1
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Liang M, Li Z, Li L, Chinchilli VM, Zhang L, Wang M. Tackling dynamic prediction of death in patients with recurrent cardiovascular events. Stat Med 2023; 42:3487-3507. [PMID: 37282984 DOI: 10.1002/sim.9815] [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: 01/15/2022] [Revised: 04/03/2023] [Accepted: 05/18/2023] [Indexed: 06/08/2023]
Abstract
In the field of cardiovascular disease, recurrent events such as stroke or myocardial infarction (MI) are often encountered, leading to an increase in the risk of death. Accurately evaluating the prognosis of patients and dynamically predicting the risk of death by considering the historical recurrent events can improve medical decisions and lead to better health care outcomes. Recently proposed joint modeling approaches within the Bayesian framework have inspired the development of a dynamic prediction tool, which can be applied for subject-level prediction of death with implementation in software packages. The prediction model incorporates subject heterogeneity with subject-level random effects that account for unobserved time-invariant factors and an extra copula function capturing the part caused by unmeasured time-dependent factors. Thereafter, given the prespecified landmark timet ' $$ {t}^{\prime } $$ , the survival probability for a prediction horizon time of interestt $$ t $$ can be estimated for each individual. The prediction accuracy is assessed by time-dependent receiving operating characteristic curve and the area under the curve and the Brier score with calibration plots is compared to traditional joint frailty models. Finally, the tool is applied to patients with multiple attacks of stroke or MI in the Cardiovascular Health study and the Atherosclerosis Risk in Communities study for illustration.
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Affiliation(s)
- Menglu Liang
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania, USA
| | - Zheng Li
- Novartis Pharmaceuticals, East Hanover, New Jersey, USA
| | - Liang Li
- Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, Texas, USA
| | - Vernon M Chinchilli
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania, USA
| | - Lijun Zhang
- Department of Population and Quantitative Health Sciences, School of Medicine, Case Western Reserve University, Cleaveland, OH, USA
| | - Ming Wang
- Department of Population and Quantitative Health Sciences, School of Medicine, Case Western Reserve University, Cleaveland, OH, USA
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2
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Sundin PT, Aralis H, Glenn B, Bastani R, Crespi CM. A semi-Markov multistate cure model for estimating intervention effects in stepped wedge design trials. Stat Methods Med Res 2023; 32:1511-1526. [PMID: 37448319 DOI: 10.1177/09622802231176123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/15/2023]
Abstract
Multistate models are useful for studying exposures that affect transitions among a set of health states. However, they can be challenging to apply when exposures are time-varying. We develop a multistate model and a method of likelihood construction that allows application of the model to data in which interventions or other exposures can be time-varying and an individual may to be exposed to multiple intervention conditions while progressing through states. The model includes cure proportions, reflecting the possibility that some individuals will never leave certain states. We apply the approach to analyze patient vaccination data from a stepped wedge design trial evaluating two interventions to increase uptake of human papillomavirus vaccination. The states are defined as the number of vaccine doses the patient has received. We model state transitions as a semi-Markov process and include cure proportions to account for individuals who will never leave a given state (e.g. never receive their next dose). Multistate models typically quantify intervention effects as hazard ratios contrasting the intensities of transitions between states in intervention versus control conditions. For multistate processes, another clinically meaningful outcome is the change in the percentage of the study population that has achieved a specific state (e.g. completion of all required doses) by a specific point in time due to an intervention. We present a method for quantifying intervention effects in this manner. We apply the model to both simulated and real-world data and also explore some conditions under which such models may give biased results.
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Affiliation(s)
| | | | - Beth Glenn
- University of California Los Angeles, CA, USA
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3
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Ma C, Crimin K. Joint Analysis of Longitudinal Data and Zero-Inflated Recurrent Events. Stat Biopharm Res 2023. [DOI: 10.1080/19466315.2023.2177726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Chenchen Ma
- Statistics, Data and Analytics, Eli Lilly and Company, Indiana, USA
| | - Kimberly Crimin
- Statistics, Data and Analytics, Eli Lilly and Company, Indiana, USA
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4
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Liu K, Balakrishnan N, He M, Xie L. Likelihood inference for Birnbaum–Saunders frailty model with an application to bone marrow transplant data. J STAT COMPUT SIM 2023. [DOI: 10.1080/00949655.2023.2174543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Kai Liu
- School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - Mu He
- Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, People's Republic of China
| | - Lingfang Xie
- School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
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5
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Liu K, Balakrishnan N, He M. Generalized Birnbaum–Saunders mixture cure frailty model: inferential method and an application to bone marrow transplant data. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1995753] [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]
Affiliation(s)
- Kai Liu
- School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, P.R. China
| | | | - Mu He
- The Department of Foundational Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, P.R. China
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6
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Rahmati M, Rezanejad Asl P, Mikaeli J, Zeraati H, Rasekhi A. Compound Poisson frailty model with a gamma process prior for the baseline hazard: accounting for a cured fraction. J Appl Stat 2021; 49:3377-3391. [DOI: 10.1080/02664763.2021.1947997] [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)
- Maryam Rahmati
- Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
- Reproductive Endocrinology Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
| | - Parisa Rezanejad Asl
- Department of Biostatistics, Faculty of Allied Medical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
| | - Javad Mikaeli
- Autoimmune and Motility Disorders Research Center, Digestive Diseases Research Institute, Tehran University of Medical Sciences, Tehran, Iran
| | - Hojjat Zeraati
- Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
| | - Aliakbar Rasekhi
- Biostatistics Department, Medical Sciences Faculty, Tarbiat Modares University, Tehran, Iran
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7
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Ha ID, Lee Y. A review of h-likelihood for survival analysis. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2021. [DOI: 10.1007/s42081-021-00125-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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8
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Ma C, Hu T, Lin Z. Semiparametric analysis of zero-inflated recurrent events with a terminal event. Stat Med 2021; 40:4053-4067. [PMID: 33963791 DOI: 10.1002/sim.9013] [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: 10/09/2020] [Revised: 04/10/2021] [Accepted: 04/13/2021] [Indexed: 11/09/2022]
Abstract
Recurrent event data frequently arise in longitudinal studies and observations on recurrent events could be terminated by a major failure event such as death. In many situations, there exist a large fraction of subjects without any recurrent events of interest. Among these subjects, some are unsusceptible to recurrent events, while others are susceptible but have no recurrent events being observed due to censoring. In this article, we propose a zero-inflated generalized joint frailty model and a sieve maximum likelihood approach to analyze zero-inflated recurrent events with a terminal event. The model provides a considerable flexibility in formulating the effects of covariates on both recurrent events and the terminal event by specifying various transformation functions. In addition, Bernstein polynomials are employed to approximate the unknown cumulative baseline hazard (intensity) function. The estimation procedure can be easily implemented and is computationally fast. Extensive simulation studies are conducted and demonstrate that our proposed method works well for practical situations. Finally, we apply the method to analyze myocardial infarction recurrences in the presence of death in a clinical trial with cardiovascular outcomes.
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Affiliation(s)
- Chenchen Ma
- Global Statistical Sciences, Eli Lilly and Company, Indianapolis, Indiana
| | - Tao Hu
- School of Mathematical Sciences, Capital Normal University, Beijing, People's Republic of China
| | - Zhantao Lin
- Global Statistical Sciences, Eli Lilly and Company, Indianapolis, Indiana
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9
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van den Berg I, Coebergh van den Braak RRJ, van Vugt JLA, Ijzermans JNM, Buettner S. Actual survival after resection of primary colorectal cancer: results from a prospective multicenter study. World J Surg Oncol 2021; 19:96. [PMID: 33820567 PMCID: PMC8022415 DOI: 10.1186/s12957-021-02207-4] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 03/19/2021] [Indexed: 02/08/2023] Open
Abstract
BACKGROUND Colorectal cancer is the third most common type of cancer in the world. We characterize a cohort of patients who survived up to 5 years without recurrence and identify factors predicting the probability of cure. METHODS We analyzed data of patients who underwent curative intent surgery for stage I-III CRC between 2007 and 2012 and who had had been included in a large multicenter study in the Netherlands. Cure was defined as 5-year survival without recurrence. Survival data were retrieved from a national registry. RESULTS Analysis of data of 754 patients revealed a cure rate of 65% (n = 490). Patients with stage I disease and T1- and N0-tumor had the highest probability of cure (94%, 95% and 90%, respectively). Those with a T4-tumor or N2-tumor had the lowest probability of cure (62% and 50%, respectively). A peak in the mortality rate for older patients early in follow-up suggests early excess mortality as an explanation. A similar trend was observed for stage III disease, poor tumor grade, postoperative complications, sarcopenia, and R1 resections. Patients with stage III disease, poor tumor grade, postoperative complications, sarcopenia, and R1 resections show a similar trend for decrease in CSS deaths over time. CONCLUSION In the studied cohort, the probability of cure for patients with stage I-III CRC ranged from 50 to 95%. Even though most patients will be cured from CRC with standard therapy, standard therapy is insufficient for those with poor prognostic factors, such as high T- and N-stage and poor differentiation grade.
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Affiliation(s)
- Inge van den Berg
- Department of Surgery, Erasmus MC - University Medical Center Rotterdam, Rotterdam, 3015 GD, The Netherlands.
| | | | - Jeroen L A van Vugt
- Department of Surgery, Erasmus MC - University Medical Center Rotterdam, Rotterdam, 3015 GD, The Netherlands
| | - Jan N M Ijzermans
- Department of Surgery, Erasmus MC - University Medical Center Rotterdam, Rotterdam, 3015 GD, The Netherlands
| | - Stefan Buettner
- Department of Surgery, Erasmus MC - University Medical Center Rotterdam, Rotterdam, 3015 GD, The Netherlands
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10
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Kim YJ. Joint model for bivariate zero-inflated recurrent event data with terminal events. J Appl Stat 2021; 48:738-749. [DOI: 10.1080/02664763.2020.1744539] [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)
- Yang-Jin Kim
- Department of Statistics, Sookmyung Women's University, Seoul, South Korea
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11
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Cavenague de Souza HC, Louzada F, de Oliveira MR, Fawole B, Akintan A, Oyeneyin L, Sanni W, Silva Castro Perdoná GD. The Log-Normal zero-inflated cure regression model for labor time in an African obstetric population. J Appl Stat 2021; 49:2416-2429. [DOI: 10.1080/02664763.2021.1896684] [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)
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil
| | | | - Bukola Fawole
- Department of Obstetrics and Gynaecology, College of Medicine, University of Ibadan, Ibadan, Nigeria
| | - Adesina Akintan
- Department of Obstetrics and Gynaecology, Mother and Child Hospital, Akure, Ondo State, Nigeria
| | - Lawal Oyeneyin
- Department of Obstetrics and Gynaecology, Mother and Child Hospital, Ondo, Ondo State, Nigeria
| | | | - Gleici da Silva Castro Perdoná
- Department of Social Medicine, Ribeirão Preto School of Medicine, University of São Paulo, Ribeirão Preto, São Paulo Brazil
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12
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Talebi-Ghane E, Baghestani A, Zayeri F, Rondeau V, Akhavan A. Joint frailty model for recurrent events and death in presence of cure fraction: Application to breast cancer data. Biom J 2020; 63:725-744. [PMID: 33368665 DOI: 10.1002/bimj.201900113] [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: 04/13/2019] [Revised: 06/22/2020] [Accepted: 06/07/2020] [Indexed: 11/10/2022]
Abstract
In many biomedical cohort studies, recurrent or repeated events for individuals can be terminated by a dependent terminal event like death. In this context, the time of death may be associated with the underlying recurrent process and there often exists the dependence between the occurrences of recurrent events. Moreover, there are some situations in which a portion of patients could be cured. In the present study, the term "cured" means that some patients may neither experience any recurrent events nor death induced by the disease under study. We proposed a joint frailty model in the presence of cure fraction for analysis of the recurrent and terminal events and estimated the effect of covariates on the cure rate and both aforementioned events concurrently. The use of two independent gamma distributed frailties in this model enabled us to consider both the dependence between the recurrences and the survival times and the interrecurrences dependence. The model parameters were estimated employing the maximum likelihood method for a piecewise constant and a parametric baseline hazard function. Our proposed model was evaluated by a simulation study and illustrated using a real data set on patients with breast cancer who had undergone surgery.
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Affiliation(s)
- Elaheh Talebi-Ghane
- Modeling of Noncommunicable Diseases Research Center, Hamadan University of Medical Sciences, Hamadan, Iran
| | - AhmadReza Baghestani
- Biostatistics Department, Physiotherapy Research Center, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
| | - Farid Zayeri
- Biostatistics Department, Proteomics Research Center, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
| | - Virgine Rondeau
- INSERM U1219, University of Bordeaux, ISPED, Bordeaux, France
| | - Ali Akhavan
- Radiation Oncology, Isfahan University of Medical Sciences, Isfahan, Iran
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13
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14
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Wang Z, Wang X. Evaluating the time-dependent predictive accuracy for event-to-time outcome with a cure fraction. Pharm Stat 2020; 19:955-974. [PMID: 32776646 DOI: 10.1002/pst.2048] [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: 07/19/2019] [Revised: 05/10/2020] [Accepted: 06/14/2020] [Indexed: 11/08/2022]
Abstract
In medical studies, it is often observed that a portion of subjects will never experience the event of interest and thus can be treated as cured or long-term survivors. Many populations of early-stage cancer patients contain both uncured and cured individuals that should be modeled using cure models. In prognostic studies, the cure status (uncure or cure) is an issue of interest for medical practitioners, and the disease status (death or alive) of an individual is not a fixed characteristic and it varies along the time. These statuses are usually predicted by a prognostic risk score. The time-dependent receiver operating characteristic (ROC) curve is a powerful tool to evaluate these predicting performances dynamically. In the context with a cure fraction, quantifying and estimating the predictive performances of the risk score is a challenge since the disease status and cure status are both unknown among individuals who are censored. In this paper, to assess the predictive accuracy for the survival outcome with a cure fraction, we propose a time-dependent ROC curve semi-parametric estimator based on the sieve maximum likelihood (ML) estimation under the mixture cure model. We also apply a Bernstein-based smoothing method in the estimation procedure, and this estimator can lead to substantial gain in efficiency. In addition, we derive the time-dependent area under the ROC curve (AUC) to summarize the discriminatory capacity of the risk score globally. Finally, we evaluate the finite sample performance of the proposed methods by extensive simulations and illustrate the estimation using two real data sets, one from a melanoma study and the other from stomach cancer.
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Affiliation(s)
- Ziwen Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Xiaoguang Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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15
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Tawiah R, McLachlan GJ, Ng SK. Mixture cure models with time-varying and multilevel frailties for recurrent event data. Stat Methods Med Res 2020; 29:1368-1385. [PMID: 31293217 DOI: 10.1177/0962280219859377] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.
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Affiliation(s)
- Richard Tawiah
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia
| | | | - Shu Kay Ng
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia
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16
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Analysis of bivariate recurrent event data with zero inflation. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2020. [DOI: 10.29220/csam.2020.27.1.037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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17
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Tawiah R, McLachlan GJ, Ng SK. A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction. Biometrics 2020; 76:753-766. [PMID: 31863594 DOI: 10.1111/biom.13202] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Revised: 12/02/2019] [Accepted: 12/04/2019] [Indexed: 12/31/2022]
Abstract
In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.
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Affiliation(s)
- Richard Tawiah
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Nathan, Australia.,School of Psychology, University of New South Wales, Sydney, Australia
| | | | - Shu Kay Ng
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Nathan, Australia
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18
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Kim Y. Joint model for recurrent event data with a cured fraction and a terminal event. Biom J 2019; 62:24-33. [DOI: 10.1002/bimj.201800321] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2018] [Revised: 04/22/2019] [Accepted: 05/24/2019] [Indexed: 11/06/2022]
Affiliation(s)
- Yang‐Jin Kim
- Department of StatisticsSookmyung Women's UniversitySeoul Korea
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19
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Liu L, Shih YCT, Strawderman RL, Zhang D, Johnson BA, Chai H. Statistical Analysis of Zero-Inflated Nonnegative Continuous Data: A Review. Stat Sci 2019. [DOI: 10.1214/18-sts681] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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20
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Charles‐Nelson A, Katsahian S, Schramm C. How to analyze and interpret recurrent events data in the presence of a terminal event: An application on readmission after colorectal cancer surgery. Stat Med 2019; 38:3476-3502. [DOI: 10.1002/sim.8168] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Revised: 03/27/2019] [Accepted: 03/27/2019] [Indexed: 11/08/2022]
Affiliation(s)
- Anaïs Charles‐Nelson
- Sorbonne Universités, UPMC Univ Paris 06, UMRS 1138Centre de Recherche des Cordeliers Paris France
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Assistance Publique Hôpitaux de Paris, Hôpital Européen Georges‐PompidouUnité d'Épidémiologie et de Recherche Clinique, INSERM, Centre d'Investigation Clinique 1418, Module Épidémiologie Clinique Paris France
| | - Sandrine Katsahian
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Assistance Publique Hôpitaux de Paris, Hôpital Européen Georges‐PompidouUnité d'Épidémiologie et de Recherche Clinique, INSERM, Centre d'Investigation Clinique 1418, Module Épidémiologie Clinique Paris France
| | - Catherine Schramm
- Sorbonne Universités, UPMC Univ Paris 06, UMRS 1138Centre de Recherche des Cordeliers Paris France
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
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21
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Li Z, Chinchilli VM, Wang M. A Bayesian joint model of recurrent events and a terminal event. Biom J 2018; 61:187-202. [PMID: 30479030 DOI: 10.1002/bimj.201700326] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 08/16/2018] [Accepted: 09/07/2018] [Indexed: 11/06/2022]
Abstract
Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. In this situation, dependent censoring is encountered because of potential dependence between these two event processes, leading to invalid inference if analyzing recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject-level frailty; however, this could be violated when the dependency may also depend on time-varying covariates across recurrences. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation with vague interpretation. In order to fill these gaps, we propose a novel joint frailty-copula approach to model recurrent events and a terminal event with relaxed assumptions. Metropolis-Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness, and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error of the proposal is smaller when the conditional independence assumption is violated. Finally, we apply our method into a real example extracted from the MarketScan database to study the association between recurrent strokes and mortality.
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Affiliation(s)
- Zheng Li
- Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennslyvania, USA
| | - Vernon M Chinchilli
- Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennslyvania, USA
| | - Ming Wang
- Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennslyvania, USA
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22
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Leão J, Leiva V, Saulo H, Tomazella V. Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data. Stat Med 2018; 37:4421-4440. [DOI: 10.1002/sim.7929] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Revised: 07/11/2018] [Accepted: 07/11/2018] [Indexed: 12/11/2022]
Affiliation(s)
- Jeremias Leão
- Department of Statistics; Universidade Federal do Amazonas; Amazonas Brazil
| | - Víctor Leiva
- School of Industrial Engineering; Pontificia Universidad Católica de Valparaíso; Valparaíso Chile
| | - Helton Saulo
- Department of Statistics; Universidade de Brasília; Distrito Federal Brazil
- Faculty of Administration, Accounting and Economics; Universidade Federal de Goiás; Goiás Brazil
| | - Vera Tomazella
- Department of Statistics; Universidade Federal de São Carlos; São Paulo Brazil
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Jung TH, Peduzzi P, Allore H, Kyriakides TC, Esserman D. A joint model for recurrent events and a semi-competing risk in the presence of multi-level clustering. Stat Methods Med Res 2018; 28:2897-2911. [PMID: 30062911 PMCID: PMC7366508 DOI: 10.1177/0962280218790107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Clinical trial designs often include multiple levels of clustering in which patients are nested within clinical sites and recurrent outcomes are nested within patients who may also experience a semi-competing risk. Traditional survival methods that analyze these processes separately may lead to erroneous inferences as they ignore possible dependencies. To account for the association between recurrent events and a semi-competing risk in the presence of two levels of clustering, we developed a semi-parametric joint model. The Gaussian quadrature with a piecewise constant baseline hazard was used to estimate the unspecified baseline hazards and the likelihood. Simulations showed that the proposed joint model has good statistical properties (i.e. <5% bias and 95% coverage) compared to the shared frailty and joint frailty models when informative censoring and multiple levels of clustering were present. The proposed method was applied to data from an AIDS clinical trial to investigate the impact of antiretroviral treatment on recurrent AIDS-defining events in the presence of a semi-competing risk of death and multi-level clustering and showed a significant dependency between AIDS-defining events and death at the patient level but not at the clinic level.
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Affiliation(s)
- Tae Hyun Jung
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Peter Peduzzi
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Heather Allore
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA.,Department of Internal Medicine, Yale School of Medicine, West Haven, CT, USA
| | - Tassos C Kyriakides
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA.,VA Cooperative Studies Program Coordinating Center, West Haven, CT, USA
| | - Denise Esserman
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
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24
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Xu C, Chinchilli VM, Wang M. Joint modeling of recurrent events and a terminal event adjusted for zero inflation and a matched design. Stat Med 2018; 37:2771-2786. [PMID: 29682772 DOI: 10.1002/sim.7682] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2017] [Revised: 02/05/2018] [Accepted: 03/19/2018] [Indexed: 12/20/2022]
Abstract
In longitudinal studies, matched designs are often employed to control the potential confounding effects in the field of biomedical research and public health. Because of clinical interest, recurrent time-to-event data are captured during the follow-up. Meanwhile, the terminal event of death is always encountered, which should be taken into account for valid inference because of informative censoring. In some scenarios, a certain large portion of subjects may not have any recurrent events during the study period due to nonsusceptibility to events or censoring; thus, the zero-inflated nature of data should be considered in analysis. In this paper, a joint frailty model with recurrent events and death is proposed to adjust for zero inflation and matched designs. We incorporate 2 frailties to measure the dependency between subjects within a matched pair and that among recurrent events within each individual. By sharing the random effects, 2 event processes of recurrent events and death are dependent with each other. The maximum likelihood based approach is applied for parameter estimation, where the Monte Carlo expectation-maximization algorithm is adopted, and the corresponding R program is developed and available for public usage. In addition, alternative estimation methods such as Gaussian quadrature (PROC NLMIXED) and a Bayesian approach (PROC MCMC) are also considered for comparison to show our method's superiority. Extensive simulations are conducted, and a real data application on acute ischemic studies is provided in the end.
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Affiliation(s)
- Cong Xu
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Pennsylvania State Hershey Medical Center, Hershey, PA, 17033, USA
| | - Vernon M Chinchilli
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Pennsylvania State Hershey Medical Center, Hershey, PA, 17033, USA
| | - Ming Wang
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Pennsylvania State Hershey Medical Center, Hershey, PA, 17033, USA
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25
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Ghavami V, Mahmoudi M, Rahimi Foroushani A, Baghishani H, Homaei Shandiz F, Yaseri M. Long-Term Disease-Free Survival of Non-Metastatic Breast Cancer Patients in Iran: A Survival Model with Competing Risks Taking Cure Fraction and Frailty into Account. Asian Pac J Cancer Prev 2017; 18:2825-2832. [PMID: 29072428 PMCID: PMC5747410 DOI: 10.22034/apjcp.2017.18.10.2825] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
Abstract
Introduction: Survival modeling is a very important tool to detect risk factors and provide a basis for health care
planning. However, cancer data may have properties leading to distorted results with routine methods. Therefore, this
study aimed to cover specific factors (competing risk, cure fraction and heterogeneity) with a real dataset of Iranian
breast cancer patients using a competing risk-cure-frailty model. Materials and methods: For this historical cohort
study, information for 550 Iranian breast cancer patients who underwent surgery for tumor removal from 2001 to 2007
and were followed up to March 2017, was analyzed using R 3.2 software. Results: In contrast to T-stage and N-stage,
hormone receptor status did not have any significant effect on the cure fraction (long-term disease-free survival).
However, T-stage, N-stage and hormone receptor status all had a significant effect on short-term disease-free survival
so that the hazard of loco-regional relapse or distant metastasis in cases positive for a hormone receptor was only 0.3
times that for their negative hormone receptor counterparts. The likelihood of locoregional relapse in the first quartile
of follow up was nearly twice that of other quartiles. The least cumulative incidence of time to locoregional relapse was
for cases with a positive hormone receptor, low N stage and low T stage. The effect of frailty term was significant in
this study and a model with frailty appeared more appropriate than a model without, based on the Akaike information
criterion (AIC); values for the frailty model and one without the frailty parameter were 1370.39 and 1381.46, respectively.
Conclusions: The data from this study indicate ae necessity to consider competing risk, cure fraction and heterogeneity
in survival modeling. The competing risk-cure-frailty model can cover complex situations with survival data.
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Affiliation(s)
- Vahid Ghavami
- Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
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26
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Koutras MV, Milienos FS. A flexible family of transformation cure rate models. Stat Med 2017; 36:2559-2575. [PMID: 28417477 DOI: 10.1002/sim.7293] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Revised: 02/20/2017] [Accepted: 03/02/2017] [Indexed: 12/14/2022]
Abstract
In this paper, we introduce a flexible family of cure rate models, mainly motivated by the biological derivation of the classical promotion time cure rate model and assuming that a metastasis-competent tumor cell produces a detectable-tumor mass only when a specific number of distinct biological factors affect the cell. Special cases of the new model are, among others, the promotion time (proportional hazards), the geometric (proportional odds), and the negative binomial cure rate model. In addition, our model generalizes specific families of transformation cure rate models and some well-studied destructive cure rate models. Exact likelihood inference is carried out by the aid of the expectationŰmaximization algorithm; a profile likelihood approach is exploited for estimating the parameters of the model while model discrimination problem is analyzed by the aid of the likelihood ratio test. A simulation study demonstrates the accuracy of the proposed inferential method. Finally, as an illustration, we fit the proposed model to a cutaneous melanoma data-set. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- M V Koutras
- Department of Statistics and Insurance Science, University of Piraeus, 80, Karaoli and Dimitriou Street, 18534, Piraeus, Greece
| | - F S Milienos
- Department of Statistics and Insurance Science, University of Piraeus, 80, Karaoli and Dimitriou Street, 18534, Piraeus, Greece
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27
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Louzada F, Macera MAC, Cancho VG. A gap time model based on a multiplicative marginal rate function that accounts for zero-recurrence units. Stat Methods Med Res 2017; 26:2000-2010. [DOI: 10.1177/0962280217708669] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we propose an alternative gap time model based on a multiplicative marginal rate function, which is formulated considering each gap time conditional on the previous recurrence times. In this formulation, the gap times are treated equally and the relation between successive events is no longer a problem. Furthermore, this article considers the inclusion of a proportion of zero-recurrence units (for which the event of interest will not occur) into the model to analyze recurrent event data. Inference aspects of the proposed model are discussed through maximum likelihood approach. A simulation study is carried out to examine the performance of the estimation procedure. The model is applied to hospital readmission data among colorectal cancer patients.
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Affiliation(s)
- Francisco Louzada
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil
| | - Márcia AC Macera
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil
| | - Vicente G Cancho
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil
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28
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de Souza HCC, da Silva Castro Perdoná G, Louzada F, Maris Peria F. On the comparison of risk of death according to different stages of breast cancer via the long-term exponentiated Weibull hazard model. Stat Methods Med Res 2016; 27:2024-2037. [PMID: 29846145 DOI: 10.1177/0962280216673245] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Long-term survivor models have been extensively used for modelling time-to-event data with a significant proportion of patients who do not experience poor outcome. In this paper, we propose a new long-term survivor hazard model, which accommodates comprehensive families of cure rate models as particular cases, including modified Weibull, exponentiated Weibull, Weibull, exponential and Rayleigh distribution, among others. The maximum likelihood estimation procedure is presented. A simulation study evaluates bias and mean square error of the considered estimation procedure as well as the coverage probabilities of the parameters asymptotic and bootstrap confidence intervals. A real Brazilian dataset on breast cancer illustrates the methodology. From the practical point of view, under our modelling, we provide a parameter that works as a metric to quantify and compare the risk between different stages of the disease. We emphasize that, we developed an online platform for oncologists to calculate the probability of survival of patients diagnosed with breast cancer according to the stage of the disease in real time.
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A Comparison between Cure Model and Recursive Partitioning: A Retrospective Cohort Study of Iranian Female with Breast Cancer. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2016; 2016:9425629. [PMID: 27660647 PMCID: PMC5021906 DOI: 10.1155/2016/9425629] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/09/2016] [Revised: 08/02/2016] [Accepted: 08/08/2016] [Indexed: 11/17/2022]
Abstract
Background. Breast cancer which is the most common cause of women cancer death has an increasing incidence and mortality rates in Iran. A proper modeling would correctly detect the factors' effect on breast cancer, which may be the basis of health care planning. Therefore, this study aimed to practically develop two recently introduced statistical models in order to compare them as the survival prediction tools for breast cancer patients. Materials and Methods. For this retrospective cohort study, the 18-year follow-up information of 539 breast cancer patients was analyzed by “Parametric Mixture Cure Model” and “Model-Based Recursive Partitioning.” Furthermore, a simulation study was carried out to compare the performance of mentioned models for different situations. Results. “Model-Based Recursive Partitioning” was able to present a better description of dataset and provided a fine separation of individuals with different risk levels. Additionally the results of simulation study confirmed the superiority of this recursive partitioning for nonlinear model structures. Conclusion. “Model-Based Recursive Partitioning” seems to be a potential instrument for processing complex mixture cure models. Therefore, applying this model is recommended for long-term survival patients.
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30
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Baghestani AR, Moghaddam SS, Majd HA, Akbari ME, Nafissi N, Gohari K. Application of a Non-Mixture Cure Rate Model for Analyzing Survival of Patients with Breast Cancer. Asian Pac J Cancer Prev 2015; 16:7359-63. [PMID: 26514537 DOI: 10.7314/apjcp.2015.16.16.7359] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND As a result of significant progress made in treatment of many types of cancers during the last few decades, there have been an increased number of patients who do not experience mortality. We refer to these observations as cure or immune and models for survival data which include cure fraction are known as cure rate models or long-term survival models. MATERIALS AND METHODS In this study we used the data collected from 438 female patients with breast cancer registered in the Cancer Research Center in Shahid Beheshti University of Medical Sciences, Tehran, Iran. The patients had been diagnosed from 1992 to 2012 and were followed up until October 2014. We had to exclude some because of incomplete information. Phone calls were made to confirm whether the patients were still alive or not. Deaths due to breast cancer were regarded as failure. To identify clinical, pathological, and biological characteristics of patients that might have had an effect on survival of the patients we used a non-mixture cure rate model; in addition, a Weibull distribution was proposed for the survival time. Analyses were performed using STATA version 14. The significance level was set at P ≤ 0.05. RESULTS A total of 75 patients (17.1%) died due to breast cancer during the study, up to the last follow-up. Numbers of metastatic lymph nodes and histologic grade were significant factors. The cure fraction was estimated to be 58%. CONCLUSIONS When a cure fraction is not available, the analysis will be changed to standard approaches of survival analysis; however when the data indicate that the cure fraction is available, we suggest analysis of survival data via cure models.
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Affiliation(s)
- Ahmad Reza Baghestani
- Department of Biostatistics, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran E-mail :
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31
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Liu L, Huang X, Yaroshinsky A, Cormier JN. Joint frailty models for zero-inflated recurrent events in the presence of a terminal event. Biometrics 2015; 72:204-14. [DOI: 10.1111/biom.12376] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2014] [Revised: 05/01/2015] [Accepted: 06/01/2015] [Indexed: 11/29/2022]
Affiliation(s)
- Lei Liu
- Department of Preventive Medicine and Robert H. Lurie Comprehensive Cancer Center; Northwestern University; Chicago, Illinois 60611 U.S.A
| | - Xuelin Huang
- Department of Biostatistics, M. D. Anderson Cancer Center; University of Texas; Houston, Texas 77030 U.S.A
| | | | - Janice N. Cormier
- Department of Surgical Oncology, M. D. Anderson Cancer Center; University of Texas; Houston, Texas 77030 U.S.A
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32
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Li H, Zhang J, Tang Y. Smooth Semi-nonparametric Analysis for Mixture Cure Models and Its Application to Breast Cancer. AUST NZ J STAT 2014. [DOI: 10.1111/anzs.12080] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Haifen Li
- School of Finance and Statistics; East China Normal University; Shanghai 200241 China
- Department of Epidemiology and Biostatistics; University of South Carolina; Columbia SC 29208 USA
| | - Jiajia Zhang
- Department of Epidemiology and Biostatistics; University of South Carolina; Columbia SC 29208 USA
| | - Yincai Tang
- School of Finance and Statistics; East China Normal University; Shanghai 200241 China
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33
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Yu X, De Angelis R, Andersson T, Lambert P, O’Connell D, Dickman P. Estimating the proportion cured of cancer: Some practical advice for users. Cancer Epidemiol 2013; 37:836-42. [DOI: 10.1016/j.canep.2013.08.014] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2013] [Accepted: 08/24/2013] [Indexed: 12/11/2022]
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