1
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Withana Gamage PW, McMahan CS, Wang L. A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model. LIFETIME DATA ANALYSIS 2023; 29:188-212. [PMID: 36208362 PMCID: PMC9852023 DOI: 10.1007/s10985-022-09579-z] [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: 01/27/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.
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Affiliation(s)
| | - Christopher S McMahan
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, 29634, USA
| | - Lianming Wang
- Department of Statistics, University of South Carolina, Columbia, SC, 29208, USA
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2
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Li Y, Liu H, Wang X, Tu W. Semi-parametric time-to-event modelling of lengths of hospital stays. J R Stat Soc Ser C Appl Stat 2022; 71:1623-1647. [PMID: 36632280 PMCID: PMC9826400 DOI: 10.1111/rssc.12593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 08/11/2022] [Indexed: 02/01/2023]
Abstract
Length of stay (LOS) is an essential metric for the quality of hospital care. Published works on LOS analysis have primarily focused on skewed LOS distributions and the influences of patient diagnostic characteristics. Few authors have considered the events that terminate a hospital stay: Both successful discharge and death could end a hospital stay but with completely different implications. Modelling the time to the first occurrence of discharge or death obscures the true nature of LOS. In this research, we propose a structure that simultaneously models the probabilities of discharge and death. The model has a flexible formulation that accounts for both additive and multiplicative effects of factors influencing the occurrence of death and discharge. We present asymptotic properties of the parameter estimates so that valid inference can be performed for the parametric as well as nonparametric model components. Simulation studies confirmed the good finite-sample performance of the proposed method. As the research is motivated by practical issues encountered in LOS analysis, we analysed data from two real clinical studies to showcase the general applicability of the proposed model.
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Affiliation(s)
- Yang Li
- Department of Biostatistics and Health Data ScienceIndiana UniversityIndianapolisIndianaUSA
| | - Hao Liu
- Department of Biostatistics and EpidemiologyRutgers School of Public HealthPiscatawayNew JerseyUSA
| | - Xiaoshen Wang
- Department of Mathematics and StatisticsUniversity of Arkansas at Little RockLittle RockArkansasUSA
| | - Wanzhu Tu
- Department of Biostatistics and Health Data ScienceIndiana UniversityIndianapolisIndianaUSA
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3
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Petti D, Eletti A, Marra G, Radice R. Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107550] [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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4
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Feng Y, Wang J, Li Y. Goodness-of-fit inference for the additive hazards regression model with clustered current status data. J Appl Stat 2022. [DOI: 10.1080/02664763.2022.2053950] [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)
- Yanqin Feng
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, People's Repubic of China
| | - Jie Wang
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, People's Repubic of China
| | - Yang Li
- Department of Biostatistics and Health Data Science, Indiana University School of Medicine, Indianapolis, IN, USA
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5
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Feng Y, Sun J, Sun L. Estimation of the additive hazards model with linear inequality restrictions based on current status data. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1742922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Yanqin Feng
- School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China
- Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, Missouri, USA
| | - Lingli Sun
- College of Science, Huazhong Agricultural University, Wuhan, P.R. China
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6
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Xu Y, Zhao S, Hu T, Sun J. Variable selection for generalized odds rate mixture cure models with interval-censored failure time data. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2020.107115] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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7
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Li H, Ma C, Li N, Sun J. A vine copula approach for regression analysis of bivariate current status data with informative censoring. J Nonparametr Stat 2020. [DOI: 10.1080/10485252.2019.1710506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Huiqiong Li
- Department of Statistics, Yunnan University, Yunnan, People's Republic of China
| | - Chenchen Ma
- Department of Statistics, University of Missouri, Columbia, MO, USA
| | - Ni Li
- School of Mathematics and Statistics, Hainan Normal University, Huainan, 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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Withana Gamage PW, Chaudari M, McMahan CS, Kim EH, Kosorok MR. An extended proportional hazards model for interval-censored data subject to instantaneous failures. LIFETIME DATA ANALYSIS 2020; 26:158-182. [PMID: 30796598 PMCID: PMC6707903 DOI: 10.1007/s10985-019-09467-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2018] [Accepted: 02/11/2019] [Indexed: 06/09/2023]
Abstract
The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies. In many such studies, the event time is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties since the event time of interest is unobserved. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation-maximization (EM) algorithm is developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference. The motivation for this work arises from a randomized clinical trial aimed at assessing the effectiveness of a new peanut allergen treatment in attaining sustained unresponsiveness in children.
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Affiliation(s)
| | - Monica Chaudari
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA
| | - Christopher S McMahan
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, 29634, USA.
| | - Edwin H Kim
- Division of Rheumatology, Allergy and Immunology, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA
| | - Michael R Kosorok
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA
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9
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Sun T, Ding Y. Copula-based semiparametric regression method for bivariate data under general interval censoring. Biostatistics 2019; 22:315-330. [PMID: 31506682 DOI: 10.1093/biostatistics/kxz032] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 08/09/2019] [Accepted: 08/11/2019] [Indexed: 11/12/2022] Open
Abstract
This research is motivated by discovering and underpinning genetic causes for the progression of a bilateral eye disease, age-related macular degeneration (AMD), of which the primary outcomes, progression times to late-AMD, are bivariate and interval-censored due to intermittent assessment times. We propose a novel class of copula-based semiparametric transformation models for bivariate data under general interval censoring, which includes the case 1 interval censoring (current status data) and case 2 interval censoring. Specifically, the joint likelihood is modeled through a two-parameter Archimedean copula, which can flexibly characterize the dependence between the two margins in both tails. The marginal distributions are modeled through semiparametric transformation models using sieves, with the proportional hazards or odds model being a special case. We develop a computationally efficient sieve maximum likelihood estimation procedure for the unknown parameters, together with a generalized score test for the regression parameter(s). For the proposed sieve estimators of finite-dimensional parameters, we establish their asymptotic normality and efficiency. Extensive simulations are conducted to evaluate the performance of the proposed method in finite samples. Finally, we apply our method to a genome-wide analysis of AMD progression using the Age-Related Eye Disease Study data, to successfully identify novel risk variants associated with the disease progression. We also produce predicted joint and conditional progression-free probabilities, for patients with different genetic characteristics.
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Affiliation(s)
- Tao Sun
- Department of Biostatistics, University of Pittsburgh, 130 DeSoto St, Pittsburgh, PA 15261, USA
| | - Ying Ding
- Department of Biostatistics, University of Pittsburgh, 130 DeSoto St, Pittsburgh, PA 15261, USA
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10
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Li S, Hu T, Tong T, Sun J. Semiparametric regression analysis of multivariate doubly censored data. STAT MODEL 2019. [DOI: 10.1177/1471082x19859949] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article discusses regression analysis of multivariate doubly censored data with a wide class of flexible semiparametric transformation frailty models. The proposed models include many commonly used regression models as special cases such as the proportional hazards and proportional odds frailty models. For inference, we propose a nonparametric maximum likelihood estimation method and develop a new expectation–maximization algorithm for its implementation. The proposed estimators of the finite-dimensional parameters are shown to be consistent, asymptotically normal and semiparametrically efficient. We also conduct a simulation study to assess the finite sample performance of the developed estimation method, and the proposed methodology is applied to a set of real data arising from an AIDS study.
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Affiliation(s)
- Shuwei Li
- School of Economics and Statistics, Guangzhou University, Guangzhou, China
| | - Tao Hu
- School of Mathematical Sciences, Capital Normal University, Beijing, China
| | - Tiejun Tong
- Department of Mathematics, Hong Kong Baptist University, Hong Kong
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, Missouri, USA
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11
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Gamage PWW, McMahan CS, Wang L, Tu W. A Gamma-frailty proportional hazards model for bivariate interval-censored data. Comput Stat Data Anal 2019; 128:354-366. [PMID: 31011236 DOI: 10.1016/j.csda.2018.07.016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. In this work, a Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation-maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.
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Affiliation(s)
| | | | - Lianming Wang
- Department of Statistics, University of South Carolina, SC 29208, U.S.A
| | - Wanzhu Tu
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN 46202, U.S.A
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12
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Chaudhari M, Kim EH, Withana Gamage PW, McMahan CS, Kosorok MR. Study design with staggered sampling times for evaluating sustained unresponsiveness to peanut sublingual immunotherapy. Stat Med 2018; 37:3944-3958. [PMID: 29974494 DOI: 10.1002/sim.7857] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Revised: 04/12/2018] [Accepted: 06/04/2018] [Indexed: 11/08/2022]
Abstract
In this work, we delineate an altered study design of a pre-existing clinical trial that is currently being implemented in the Department of Pediatrics at the University of North Carolina at Chapel Hill. The purpose of the ongoing investigation of the desensitized pediatric cohort is to address the effectiveness of sublingual immunotherapy in achieving sustained unresponsiveness (SU) as assessed by repeated double-blind placebo-controlled food challenges (DBPCFC). With scarce published literature characterizing SU, the length of time off-therapy that would represent clinically meaningful benefit remains undefined. We use the new design features to assess time to loss of SU, an important efficacy endpoint, that to our knowledge, no prior study has investigated. Our work has two-fold objectives: first is to propose and discuss aspects of the altered design that would allow us to study SU and second is to explore methodology to evaluate the time to loss of SU and its association with risk factors in the context of the data originating from the trial. The salient feature of the new design is the allocation scheme of study subjects to staggered sampling timepoints when a subsequent DBPCFC is administered. Due to this feature, the time to loss of SU is either left or right censored. Additionally, some participants at study entry fail the DBPCFC, leading to what can be construed as an instantaneous failure. Through in-depth numerical studies, we examine the performance and power of a recently proposed mixture proportional hazards model specifically designed for the analysis of interval-censored data subject to instantaneous failures.
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Affiliation(s)
- Monica Chaudhari
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
| | - Edwin H Kim
- Division of Allergy and Immunology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
| | | | | | - Michael R Kosorok
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
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13
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Feng Y, Dong Y, Li Y. Additive hazards regression of current status data with auxiliary covariates. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1242737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Yanqin Feng
- School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China
| | - Yuan Dong
- School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China
| | - Yang Li
- Department of Mathematics and Statistics, University of North Carolina-Charlotte, Charlotte, NC, USA
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14
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Zeng D, Gao F, Lin DY. Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data. Biometrika 2017; 104:505-525. [PMID: 29391606 PMCID: PMC5787874 DOI: 10.1093/biomet/asx029] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2016] [Indexed: 11/13/2022] Open
Abstract
Interval-censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval. We investigate the effects of possibly time-dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects, and we study nonparametric maximum likelihood estimation under general interval-censoring schemes. We show that the proposed estimators for the finite-dimensional parameters are consistent and asymptotically normal, with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we develop an EM algorithm that converges stably for arbitrary datasets. Finally, we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the Atherosclerosis Risk in Communities Study.
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Affiliation(s)
- Donglin Zeng
- Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
| | - Fei Gao
- Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
| | - D. Y. Lin
- Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
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15
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Li S, Hu T, Wang P, Sun J. Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments. Comput Stat Data Anal 2017. [DOI: 10.1016/j.csda.2016.12.011] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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16
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Liu H, Qin J. Semiparametric probit models with univariate and bivariate current-status data. Biometrics 2017; 74:68-76. [PMID: 28437561 DOI: 10.1111/biom.12709] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Revised: 03/01/2017] [Accepted: 03/01/2017] [Indexed: 11/29/2022]
Abstract
Multivariate current-status data are frequently encountered in biomedical and public health studies. Semiparametric regression models have been extensively studied for univariate current-status data, but most existing estimation procedures are computationally intensive, involving either penalization or smoothing techniques. It becomes more challenging for the analysis of multivariate current-status data. In this article, we study the maximum likelihood estimations for univariate and bivariate current-status data under the semiparametric probit regression models. We present a simple computational procedure combining the expectation-maximization algorithm with the pool-adjacent-violators algorithm for solving the monotone constraint on the baseline function. Asymptotic properties of the maximum likelihood estimators are investigated, including the calculation of the explicit information bound for univariate current-status data, as well as the asymptotic consistency and convergence rate for bivariate current-status data. Extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes. We demonstrate the estimation procedure with two real data examples in the areas of diabetic and HIV research.
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Affiliation(s)
- Hao Liu
- Division of Biostatistics, Dan L. Duncan Cancer Center, Baylor College of Medicine, Houston, Texas 77030, U.S.A
| | - Jing Qin
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases National Institutes of Health, Bethesda, Maryland 20892, U.S.A
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17
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Zhou Q, Hu T, Sun J. A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data. J Am Stat Assoc 2017. [DOI: 10.1080/01621459.2016.1158113] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Qingning Zhou
- Department of Statistics, University of Missouri, Columbia, MO
| | - Tao Hu
- School of Mathematical Sciences & BCMIIS, Capital Normal University, Beijing, China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MO
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18
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Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.01.015] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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