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Zhang Z, Charalambous C, Foster P. A Gaussian copula joint model for longitudinal and time-to-event data with random effects. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107685] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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Zhang Z, Charalambous C, Foster P. Joint modelling of longitudinal measurements and survival times via a multivariate copula approach. J Appl Stat 2022; 50:2739-2759. [PMID: 37720246 PMCID: PMC10503460 DOI: 10.1080/02664763.2022.2081965] [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: 08/17/2021] [Accepted: 05/21/2022] [Indexed: 10/18/2022]
Abstract
Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the random effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas to introduce non-linear correlation between the marginal distributions of the longitudinal and time-to-event processes. The multivariate Gaussian copula joint model has been proposed in the literature to fit joint data by applying a Monte Carlo expectation-maximisation algorithm. In this paper, we propose an exact likelihood estimation approach to replace the more computationally expensive Monte Carlo expectation-maximisation algorithm and we consider results based on using both the multivariate Gaussian and t copula functions. We also provide a straightforward way to compute dynamic predictions of survival probabilities, showing that our proposed model is comparable in prediction performance to the shared random effects joint model.
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Affiliation(s)
- Zili Zhang
- Department of Mathematics, University of Manchester, Manchester, UK
| | | | - Peter Foster
- Department of Mathematics, University of Manchester, Manchester, UK
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Park JY, Wall MM, Moustaki I, Grossman AH. A Joint Modeling Approach for Longitudinal Outcomes and Non-ignorable Dropout under Population Heterogeneity in Mental Health Studies. J Appl Stat 2021; 49:3361-3376. [DOI: 10.1080/02664763.2021.1945000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Jung Yeon Park
- Division of Educational Psychology and Research Methods, George Mason University, Fairfax, VA, USA
| | - Melanie M. Wall
- Department of Biostatistics and Psychiatry, Columbia University, New York, NY, USA
- New York State Psychiatric Institute, New York, NY, USA
| | - Irini Moustaki
- Department of Statistics, London School of Economics and Political Science, London, UK
| | - Arnold H. Grossman
- Department of Applied Psychology, New York University, New York, NY, USA
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Baghfalaki T, Ganjali M. Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data. Stat Methods Med Res 2021; 30:1484-1501. [PMID: 33872092 DOI: 10.1177/09622802211002868] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.
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Affiliation(s)
- T Baghfalaki
- Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
| | - M Ganjali
- Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
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Imai T, Tanaka S, Kawakami K. Exploratory assessment of treatment-dependent random-effects distribution using gradient functions. Stat Med 2020; 40:226-239. [PMID: 33124051 DOI: 10.1002/sim.8770] [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: 01/06/2020] [Revised: 07/24/2020] [Accepted: 09/17/2020] [Indexed: 11/06/2022]
Abstract
In analyzing repeated measurements from randomized controlled trials with mixed-effects models, it is important to carefully examine the conventional normality assumption regarding the random-effects distribution and its dependence on treatment allocation in order to avoid biased estimation and correctly interpret the estimated random-effects distribution. In this article, we propose the use of a gradient function method in modeling with the different random-effects distributions depending on the treatment allocation. This method can be effective for considering in advance whether a proper fit requires a model that allows dependence of the random-effects distribution on covariates, or for finding the subpopulations in the random effects.
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Affiliation(s)
- Takumi Imai
- Department of Medical Statistics, Graduate School of Medicine, Osaka City University, Osaka, Japan
| | - Shiro Tanaka
- Department of Clinical Biostatistics, Graduate School of Medicine, Kyoto University, Kyoto, Japan
| | - Koji Kawakami
- Department of Pharmacoepidemiology, Graduate School of Medicine and Public Health, Kyoto University, Kyoto, Japan
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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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Baghfalaki T, Kalantari S, Ganjali M, Hadaegh F, Pahlavanzadeh B. Bayesian joint modeling of ordinal longitudinal measurements and competing risks survival data for analysing Tehran Lipid and Glucose Study. J Biopharm Stat 2020; 30:689-703. [DOI: 10.1080/10543406.2020.1730876] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Taban Baghfalaki
- Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
| | - Shiva Kalantari
- Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
| | - Mojtaba Ganjali
- Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
| | - Farzad Hadaegh
- Prevention of Metabolic Disorders Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
| | - Bagher Pahlavanzadeh
- Department of Community Medicine and Health, Shahid Beheshti University of Medical Sciences, Tehran, Iran
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Iddrisu AK, Gumedze F. Sensitivity analysis for the generalized shared-parameter model framework. J Biopharm Stat 2019; 30:197-215. [PMID: 31246135 DOI: 10.1080/10543406.2019.1632875] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
In this paper, we assess the effect of tuberculosis pericarditis treatment (prednisolone) on CD4 count changes over time and draw inferences in the presence of missing data. We accounted for the missing data and performed sensitivity analyses to assess robustness of inferences, from a model that assumes that the data are missing at random, to models that assume that the data are not missing at random. Our sensitivity approaches are within the shared-parameter model framework. We implemented the approach by Creemers and colleagues to the CD4 count data and performed simulation studies to evaluate the performance of this approach. We also assessed the influence of potentially influential subjects, on parameter estimates, via the global influence approach. Our results revealed that inferences from missing at random analysis model are robust to not missing at random models and influential subjects did not overturn the study conclusions about prednisolone effect and missing data mechanism. Prednisolone was found to have no significant effect on CD4 count changes over time and also did not interact with anti-retroviral therapy. The simulation studies produced unbiased estimates of prednisolone effect with lower mean square errors and coverage probabilities approximately equal the nominal coverage probability.
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Affiliation(s)
- Abdul-Karim Iddrisu
- Department of Statistical Sciences, University of Cape Town, Rondebosch South Africa
| | - Freedom Gumedze
- Department of Statistical Sciences, University of Cape Town, Rondebosch South Africa
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Choi J, Zeng D, Olshan AF, Cai J. Joint modeling of survival time and longitudinal outcomes with flexible random effects. LIFETIME DATA ANALYSIS 2018; 24:126-152. [PMID: 28856493 PMCID: PMC5756108 DOI: 10.1007/s10985-017-9405-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2016] [Accepted: 08/17/2017] [Indexed: 06/07/2023]
Abstract
Joint models with shared Gaussian random effects have been conventionally used in analysis of longitudinal outcome and survival endpoint in biomedical or public health research. However, misspecifying the normality assumption of random effects can lead to serious bias in parameter estimation and future prediction. In this paper, we study joint models of general longitudinal outcomes and survival endpoint but allow the underlying distribution of shared random effect to be completely unknown. For inference, we propose to use a mixture of Gaussian distributions as an approximation to this unknown distribution and adopt an Expectation-Maximization (EM) algorithm for computation. Either AIC and BIC criteria are adopted for selecting the number of mixtures. We demonstrate the proposed method via a number of simulation studies. We illustrate our approach with the data from the Carolina Head and Neck Cancer Study (CHANCE).
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Affiliation(s)
- Jaeun Choi
- Department of Epidemiology and Population Health, Albert Einstein College of Medicine, 1300 Morris Park Avenue, New York, NY, 10461, USA
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina at Chapel Hill, McGavran-Greenberg Hl, 135 Dauer Drive, CB 7420, Chapel Hill, NC, 27599, USA
| | - Andrew F Olshan
- Department of Epidemiology, University of North Carolina at Chapel Hill, McGavran-Greenberg Hl, 135 Dauer Drive, CB 7435, Chapel Hill, NC, 27599, USA
| | - Jianwen Cai
- Department of Biostatistics, University of North Carolina at Chapel Hill, McGavran-Greenberg Hl, 135 Dauer Drive, CB 7420, Chapel Hill, NC, 27599, USA.
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