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Volume 6, Issue 4, July 2017, Page: 182-190
Bayesian Joint Modelling of Longitudinal and Survival Data of HIV/AIDS Patients: A Case Study at Bale Robe General Hospital, Ethiopia
Ahmed Hasan Dessiso, Department of Statistics, College of Natural and Computational Science, Madda Walabu University, Bale Robe, Ethiopia
Ayele Taye Goshu, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Received: Feb. 14, 2017;       Accepted: Feb. 25, 2017;       Published: Jun. 23, 2017
Abstract
Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for AIDS. This study explores application of Bayesian joint modeling of HIV/AIDS data obtained from Bale Robe General Hospital, Ethiopia. The objective is to develop separate and joint statistical models in the Bayesian framework for longitudinal measurements and time to death event data of HIV/AIDS patients. A linear mixed effects model (LMEM), assuming homogenous and heterogeneous CD4 variances, is used for modeling the CD4 counts and a Weibull survival model is used for describing the time to death event. Then, both processes are linked using unobserved random effects through the use of a shared parameter model. The analysis of both the separate and the joint models reveal that the assumption of heterogeneous (patient-specific) CD4 variances brings improvement in the model fit. The Bayesian joint model is found to best fit to the data, and provided more precise estimates of parameters. The shared frailty is significant showing the association between the linear mixed effect (LME) and survival models.
Keywords
ART, Bayesian, CD4 Count, HIV/AIDS, Joint Model, Longitudinal Model, Survival Model
Ahmed Hasan Dessiso, Ayele Taye Goshu, Bayesian Joint Modelling of Longitudinal and Survival Data of HIV/AIDS Patients: A Case Study at Bale Robe General Hospital, Ethiopia, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 4, 2017, pp. 182-190. doi: 10.11648/j.ajtas.20170604.13
Reference
[1]
Wu L. Mixed effects models for complex data. CRC Press; 2009 Nov 11.
[2]
Guo X, Carlin BP. Separate and joint modeling of longitudinal and event time data using standard computer packages. The American Statistician. 2004 Feb 1; 58 (1): 16-24.
[3]
Diggle P. Analysis of longitudinal data. Oxford University Press; 2002 Jun 20.
[4]
Verbeke G, Molenberghs G. Linear mixed models for longitudinal data. Springer Science Business Media; 2009 May 12.
[5]
Viviani S. Mixed effect joint models for longitudinal responses with drop-out: estimation and sensitivity issues.
[6]
Henderson R, Diggle P, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000 Dec 1; 1 (4): 465-80.
[7]
Lyles RH, Munõz A, Xu J, Taylor JM, Chmiel JS. Adjusting for measurement error to assess health effects of variability in biomarkers. Statistics in medicine. 1999 May 15; 18 (9): 1069-86.
[8]
Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982 Dec 1: 963-74.
[9]
Huang X, Li G, Elashoff RM, Pan J. A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects. Lifetime data analysis. 2011 Jan 1; 17 (1): 80-100.
[10]
Faucett CL, Thomas DC. Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statistics in medicine. 1996 Aug 15; 15 (15): 1663-85.
[11]
Ibrahim JG, Chen MH, Sinha D. Bayesian methods for joint modeling of longitudinal and survival data with applications to cancer vaccine trials. Statistica Sinica. 2004 Jul 1: 863-83.
[12]
Law NJ, Taylor JM, Sandler H. The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure. Biostatistics. 2002 Dec 1; 3 (4): 547-63.
[13]
Wang Y, Taylor JM. Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association. 2001 Sep 1; 96 (455): 895-905.
[14]
Buta GB, Goshu AT, Worku HM. Bayesian Joint Modelling of Disease Progression Marker and Time to Death Event of HIV/AIDS Patients under ART Follow-up. British Journal of Medicine and Medical Research. 2015 Jan 1; 5 (8): 1034.
[15]
Erango MA, Goshu AT, Buta GB, Dessiso AH. Bayesian Joint Modelling of Survival of HIV/AIDS Patients Using Accelerated Failure Time Data and Longitudinal CD4 Cell Counts.
[16]
Dobson AJ, Barnett A. An introduction to generalized linear models. CRC press; 2008 May 12.
[17]
Spiegelhalter D, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. Quality control and applied statistics. 2003; 48 (4): 431-2.
[18]
Manatunga A, Schmotzer B, Lyles RH, Small C, Guo Y, Marcus M. Statistical issues related to modeling menstrual length. InProceedings of the American Statistical Association, Section on Statistics in Epidemiology 2005.