hobbs
- Dell Medical School, The University of Texas at Austin, Austin, Texas, USA
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6
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Zhou Q, Sun Y, Gilbert PB. Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial. Stat Med 2021; 40:4376-4394. [PMID: 34080723 DOI: 10.1002/sim.9035] [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: 12/07/2020] [Revised: 04/04/2021] [Accepted: 05/03/2021] [Indexed: 11/11/2022]
Abstract
Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.
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Affiliation(s)
- Qingning Zhou
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina, USA
| | - Yanqing Sun
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina, USA
| | - Peter B Gilbert
- Department of Biostatistics, University of Washington, Seattle, Washington, USA.,Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Research Center, Seattle, Washington, USA
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7
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Liu T, Yuan X, Sun J. Weighted rank estimation of nonparametric transformation models with case-1 and case-2 interval-censored failure time data. J Nonparametr Stat 2021. [DOI: 10.1080/10485252.2021.1929219] [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)
- Tianqing Liu
- Center for Applied Statistical Research and School of Mathematics, Jilin University, Changchun, People's Republic of China
| | - Xiaohui Yuan
- School of Mathematics and Statistics, Changchun University of Technology, Changchun, People's Republic of China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MO, USA
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8
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Wang L, Wang L. Regression analysis of arbitrarily censored survival data under the proportional odds model. Stat Med 2021; 40:3724-3739. [PMID: 33882618 DOI: 10.1002/sim.8994] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 02/13/2021] [Accepted: 03/29/2021] [Indexed: 11/09/2022]
Abstract
Arbitrarily censored data are referred to as the survival data that contain a mixture of exactly observed, left-censored, interval-censored, and right-censored observations. Existing research work on regression analysis on arbitrarily censored data is relatively sparse and mainly focused on the proportional hazards model and the accelerated failure time model. This article studies the proportional odds (PO) model and proposes a novel estimation approach through an expectation-maximization (EM) algorithm for analyzing such data. The proposed EM algorithm has many appealing properties such as being robust to initial values, easy to implement, converging fast, and providing the variance estimate of the regression parameter estimate in closed form. An informal diagnosis plot is developed for checking the PO model assumption. Our method has shown excellent performance in estimating the regression parameters as well as the baseline survival function in a simulation study. A real-life dataset about metastatic colorectal cancer is analyzed for illustration. An R package regPO has been created for practitioners to implement our method.
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Affiliation(s)
- Lu Wang
- Department of Mathematics, Western New England University, Springfield, Massachusetts, USA
| | - Lianming Wang
- Department of Statistics, University of South Carolina, Columbia, South Carolina, USA
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9
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Shen PS, Chen HJ, Pan WH, Chen CM. Semiparametric regression analysis for left-truncated and interval-censored data without or with a cure fraction. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2019.06.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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10
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Gao F, Zeng D, Lin DY. Semiparametric regression analysis of interval-censored data with informative dropout. Biometrics 2018; 74:1213-1222. [PMID: 29870067 PMCID: PMC6309250 DOI: 10.1111/biom.12911] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2017] [Revised: 02/01/2018] [Accepted: 04/01/2018] [Indexed: 12/01/2022]
Abstract
Interval-censored data arise when the event time of interest can only be ascertained through periodic examinations. In medical studies, subjects may not complete the examination schedule for reasons related to the event of interest. In this article, we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval-censored data. Specifically, we propose a broad class of joint models, under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect. We consider nonparametric maximum likelihood estimation and develop an EM algorithm that involves simple and stable calculations. We prove that the resulting estimators of the regression parameters are consistent, asymptotically normal, and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood. In addition, we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event. Furthermore, we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies. Finally, we provide an application to data on the incidence of diabetes from a major epidemiological cohort study.
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Affiliation(s)
- Fei Gao
- Department of Biostatistics, University of Washington, Seattle, Washington, U.S.A
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina, U.S.A
| | - Dan-Yu Lin
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina, U.S.A
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11
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Zhao X, Wu Y, Yin G. Sieve maximum likelihood estimation for a general class of accelerated hazards models with bundled parameters. BERNOULLI 2017. [DOI: 10.3150/16-bej850] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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12
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Abstract
The case-cohort design has been widely used as a means of cost reduction in assembling or measuring expensive covariates in large cohort studies. The existing literature on the case-cohort design is mainly focused on right-censored data. In practice, however, the failure time is often subject to interval-censoring; it is known only to fall within some random time interval. In this paper, we consider the case-cohort study design for interval-censored failure time and develop a sieve semiparametric likelihood approach for analyzing data from this design under the proportional hazards model. We construct the likelihood function using inverse probability weighting and build the sieves with Bernstein polynomials. The consistency and asymptotic normality of the resulting regression parameter estimator are established and a weighted bootstrap procedure is considered for variance estimation. Simulations show that the proposed method works well for practical situations, and an application to real data is provided.
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Affiliation(s)
- Q Zhou
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A
| | - H Zhou
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A
| | - J Cai
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A
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13
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Zhou J, Zhang J, Lu W. An Expectation Maximization algorithm for fitting the generalized odds-rate model to interval censored data. Stat Med 2016; 36:1157-1171. [PMID: 28004414 DOI: 10.1002/sim.7204] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 10/25/2016] [Accepted: 11/28/2016] [Indexed: 11/12/2022]
Abstract
The generalized odds-rate model is a class of semiparametric regression models, which includes the proportional hazards and proportional odds models as special cases. There are few works on estimation of the generalized odds-rate model with interval censored data because of the challenges in maximizing the complex likelihood function. In this paper, we propose a gamma-Poisson data augmentation approach to develop an Expectation Maximization algorithm, which can be used to fit the generalized odds-rate model to interval censored data. The proposed Expectation Maximization algorithm is easy to implement and is computationally efficient. The performance of the proposed method is evaluated by comprehensive simulation studies and illustrated through applications to datasets from breast cancer and hemophilia studies. In order to make the proposed method easy to use in practice, an R package 'ICGOR' was developed. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Jie Zhou
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, U.S.A
| | - Jiajia Zhang
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, U.S.A
| | - Wenbin Lu
- Department of Statistics, North Carolina State University, Raleigh, NC, U.S.A
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14
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Zeng D, Mao L, Lin DY. Maximum likelihood estimation for semiparametric transformation models with interval-censored data. Biometrika 2016; 103:253-271. [PMID: 27279656 PMCID: PMC4890294 DOI: 10.1093/biomet/asw013] [Citation(s) in RCA: 76] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022] Open
Abstract
Interval censoring arises frequently in clinical, epidemiological, financial and
sociological studies, where the event or failure of interest is known only to occur within
an interval induced by periodic monitoring. We formulate the effects of potentially
time-dependent covariates on the interval-censored failure time through a broad class of
semiparametric transformation models that encompasses proportional hazards and
proportional odds models. We consider nonparametric maximum likelihood estimation for this
class of models with an arbitrary number of monitoring times for each subject. We devise
an EM-type algorithm that converges stably, even in the presence of time-dependent
covariates, and show that the estimators for the regression parameters are consistent,
asymptotically normal, and asymptotically efficient with an easily estimated covariance
matrix. Finally, we demonstrate the performance of our procedures through simulation
studies and application to an HIV/AIDS study conducted in Thailand.
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Affiliation(s)
- Donglin Zeng
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. , ,
| | - Lu Mao
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. , ,
| | - D Y Lin
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. , ,
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15
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Li Z, Owzar K. Fitting Cox Models with Doubly Censored Data Using Spline-Based Sieve Marginal Likelihood. Scand Stat Theory Appl 2015; 43:476-486. [PMID: 27239090 DOI: 10.1111/sjos.12186] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In some applications, the failure time of interest is the time from an originating event to a failure event, while both event times are interval censored. We propose fitting Cox proportional hazards models to this type of data using a spline-based sieve maximum marginal likelihood, where the time to the originating event is integrated out in the empirical likelihood function of the failure time of interest. This greatly reduces the complexity of the objective function compared with the fully semiparametric likelihood. The dependence of the time of interest on time to the originating event is induced by including the latter as a covariate in the proportional hazards model for the failure time of interest. The use of splines results in a higher rate of convergence of the estimator of the baseline hazard function compared with the usual nonparametric estimator. The computation of the estimator is facilitated by a multiple imputation approach. Asymptotic theory is established and a simulation study is conducted to assess its finite sample performance. It is also applied to analyzing a real data set on AIDS incubation time.
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Affiliation(s)
- Zhiguo Li
- Department of Biostatistics and Bioinformatics, Duke University
| | - Kouros Owzar
- Department of Biostatistics and Bioinformatics, Duke University
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16
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Parameter estimation of partial linear model under monotonicity constraints with censored data. J Korean Stat Soc 2015. [DOI: 10.1016/j.jkss.2014.12.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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17
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Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm. Comput Stat Data Anal 2015. [DOI: 10.1016/j.csda.2014.10.013] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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18
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19
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Yuan M, Diao G. Semiparametric odds rate model for modeling short-term and long-term effects with application to a breast cancer genetic study. Int J Biostat 2014; 10:231-49. [PMID: 24815054 PMCID: PMC4221565 DOI: 10.1515/ijb-2013-0037] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
The proportional odds model is commonly used in the analysis of failure time data. The assumption of constant odds ratios over time in the proportional odds model, however, can be violated in some applications. Motivated by a genetic study with breast cancer patients, we propose a novel semiparametric odds rate model for the analysis of right-censored survival data. The proposed model incorporates the short-term and long-term covariate effects on the failure time data and includes the proportional odds model as a nested model. We develop efficient likelihood-based inference procedures and establish the large sample properties of the proposed nonparametric maximum likelihood estimators. Simulation studies demonstrate that the proposed methods perform well in practical settings. An application to the motivating example is provided.
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Affiliation(s)
- Mengdie Yuan
- Department of Statistics, George Mason University
| | - Guoqing Diao
- Department of Statistics, George Mason University
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20
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21
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Hu T, Xiang L. Efficient estimation for semiparametric cure models with interval-censored data. J MULTIVARIATE ANAL 2013. [DOI: 10.1016/j.jmva.2013.06.006] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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22
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Han S, Andrei AC, Tsui KW. A Semiparametric Regression Method for Interval-Censored Data. COMMUN STAT-SIMUL C 2013. [DOI: 10.1080/03610918.2012.697962] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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23
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Hothorn T, Kneib T, Bühlmann P. Conditional transformation models. J R Stat Soc Series B Stat Methodol 2013. [DOI: 10.1111/rssb.12017] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Torsten Hothorn
- Ludwig-Maximilians-Universität München, Germany, and Universität Zürich; Switzerland
| | | | - Peter Bühlmann
- Eidgenössische Technische Hochschule; Zürich Switzerland
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24
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McLain AC, Ghosh SK. Efficient Sieve Maximum Likelihood Estimation of Time-Transformation Models. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2013. [DOI: 10.1080/15598608.2013.772835] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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25
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Exploring the varying covariate effects in proportional odds models with censored data. J MULTIVARIATE ANAL 2012. [DOI: 10.1016/j.jmva.2012.02.013] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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26
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Wu Y, Zhang Y. Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data. Ann Stat 2012. [DOI: 10.1214/12-aos1016] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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27
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Guan Z, Peng C. A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness of fit. J Nonparametr Stat 2011. [DOI: 10.1080/10485252.2011.559726] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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28
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A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model. Stat Probab Lett 2011. [DOI: 10.1016/j.spl.2011.02.034] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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29
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Lin X, Wang L. Bayesian Proportional Odds Models for Analyzing Current Status Data: Univariate, Clustered, and Multivariate. COMMUN STAT-SIMUL C 2011. [DOI: 10.1080/03610918.2011.566971] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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30
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Cheng G, Wang X. Semiparametric additive transformation model under current status data. Electron J Stat 2011. [DOI: 10.1214/11-ejs656] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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31
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Wang L, Dunson DB. Semiparametric bayes' proportional odds models for current status data with underreporting. Biometrics 2010; 67:1111-8. [PMID: 21175554 DOI: 10.1111/j.1541-0420.2010.01532.x] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Current status data are a type of interval-censored event time data in which all the individuals are either left or right censored. For example, our motivation is drawn from a cross-sectional study, which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman. We propose a semiparametric Bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure. The proposed approach has the advantage of being straightforward to implement using a simple and efficient Gibbs sampler, whereas alternative semiparametric Bayes' event time models encounter problems for current status data. The model is generalized to allow systematic underreporting in a subset of the data, and the methods are applied to an epidemiologic study of uterine fibroids.
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Affiliation(s)
- Lianming Wang
- Department of Statistics, University of South Carolina, Columbia, South Carolina 29208, USA.
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32
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Lu M. Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints. J MULTIVARIATE ANAL 2010. [DOI: 10.1016/j.jmva.2010.07.002] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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Zhao X, Zhou X. Semiparametric Estimation in Transformation Models with Cure Fraction. COMMUN STAT-THEOR M 2010. [DOI: 10.1080/03610920903268840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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35
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Abstract
Interval-censored failure time data occur in many medical investigations as well as other studies such as demographical and sociological studies. They include the usual right-censored failure time data as a special case but provide much more complex structure and less relevant information than the right-censored data. This article reviews some basic concepts, issues and the corresponding statistical approaches related to the analysis of interval-censored data as well as recent advances. In particular, we discuss estimation of a survival function, comparison of several treatments and regression analysis as well as competing risks analysis and truncation in the presence of interval censoring. A well-known example of interval-censored data is described and analysed to illustrate some of the statistical procedures discussed.
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Affiliation(s)
- Zhigang Zhang
- Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, 307 East 63rd Street, New York, NY 10065, U.S.A
| | - Jianguo Sun
- Department of Statistics, University of Missouri, 146 Middlebush Hall, Columbia, Missouri 65211, U.S.A
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36
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ZHANG YING, HUA LEI, HUANG JIAN. A Spline-Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval-Censored Data. Scand Stat Theory Appl 2010. [DOI: 10.1111/j.1467-9469.2009.00680.x] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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37
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Lin X, Wang L. A semiparametric probit model for case 2 interval-censored failure time data. Stat Med 2010; 29:972-81. [PMID: 20069532 DOI: 10.1002/sim.3832] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2009] [Accepted: 11/30/2009] [Indexed: 11/07/2022]
Abstract
Interval-censored data occur naturally in many fields and the main feature is that the failure time of interest is not observed exactly, but is known to fall within some interval. In this paper, we propose a semiparametric probit model for analyzing case 2 interval-censored data as an alternative to the existing semiparametric models in the literature. Specifically, we propose to approximate the unknown nonparametric nondecreasing function in the probit model with a linear combination of monotone splines, leading to only a finite number of parameters to estimate. Both the maximum likelihood and the Bayesian estimation methods are proposed. For each method, regression parameters and the baseline survival function are estimated jointly. The proposed methods make no assumptions about the observation process and can be applicable to any interval-censored data with easy implementation. The methods are evaluated by simulation studies and are illustrated by two real-life interval-censored data applications.
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Affiliation(s)
- Xiaoyan Lin
- Department of Statistics, University of South Carolina, 1523 Greene Street, Columbia, SC 29208, U.S.A
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38
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Abstract
In statistical analysis, when the value of a random variable is only known to be between two bounds, we say that this random variable is interval censored. This complicated censoring pattern is a common problem in research fields such as clinical trials or actuarial studies and raises challenges for statistical analysis. In this paper, we focus on regression analysis of case 2 interval-censored data. We first briefly review existing regression methods and an estimation approach under the class of linear transformation models developed by Zhang et al. We then propose a method for survival probability prediction via generalized estimating equations. We also consider a graphical model checking technique and a model selection tool. Some theoretical properties are established and the performance of our procedures is evaluated and illustrated by numerical studies including a real-life data analysis.
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Affiliation(s)
- Zhigang Zhang
- Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, USA
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39
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Kosorok MR, Song R. Inference under right censoring for transformation models with a change-point based on a covariate threshold. Ann Stat 2007. [DOI: 10.1214/009053606000001244] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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40
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Xue H, Lam KF, Cowling BJ, de Wolf F. Semi-parametric accelerated failure time regression analysis with application to interval-censored HIV/AIDS data. Stat Med 2007; 25:3850-63. [PMID: 16372386 DOI: 10.1002/sim.2486] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
This paper demonstrates a way to investigate a potentially non-linear relationship between an interval-censored response variable and a continuously distributed explanatory variable. A potentially non-linear effect of a continuous explanatory variable on the response is incorporated into an accelerated failure time model, forming a partial linear model. A sieve maximum likelihood estimator (MLE) is suggested to simultaneously estimate all the parameters. The sieve MLE is shown to be asymptotically efficient and normally distributed. Simulation studies show that the proposed estimators for the scale and regression parameters are robust and efficient, and the estimator for the non-linear function is able to capture the shape of a variety of smooth non-linear functions. The model is applied to observational HIV data, where the response variable is the time to suppression of HIV viral load after initiation of antiretroviral therapy, and baseline viral load is investigated as a potentially non-linear effect.
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Affiliation(s)
- Hongqi Xue
- Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing, China
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41
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Gu MG, Sun L, Zuo G. A baseline-free procedure for transformation models under interval censorship. LIFETIME DATA ANALYSIS 2005; 11:473-88. [PMID: 16328572 DOI: 10.1007/s10985-005-5235-x] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2005] [Accepted: 07/25/2005] [Indexed: 05/05/2023]
Abstract
An important property of Cox regression model is that the estimation of regression parameters using the partial likelihood procedure does not depend on its baseline survival function. We call such a procedure baseline-free. Using marginal likelihood, we show that an baseline-free procedure can be derived for a class of general transformation models under interval censoring framework. The baseline-free procedure results a simplified and stable computation algorithm for some complicated and important semiparametric models, such as frailty models and heteroscedastic hazard/rank regression models, where the estimation procedures so far available involve estimation of the infinite dimensional baseline function. A detailed computational algorithm using Markov Chain Monte Carlo stochastic approximation is presented. The proposed procedure is demonstrated through extensive simulation studies, showing the validity of asymptotic consistency and normality. We also illustrate the procedure with a real data set from a study of breast cancer. A heuristic argument showing that the score function is a mean zero martingale is provided.
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Affiliation(s)
- Ming Gao Gu
- Department of Statistics, The Chinese University of Hong Kong, Hong Kong, PRC.
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42
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Kosorok MR, Lee BL, Fine JP. Robust inference for univariate proportional hazards frailty regression models. Ann Stat 2004. [DOI: 10.1214/009053604000000535] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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43
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44
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Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med 2002; 21:2175-97. [PMID: 12210632 DOI: 10.1002/sim.1203] [Citation(s) in RCA: 912] [Impact Index Per Article: 41.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Modelling of censored survival data is almost always done by Cox proportional-hazards regression. However, use of parametric models for such data may have some advantages. For example, non-proportional hazards, a potential difficulty with Cox models, may sometimes be handled in a simple way, and visualization of the hazard function is much easier. Extensions of the Weibull and log-logistic models are proposed in which natural cubic splines are used to smooth the baseline log cumulative hazard and log cumulative odds of failure functions. Further extensions to allow non-proportional effects of some or all of the covariates are introduced. A hypothesis test of the appropriateness of the scale chosen for covariate effects (such as of treatment) is proposed. The new models are applied to two data sets in cancer. The results throw interesting light on the behaviour of both the hazard function and the hazard ratio over time. The tools described here may be a step towards providing greater insight into the natural history of the disease and into possible underlying causes of clinical events. We illustrate these aspects by using the two examples in cancer.
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Affiliation(s)
- Patrick Royston
- Cancer Division, MRC Clinical Trials Unit, 222 Euston Road, London NW1 2DA, UK.
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45
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Lam KF, Lee YW, Leung TL. Modeling multivariate survival data by a semiparametric random effects proportional odds model. Biometrics 2002; 58:316-23. [PMID: 12071404 DOI: 10.1111/j.0006-341x.2002.00316.x] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.
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Affiliation(s)
- K F Lam
- Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong.
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46
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Cheung YK, Fine JP. Likelihood estimation after nonparametric transformation. Stat Probab Lett 2001. [DOI: 10.1016/s0167-7152(01)00106-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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47
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Abstract
A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect beta(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in k-sample transformation models when the random error belongs to the G(rho) family of Harrington and Fleming (1982, Biometrika 69, 553-566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression.
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Affiliation(s)
- R Xu
- Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA.
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49
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Van Der Laan MJ, Van Der Laan P. Subset Selection Based on Order Statistics from Logistic Populations. STATISTICS-ABINGDON 2000. [DOI: 10.1080/02331880008802715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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