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Ning X, Pan Y, Sun Y, Gilbert PB. A semiparametric Cox-Aalen transformation model with censored data. Biometrics 2023; 79:3111-3125. [PMID: 37403227 PMCID: PMC10764654 DOI: 10.1111/biom.13895] [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: 08/17/2022] [Accepted: 05/31/2023] [Indexed: 07/06/2023]
Abstract
We propose a broad class of so-called Cox-Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox-Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox-Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an expectation-solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled human immunodeficiency virus (HIV) prevention efficacy trials. The data example shows the utility of the proposed Cox-Aalen transformation models in enhancing statistical power for discovering covariate effects.
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Affiliation(s)
- Xi Ning
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina, U.S.A
| | - Yinghao Pan
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina, U.S.A
| | - Yanqing Sun
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina, U.S.A
| | - Peter B. Gilbert
- Department of Biostatistics, University of Washington, Seattle, Washington, U.S.A
- Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Center, Seattle, Washington, U.S.A
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2
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Shen PS. Equivalence tests before end of follow-up under the class of log transformation model. J Biopharm Stat 2022; 33:324-334. [PMID: 36484478 DOI: 10.1080/10543406.2022.2149771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
One important topic in clinical trials is to show that the effects of new and standard treatments are equivalent in terms of clinical relevance. In literature, many equivalence tests based on the maximal difference between two survival functions for the two treatments over the whole time axis have been proposed. However, since survival times can only be observed until the end of follow-up, an equivalence test should be based on a comparison only in the observed time-window dictated by the end of follow-up. In this article, under the class of log transformation model, we propose an asymptotical α-level equivalence test for the difference between two survival functions that only addresses equivalence until the end of follow-up. We demonstrate that the hypothesis of equivalence of two survival functions before the end of follow-up can be formulated as interval-based hypothesis testing which involves the treatment effect parameter. Simulation results indicate that when sample size is sufficiently large the proposed test controls the type I error effectively and performs well at detecting the equivalence. The proposed test is applied to a dataset from veteran's administration lung cancer trial.
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Affiliation(s)
- Pao-Sheng Shen
- Department of Statistics, Tunghai University, Taichung, Taiwan
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3
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Shen PS. Equivalence tests for the difference of two survival functions under the class of Box–Cox transformation model. J Korean Stat Soc 2022. [DOI: 10.1007/s42952-022-00197-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2022]
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4
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Alukal JJ, Zhang T, Thuluvath PJ. Outcomes of status 1 liver transplantation for Budd-Chiari Syndrome with fulminant hepatic failure. Am J Transplant 2021; 21:2211-2219. [PMID: 33236517 DOI: 10.1111/ajt.16410] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2020] [Revised: 10/22/2020] [Accepted: 11/10/2020] [Indexed: 01/25/2023]
Abstract
There is a paucity of data on the outcome of liver transplantation (LT) in Budd-Chiari Syndrome (BCS) patients who are listed as status 1. The objective of our study was to determine patient or graft survival following LT in status 1 BCS patients. We utilized United Network for Organ Sharing (UNOS) database to identify all adult patients (> 18 years of age) listed as status 1 with a primary diagnosis of BCS in the United States from 1998 to 2018, and analyzed their outcomes and compared it to non-status 1 BCS patients. Four hundred and forty-six patients with BCS underwent LT between 1998 and 2018, and of these 55 (12.3%) were listed as status 1. There was no difference in long-term post-liver transplant or "intention-to-treat" survival from the time of listing to death or the last day of follow-up between status 1 and non-status 1 groups. Graft and patient survival at 5 years for status 1 patients were 75% and 82%, respectively. Cox regression analysis showed that patients listed as status 1 (aHR: 0.45, p < .02) were associated with a better survival. BCS patients listed as status 1 have excellent survival following emergency LT.
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Affiliation(s)
- Joseph J Alukal
- Institute of Digestive Health & Liver Diseases, Mercy Medical Center, Baltimore, Maryland, USA
| | - Talan Zhang
- Institute of Digestive Health & Liver Diseases, Mercy Medical Center, Baltimore, Maryland, USA
| | - Paul J Thuluvath
- Institute of Digestive Health & Liver Diseases, Mercy Medical Center, Baltimore, Maryland, USA.,Department of Medicine, University of Maryland School of Medicine, Baltimore, Maryland, USA
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5
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Chang YM, Shen PS, Tang YH. Confidence interval for the difference between two median survival times with semiparametric transformation models. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2018.1563156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Yu-Mei Chang
- Department of Statistics, Tunghai University, Taichung, Taiwan
| | - Pao-Sheng Shen
- Department of Statistics, Tunghai University, Taichung, Taiwan
| | - Yu-Hsin Tang
- Department of Statistics, Tunghai University, Taichung, Taiwan
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6
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Chen CM, Shen PS, Liu Y. On semiparametric transformation model with LTRC data: pseudo likelihood approach. Stat Pap (Berl) 2021. [DOI: 10.1007/s00362-018-01080-w] [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]
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7
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Zhong W, Lu X, Wu J. Bi-level variable selection in semiparametric transformation models with right-censored data. Comput Stat 2021. [DOI: 10.1007/s00180-021-01075-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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8
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Ma H, Zhao W, Zhou Y. Semiparametric model of mean residual life with biased sampling data. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2019.106826] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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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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Li S, Wu Q, Sun J. Penalized estimation of semiparametric transformation models with interval-censored data and application to Alzheimer's disease. Stat Methods Med Res 2019; 29:2151-2166. [PMID: 31718478 DOI: 10.1177/0962280219884720] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Variable selection or feature extraction is fundamental to identify important risk factors from a large number of covariates and has applications in many fields. In particular, its applications in failure time data analysis have been recognized and many methods have been proposed for right-censored data. However, developing relevant methods for variable selection becomes more challenging when one confronts interval censoring that often occurs in practice. In this article, motivated by an Alzheimer's disease study, we develop a variable selection method for interval-censored data with a general class of semiparametric transformation models. Specifically, a novel penalized expectation-maximization algorithm is developed to maximize the complex penalized likelihood function, which is shown to perform well in the finite-sample situation through a simulation study. The proposed methodology is then applied to the interval-censored data arising from the Alzheimer's disease study mentioned above.
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Affiliation(s)
- Shuwei Li
- School of Economics and Statistics, Guangzhou University, Guangzhou, China
| | - Qiwei Wu
- Department of Statistics, University of Missouri, Columbia, MO, USA
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MO, USA
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11
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Shen PS, Liu Y. Pseudo MLE for semiparametric transformation model with doubly truncated data. J Korean Stat Soc 2019. [DOI: 10.1016/j.jkss.2018.12.003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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12
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Flandre P, O’Quigley J. Comparing Kaplan–Meier curves with delayed treatment effects: applications in immunotherapy trials. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12345] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Philippe Flandre
- Sorbonne Université, and Institut Pierre Louis d’Epidémiologie et de Santé Publique Paris France
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Huang CH. Mixture regression models for the gap time distributions and illness-death processes. LIFETIME DATA ANALYSIS 2019; 25:168-188. [PMID: 29374789 DOI: 10.1007/s10985-018-9418-7] [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: 12/16/2016] [Accepted: 01/11/2018] [Indexed: 06/07/2023]
Abstract
The aim of this study is to provide an analysis of gap event times under the illness-death model, where some subjects experience "illness" before "death" and others experience only "death." Which event is more likely to occur first and how the duration of the "illness" influences the "death" event are of interest. Because the occurrence of the second event is subject to dependent censoring, it can lead to bias in the estimation of model parameters. In this work, we generalize the semiparametric mixture models for competing risks data to accommodate the subsequent event and use a copula function to model the dependent structure between the successive events. Under the proposed method, the survival function of the censoring time does not need to be estimated when developing the inference procedure. We incorporate the cause-specific hazard functions with the counting process approach and derive a consistent estimation using the nonparametric maximum likelihood method. Simulations are conducted to demonstrate the performance of the proposed analysis, and its application in a clinical study on chronic myeloid leukemia is reported to illustrate its utility.
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Affiliation(s)
- Chia-Hui Huang
- Department of Statistics, National Taipei University, Taipei, Taiwan.
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14
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Lee SH. Assessing the censored linear regression model using martingale approximation. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1485938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Seung-Hwan Lee
- Department of Mathematics, Illinois Wesleyan University, Bloomington, IL, USA
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15
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Semiparametric transformation joint models for longitudinal covariates and interval-censored failure time. Comput Stat Data Anal 2018. [DOI: 10.1016/j.csda.2018.07.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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16
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Wang P, Zhao H, Du M, Sun J. Inference on semiparametric transformation model with general interval-censored failure time data. J Nonparametr Stat 2018. [DOI: 10.1080/10485252.2018.1478091] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Peijie Wang
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, People's Republic of China
- Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, People's Republic of China
| | - Hui Zhao
- School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China
| | - Mingyue Du
- Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, People's Republic of China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MI, USA
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17
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Chen CM, Shen PS. Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data. LIFETIME DATA ANALYSIS 2018; 24:250-272. [PMID: 28168333 DOI: 10.1007/s10985-016-9385-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2015] [Accepted: 11/04/2016] [Indexed: 06/06/2023]
Abstract
Left-truncated data often arise in epidemiology and individual follow-up studies due to a biased sampling plan since subjects with shorter survival times tend to be excluded from the sample. Moreover, the survival time of recruited subjects are often subject to right censoring. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of left-truncated and right-censored data. We propose a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of these models. The derived score equations for regression parameter and infinite-dimensional function suggest an iterative algorithm for cMLE. The cMLE is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated using the inverse of negative Hessian matrix. Intensive simulation studies are conducted to investigate the performance of the cMLE. An application to the Channing House data is given to illustrate the methodology.
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Affiliation(s)
- Chyong-Mei Chen
- Institute of Public Health, School of Medicine, National Yang-Ming University, Taipei, Taiwan, ROC
| | - Pao-Sheng Shen
- Department of Statistics, Tunghai University, Xitun District, Taichung, 40704, Taiwan, ROC.
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18
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Li S. Estimating time-dependent ROC curves using data under prevalent sampling. Stat Med 2017; 36:1285-1301. [PMID: 27891650 DOI: 10.1002/sim.7184] [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: 03/05/2016] [Revised: 10/09/2016] [Accepted: 11/03/2016] [Indexed: 11/10/2022]
Abstract
Prevalent sampling is frequently a convenient and economical sampling technique for the collection of time-to-event data and thus is commonly used in studies of the natural history of a disease. However, it is biased by design because it tends to recruit individuals with longer survival times. This paper considers estimation of time-dependent receiver operating characteristic curves when data are collected under prevalent sampling. To correct the sampling bias, we develop both nonparametric and semiparametric estimators using extended risk sets and the inverse probability weighting techniques. The proposed estimators are consistent and converge to Gaussian processes, while substantial bias may arise if standard estimators for right-censored data are used. To illustrate our method, we analyze data from an ovarian cancer study and estimate receiver operating characteristic curves that assess the accuracy of the composite markers in distinguishing subjects who died within 3-5 years from subjects who remained alive. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Shanshan Li
- Department of Biostatistics, Indiana University Fairbanks School of Public Health, Indianapolis, 46202, IN, U.S.A
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19
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Shen PS. Linear transformation models for survival analysis with tumor growth information in cancer screening study. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1030425] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Pao-Sheng Shen
- Department of Statistics, Tunghai University, Taichung, Taiwan
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20
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Chen CM, Shen PS, Wei JCC, Lin L. A semiparametric mixture cure survival model for left-truncated and right-censored data. Biom J 2016; 59:270-290. [PMID: 27878856 DOI: 10.1002/bimj.201500267] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Revised: 08/26/2016] [Accepted: 09/08/2016] [Indexed: 11/07/2022]
Abstract
In follow-up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left-truncated and right-censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum-likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput-wall distance event for patients with ankylosing spondylitis.
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Affiliation(s)
- Chyong-Mei Chen
- Institute of Public Health, School of Medicine, National Yang-Ming University, Taipei City, Taiwan
| | - Pao-Sheng Shen
- Department of Statistics, Tunghai University, Taichung City, Taiwan
| | - James Cheng-Chung Wei
- Division of Allergy, Immunology and Rheumatology, Department of Medicine, Chung Shan Medical University Hospital, Taichung City, Taiwan.,Division of Allergy, Immunology and Rheumatology, Chung Shan Medical University Hospital, Taichung City, Taiwan
| | - Lichi Lin
- Division of Allergy, Immunology and Rheumatology, Chung Shan Medical University Hospital, Taichung City, Taiwan.,Department of Statistics, Oklahoma State University, Stillwater, OK 74074, USA
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21
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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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22
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Mao L, Lin DY. Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks. J R Stat Soc Series B Stat Methodol 2016; 79:573-587. [PMID: 28239261 DOI: 10.1111/rssb.12177] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks. A semiparametric regression model proposed by Fine and Gray (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not statistically efficient. In this paper, we present a broad class of semiparametric transformation models which extends the Fine and Gray model, and we allow for unknown causes of failure. We derive the nonparametric maximum likelihood estimators (NPMLEs) and develop simple and fast numerical algorithms using the profile likelihood. We establish the consistency, asymptotic normality, and semiparametric efficiency of the NPMLEs. In addition, we construct graphical and numerical procedures to evaluate and select models. Finally, we demonstrate the advantages of the proposed methods over the existing ones through extensive simulation studies and an application to a major study on bone marrow transplantation.
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Affiliation(s)
- Lu Mao
- Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA
| | - D Y Lin
- Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA
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23
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Shen PS. Semiparametric analysis of transformation models with dependently left-truncated and right-censored data. COMMUN STAT-SIMUL C 2015. [DOI: 10.1080/03610918.2015.1048879] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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24
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Yang S, Prentice RL. Assessing potentially time-dependent treatment effect from clinical trials and observational studies for survival data, with applications to the Women's Health Initiative combined hormone therapy trial. Stat Med 2015; 34:1801-17. [PMID: 25689356 PMCID: PMC4393788 DOI: 10.1002/sim.6453] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2014] [Revised: 01/15/2015] [Accepted: 01/20/2015] [Indexed: 11/07/2022]
Abstract
For risk and benefit assessment in clinical trials and observational studies with time-to-event data, the Cox model has usually been the model of choice. When the hazards are possibly non-proportional, a piece-wise Cox model over a partition of the time axis may be considered. Here, we propose to analyze clinical trials or observational studies with time-to-event data using a certain semiparametric model. The model allows for a time-dependent treatment effect. It includes the important proportional hazards model as a sub-model and can accommodate various patterns of time-dependence of the hazard ratio. After estimation of the model parameters using a pseudo-likelihood approach, simultaneous confidence intervals for the hazard ratio function are established using a Monte Carlo method to assess the time-varying pattern of the treatment effect. To assess the overall treatment effect, estimated average hazard ratio and its confidence intervals are also obtained. The proposed methods are applied to data from the Women's Health Initiative. To compare the Women's Health Initiative clinical trial and observational study, we use the propensity score in building the regression model. Compared with the piece-wise Cox model, the proposed model yields a better model fit and does not require partitioning of the time axis.
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Affiliation(s)
- Song Yang
- Office of Biostatistics Research, National Heart, Lung, and Blood Institute, Bethesda, 20892, MD, U. S. A
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25
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Choi S, Huang X, Cormier JN, Doksum KA. A semiparametric inverse-Gaussian model and inference for survival data with a cured proportion. CAN J STAT 2014. [DOI: 10.1002/cjs.11226] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Sangbum Choi
- Division of Clinical and Translational Sciences, Department of Internal Medicine; The University of Texas Health Science Center at Houston; Houston, TX U.S.A
| | - Xuelin Huang
- Department of Biostatistics; The University of Texas MD Anderson Cancer Center; Houston, TX U.S.A
| | - Janice N. Cormier
- Department of Surgical Oncology; The University of Texas MD Anderson Cancer Center; Houston, TX U.S.A
| | - Kjell A. Doksum
- Department of Statistics; University of Wisconsin; Madison, WI U.S.A
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26
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Choi S, Huang X. Maximum likelihood estimation of semiparametric mixture component models for competing risks data. Biometrics 2014; 70:588-98. [PMID: 24734912 DOI: 10.1111/biom.12167] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2013] [Revised: 01/01/2014] [Accepted: 03/01/2014] [Indexed: 02/03/2023]
Abstract
In the analysis of competing risks data, the cumulative incidence function is a useful quantity to characterize the crude risk of failure from a specific event type. In this article, we consider an efficient semiparametric analysis of mixture component models on cumulative incidence functions. Under the proposed mixture model, latency survival regressions given the event type are performed through a class of semiparametric models that encompasses the proportional hazards model and the proportional odds model, allowing for time-dependent covariates. The marginal proportions of the occurrences of cause-specific events are assessed by a multinomial logistic model. Our mixture modeling approach is advantageous in that it makes a joint estimation of model parameters associated with all competing risks under consideration, satisfying the constraint that the cumulative probability of failing from any cause adds up to one given any covariates. We develop a novel maximum likelihood scheme based on semiparametric regression analysis that facilitates efficient and reliable estimation. Statistical inferences can be conveniently made from the inverse of the observed information matrix. We establish the consistency and asymptotic normality of the proposed estimators. We validate small sample properties with simulations and demonstrate the methodology with a data set from a study of follicular lymphoma.
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Affiliation(s)
- Sangbum Choi
- Division of Clinical and Translational Sciences, Department of Internal Medicine, The University of Texas, Health Science Center at Houston, Houston, Texas 77030, U.S.A
| | - Xuelin Huang
- Department of Biostatistics, The University of Texas, MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 1411, Houston, Texas 77030, U.S.A
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27
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Hu C, Tsodikov A. Semiparametric regression analysis for time-to-event marked endpoints in cancer studies. Biostatistics 2013; 15:513-25. [PMID: 24379192 DOI: 10.1093/biostatistics/kxt056] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In cancer studies the disease natural history process is often observed only at a fixed, random point of diagnosis (a survival time), leading to a current status observation (Sun (2006). The statistical analysis of interval-censored failure time data. Berlin: Springer.) representing a surrogate (a mark) (Jacobsen (2006). Point process theory and applications: marked point and piecewise deterministic processes. Basel: Birkhauser.) attached to the observed survival time. Examples include time to recurrence and stage (local vs. metastatic). We study a simple model that provides insights into the relationship between the observed marked endpoint and the latent disease natural history leading to it. A semiparametric regression model is developed to assess the covariate effects on the observed marked endpoint explained by a latent disease process. The proposed semiparametric regression model can be represented as a transformation model in terms of mark-specific hazards, induced by a process-based mixed effect. Large-sample properties of the proposed estimators are established. The methodology is illustrated by Monte Carlo simulation studies, and an application to a randomized clinical trial of adjuvant therapy for breast cancer.
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Affiliation(s)
- Chen Hu
- RTOG Statistical Center, American College of Radiology, Philadelphia, PA 19103, USA
| | - Alex Tsodikov
- Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48109, USA
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Liu H, Qin J, Shen Y. Imputation for semiparametric transformation models with biased-sampling data. LIFETIME DATA ANALYSIS 2012; 18:470-503. [PMID: 22903245 PMCID: PMC3440536 DOI: 10.1007/s10985-012-9225-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2011] [Accepted: 08/01/2012] [Indexed: 06/01/2023]
Abstract
Widely recognized in many fields including economics, engineering, epidemiology, health sciences, technology and wildlife management, length-biased sampling generates biased and right-censored data but often provide the best information available for statistical inference. Different from traditional right-censored data, length-biased data have unique aspects resulting from their sampling procedures. We exploit these unique aspects and propose a general imputation-based estimation method for analyzing length-biased data under a class of flexible semiparametric transformation models. We present new computational algorithms that can jointly estimate the regression coefficients and the baseline function semiparametrically. The imputation-based method under the transformation model provides an unbiased estimator regardless whether the censoring is independent or not on the covariates. We establish large-sample properties using the empirical processes method. Simulation studies show that under small to moderate sample sizes, the proposed procedure has smaller mean square errors than two existing estimation procedures. Finally, we demonstrate the estimation procedure by a real data example.
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Affiliation(s)
- Hao Liu
- Division of Biostatistics, Dan L. Duncan Cancer Center, Baylor College of Medicine, Houston, Texas, 77030, USA
| | - Jing Qin
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institute of Health, Bethesda, Maryland, 20892, USA
| | - Yu Shen
- Department of Biostatistics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas, 77030, USA
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