Semiparametric Bayesian inference on skew-normal joint modeling of multivariate longitudinal and survival data
We propose a semiparametric multivariate skew–normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within‐subject error by using a centered Dirichlet proce...
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| Published in | Statistics in medicine Vol. 34; no. 5; pp. 824 - 843 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
28.02.2015
Wiley Subscription Services, Inc |
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| Abstract | We propose a semiparametric multivariate skew–normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within‐subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew–normal distribution to specify the within‐subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis–Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within‐subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies. Copyright © 2014 John Wiley & Sons, Ltd. |
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| AbstractList | We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies.We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies. We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies. We propose a semiparametric multivariate skew–normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within‐subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew–normal distribution to specify the within‐subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis–Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within‐subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies. Copyright © 2014 John Wiley & Sons, Ltd. |
| Author | Tang, An-Min Tang, Nian-Sheng |
| Author_xml | – sequence: 1 givenname: An-Min surname: Tang fullname: Tang, An-Min organization: Department of Statistics, Yunnan University, Yunnan, 650091, Kunming, China – sequence: 2 givenname: Nian-Sheng surname: Tang fullname: Tang, Nian-Sheng email: Correspondence to: Nian-Sheng Tang, Department of Statistics, Yunnan University, Kunming, Yunnan 650091, China., nstang@ynu.edu.cn organization: Department of Statistics, Yunnan University, Yunnan, 650091, Kunming, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25404574$$D View this record in MEDLINE/PubMed |
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| Keywords | Bayesian local influence analysis skew-normal distribution survival data joint models centered Dirichlet process prior |
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British Journal of Mathematical and Statistical Psychology 2011; 64:69-106. Baghfalaki T, Ganjali M, Berridge D. Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: a Bayesian approach. Biometrical Journal 2013; 55:844-865. Tsiatis AA, Degruttola V, Wulfsohn MS. Modeling the relationship of survival to longitudinal data measure with error: applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association 1995; 90:27-37. Fahrmeir L, Raach A. A Bayesian semiparametric latent variable model for mixed responses. Psychometrika 2007; 72:327-346. Ding J, Wang JL. Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics 2008; 64:546-556. Lang S, Brezger A. Bayesian P-splines. Journal of Computational and Graphical Statistics 2004; 13:183-212. Gelman A, Meng XL, Stern H. 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Tsiatis A, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica 2004; 14:809-834. Lee SY, Tang NS. Bayesian analysis of nonlinear structural equation models with nonignorable missing data. Psychometrika 2006; 71:541-564. Taylor JMG, Park Y, Ankerst DP, Proust-Lima C, Williams S, Kestin L, Bae K, Pickles T, Sandler H. Real-time individual predictions of prostate cancer recurrence using joint models. Biometrics 2013; 69:206-213. Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association 1987; 82:528-550. Chi YY, Ibrahim JG. Joint models for multivariate longitudinal and multivariate survival data. Biometrics 2006; 62:432-445. Rizopoulos D, Ghosh P. A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Statistics in Medicine 2011; 30:1366-1380. Zhu HT, Ibrahim JG, Chi YY, Tang N. 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| References_xml | – reference: Zhu HT, Ibrahim JG, Tang NS. Bayesian influence analysis: a geometric approach. Biometrika 2011; 98:307-323. – reference: Fahrmeir L, Raach A. A Bayesian semiparametric latent variable model for mixed responses. Psychometrika 2007; 72:327-346. – reference: Sahu SK, Dey DK, Branco MD. A new class of multivariate skew distributions with applications to Bayesian regression models. Canadian Journal of Statistics 2003; 31:129-150. – reference: Sethuraman J. A constructive definition of Dirichlet priors. Statistica Sinica 1994; 4:639-650. – reference: Song XY, Lu ZH. Semiparametric latent variable models with Bayesian P-splines. Journal of Computational and Graphical Statistics 2010; 19:590-608. – reference: Ding J, Wang JL. Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics 2008; 64:546-556. – reference: Tsiatis AA, Degruttola V, Wulfsohn MS. Modeling the relationship of survival to longitudinal data measure with error: applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association 1995; 90:27-37. – reference: Song XY, Lu ZH, Feng X. Latent variable models with nonparametric interaction effects of latent variables. Statistics in Medicine 2014; 33:1723-1737. – reference: Lang S, Brezger A. Bayesian P-splines. Journal of Computational and Graphical Statistics 2004; 13:183-212. – reference: Li N, Elashoff RM, Li G. Robust joint modeling of longitudinal measurements and competing risks failure time data. Biometrics 2009; 51:19-30. – reference: Ruppert D, Wand MP, Carroll RJ. Semiparametric Regression. Cambridge University Press: New York, 2003. – reference: Hu WH, Li G, Li N. A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data. Statistics in Medicine 2009; 29:1601-1619. – reference: Lee SY, Tang NS. Bayesian analysis of nonlinear structural equation models with nonignorable missing data. Psychometrika 2006; 71:541-564. – reference: Taylor JMG, Park Y, Ankerst DP, Proust-Lima C, Williams S, Kestin L, Bae K, Pickles T, Sandler H. Real-time individual predictions of prostate cancer recurrence using joint models. Biometrics 2013; 69:206-213. – reference: Wang Y, Taylor JMG. Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association 2001; 96:895-905. – reference: Chow SM, Tang NS, Yuan Y, Song XY, Zhu HT. Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior. British Journal of Mathematical and Statistical Psychology 2011; 64:69-106. – reference: Zhu HT, Ibrahim JG, Chi YY, Tang N. Bayesian influence measures for joint models for longitudinal and survival data. Biometrics 2012; 68:954-964. – reference: Song X, Wang CY. Semiparametric approaches for joint modeling of longitudinal and survival data with time-varying coefficients. Biometrics 2008; 64:557-566. – reference: Geman S, Geman D. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984; 6:721-741. – reference: Rizopoulos D, Verbeke G, Lesaffre E. Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society 2009; 71:637-654. – reference: De Gruttola V, Tu XM. Modelling progression of CD4-lymphocyte count and its relationship to survival time. Biometrics 1994; 50:1003-1014. – reference: Rizopoulos D, Ghosh P. A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Statistics in Medicine 2011; 30:1366-1380. – reference: Gelman A, Meng XL, Stern H. Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica 1996; 6:733-807. – reference: Chi YY, Ibrahim JG. Joint models for multivariate longitudinal and multivariate survival data. Biometrics 2006; 62:432-445. – reference: Li N, Elashoff RM, Li G, Tseng CH. Joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects. Statistics in Medicine 2012; 31:1707-1721. – reference: Huang X, Li G, Elashoff RM. A joint model of longitudinal and competing risks survival data with heterogeneous random effects and outlying longitudinal measurements. Statistics Interface 2010; 3:185-195. – reference: Yang M, Dunson DB, Baird D. Semiparametric Bayes hierarchical models with mean and variance constraints. Computational Statistics and Data Analysis 2010; 54:2172-2186. – reference: Tsiatis A, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica 2004; 14:809-834. – reference: Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association 1987; 82:528-550. – reference: Song X, Davidian M, Tsiatis AA. An estimator for the proportional hazards model with multiple longitudinal covariates measured with error. Biostatistics 2002; 3:511-528. – reference: Baghfalaki T, Ganjali M, Berridge D. Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: a Bayesian approach. Biometrical Journal 2013; 55:844-865. – reference: Eilers P, Marx B. Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinder). Statistical Science 1996; 11:89-121. – reference: Ibrahim JG, Chen MH, Sinha D. Bayesian Survival Analysis. 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| Snippet | We propose a semiparametric multivariate skew–normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited... We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited... |
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| SubjectTerms | Algorithms Bayes Theorem Bayesian analysis Bayesian local influence analysis Biostatistics - methods Breast Neoplasms - mortality Breast Neoplasms - psychology centered Dirichlet process prior Clinical Trials as Topic - statistics & numerical data Computer Simulation Female Humans joint models Longitudinal Studies Medical statistics Models, Statistical Multivariate Analysis Normal distribution Quality of Life Simulation skew-normal distribution Survival Analysis survival data |
| Title | Semiparametric Bayesian inference on skew-normal joint modeling of multivariate longitudinal and survival data |
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