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Wang Z, Xu H, Liu H, Song H, Tu D. A joint model for longitudinal outcomes with potential ceiling and floor effects and survival times, with applications to analysis of quality of life data from a cancer clinical trial. Stat (Int Stat Inst) 2022. [DOI: 10.1002/sta4.412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Zhanfeng Wang
- Department of Statistics and Finance University of Science and Technology of China Anhui 230026 China
| | - Honghong Xu
- Department of Statistics and Finance University of Science and Technology of China Anhui 230026 China
| | - Haijiao Liu
- Department of Statistics and Finance University of Science and Technology of China Anhui 230026 China
| | - Hui Song
- School of Mathematical Sciences Dalian University of Technology Liaoning 116024 China
| | - Dongsheng Tu
- Canadian Cancer Trials Group Queen's University Kingston Ontario K7L 3N6 Canada
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Alsefri M, Sudell M, García-Fiñana M, Kolamunnage-Dona R. Bayesian joint modelling of longitudinal and time to event data: a methodological review. BMC Med Res Methodol 2020; 20:94. [PMID: 32336264 PMCID: PMC7183597 DOI: 10.1186/s12874-020-00976-2] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 04/12/2020] [Indexed: 02/07/2023] Open
Abstract
BACKGROUND In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches. METHODS We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation. RESULTS A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes. CONCLUSION Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.
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Affiliation(s)
- Maha Alsefri
- Department of Health Data Science, Institute of Population Health, University of Liverpool, L69 3GL, Liverpool, UK.
- Department of Statistics, University of Jeddah, Jeddah, Saudi Arabia.
| | - Maria Sudell
- Department of Health Data Science, Institute of Population Health, University of Liverpool, L69 3GL, Liverpool, UK
| | - Marta García-Fiñana
- Department of Health Data Science, Institute of Population Health, University of Liverpool, L69 3GL, Liverpool, UK
| | - Ruwanthi Kolamunnage-Dona
- Department of Health Data Science, Institute of Population Health, University of Liverpool, L69 3GL, Liverpool, UK
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Brilleman SL, Crowther MJ, Moreno-Betancur M, Buros Novik J, Dunyak J, Al-Huniti N, Fox R, Hammerbacher J, Wolfe R. Joint longitudinal and time-to-event models for multilevel hierarchical data. Stat Methods Med Res 2018; 28:3502-3515. [PMID: 30378472 DOI: 10.1177/0962280218808821] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation.
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Affiliation(s)
- Samuel L Brilleman
- Department of Epidemiology and Preventive Medicine, School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia.,Victorian Centre for Biostatistics (ViCBiostat), Melbourne, Australia
| | - Michael J Crowther
- Biostatistics Research Group, Department of Health Sciences, University of Leicester, Leicester, UK
| | - Margarita Moreno-Betancur
- Victorian Centre for Biostatistics (ViCBiostat), Melbourne, Australia.,Clinical Epidemiology and Biostatistics Unit, Murdoch Children's Research Institute, Melbourne, Australia.,Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Australia
| | - Jacqueline Buros Novik
- Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, USA
| | - James Dunyak
- Quantitative Clinical Pharmacology, IMED Biotech Unit, AstraZeneca, Waltham, MA, USA
| | - Nidal Al-Huniti
- Quantitative Clinical Pharmacology, IMED Biotech Unit, AstraZeneca, Waltham, MA, USA
| | - Robert Fox
- Quantitative Clinical Pharmacology, IMED Biotech Unit, AstraZeneca, Waltham, MA, USA
| | - Jeff Hammerbacher
- Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, USA.,Department of Microbiology and Immunology, Medical University of South Carolina, Charleston, SC, USA
| | - Rory Wolfe
- Department of Epidemiology and Preventive Medicine, School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia.,Victorian Centre for Biostatistics (ViCBiostat), Melbourne, Australia
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A Proposed Approach for Joint Modeling of the Longitudinal and Time-To-Event Data in Heterogeneous Populations: An Application to HIV/AIDS's Disease. BIOMED RESEARCH INTERNATIONAL 2018; 2018:7409284. [PMID: 29546067 PMCID: PMC5818956 DOI: 10.1155/2018/7409284] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Revised: 11/15/2017] [Accepted: 12/05/2017] [Indexed: 11/25/2022]
Abstract
In recent years, the joint models have been widely used for modeling the longitudinal and time-to-event data simultaneously. In this study, we proposed an approach (PA) to study the longitudinal and survival outcomes simultaneously in heterogeneous populations. PA relaxes the assumption of conditional independence (CI). We also compared PA with joint latent class model (JLCM) and separate approach (SA) for various sample sizes (150, 300, and 600) and different association parameters (0, 0.2, and 0.5). The average bias of parameters estimation (AB-PE), average SE of parameters estimation (ASE-PE), and coverage probability of the 95% confidence interval (CP) among the three approaches were compared. In most cases, when the sample sizes increased, AB-PE and ASE-PE decreased for the three approaches, and CP got closer to the nominal level of 0.95. When there was a considerable association, PA in comparison with SA and JLCM performed better in the sense that PA had the smallest AB-PE and ASE-PE for the longitudinal submodel among the three approaches for the small and moderate sample sizes. Moreover, JLCM was desirable for the none-association and the large sample size. Finally, the evaluated approaches were applied on a real HIV/AIDS dataset for validation, and the results were compared.
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Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J. Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Med Res Methodol 2017; 17:105. [PMID: 28716060 PMCID: PMC5513366 DOI: 10.1186/s12874-017-0382-9] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2017] [Accepted: 06/30/2017] [Indexed: 12/02/2022] Open
Abstract
BACKGROUND Joint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. However the difficulty to perform inference in nonlinear models and to calculate the distribution of individual parameters has long limited this approach to linear mixed-effect models for the longitudinal part. Here we use a Bayesian algorithm and a nonlinear joint model to calculate individual dynamic predictions. We apply this approach to predict the risk of death in metastatic castration-resistant prostate cancer (mCRPC) patients with frequent Prostate-Specific Antigen (PSA) measurements. METHODS A joint model is built using a large population of 400 mCRPC patients where PSA kinetics is described by a biexponential function and the hazard function is a PSA-dependent function. Using Hamiltonian Monte Carlo algorithm implemented in Stan software and the estimated population parameters in this population as priors, the a posteriori distribution of the hazard function is computed for a new patient knowing his PSA measurements until a given landmark time. Time-dependent area under the ROC curve (AUC) and Brier score are derived to assess discrimination and calibration of the model predictions, first on 200 simulated patients and then on 196 real patients that are not included to build the model. RESULTS Satisfying coverage probabilities of Monte Carlo prediction intervals are obtained for longitudinal and hazard functions. Individual dynamic predictions provide good predictive performances for landmark times larger than 12 months and horizon time of up to 18 months for both simulated and real data. CONCLUSIONS As nonlinear joint models can characterize the kinetics of biomarkers and their link with a time-to-event, this approach could be useful to improve patient's follow-up and the early detection of most at risk patients.
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Affiliation(s)
- Solène Desmée
- IAME, UMR 1137, INSERM, Université Paris Diderot, Sorbonne Paris Cité, 16, rue Henri Huchard, Paris, 75018 France
| | - France Mentré
- IAME, UMR 1137, INSERM, Université Paris Diderot, Sorbonne Paris Cité, 16, rue Henri Huchard, Paris, 75018 France
| | | | | | - Jérémie Guedj
- IAME, UMR 1137, INSERM, Université Paris Diderot, Sorbonne Paris Cité, 16, rue Henri Huchard, Paris, 75018 France
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