Predicting the Survival of AIDS Patients Using Two Frameworks of Statistical Joint Modeling and Comparing Their Predictive Accuracy

  • Fatemeh KHORASHADIZADEH Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
  • Hamed TABESH Department of Medical Informatics, School of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran
  • Mahboubeh PARSAEIAN Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
  • Habibollah ESMAILY Social Determinants of Health Research Center, Mashhad University of Medical Sciences, Mashhad, Iran
  • Abbas RAHIMI FOROUSHANI Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
ROC curve;, HIV, Joint latent class model, Shared random effect model


Background: The present study aimed to estimate the survival of HIV-positive patients and compare the accuracy of two commonly used models, Shared Random-Effect Model (SREM) and Joint Latent Class Model (JLCM) for the analysis of time to death among these patients.

Methods: Data on a retrospective survey among HIV-positive patients diagnosed during 1989-2014 who referred to the Behavioral Diseases Consultation Center of Mashhad University of Medical Sciences was used in this study. Participants consisted of HIV-positive high-risk volunteers, referrals of new HIV cases from prisons, blood transfusion organization and hospitals. Subjects were followed from diagnosis until death or the end of study. SREM and JLCM were used to predict the survival of HIV/AIDS patients. In both models age, sex and addiction were included as covariates. To compare the accuracy of these alternative models, dynamic predictions were calculated at specific time points. The receiver operating characteristic (ROC) curve was used to select the more accurate model.

Results: Overall, 213 patients were eligible that met entry conditions for the present analysis. Based on BIC criteria, three heterogeneous sub-populations of patients were identified by JLCM and individuals were categorized in these classes (“High Risk”, “Moderate Risk” and “Low Risk”) according to their health status. JLCM had a better predictive accuracy than SREM. The average area under ROC curve for JLCM and SREM was 0.75 and 0.64 respectively. In both models CD4 count decreased with time. Based on the result of JLCM, men had higher hazard rate than women and the CD4 counts levels of patients decreased with increasing age.

Conclusion: Predicting risk of death (or survival) is vital for patients care in most medical research. In a heterogeneous population, such as HIV-positive patients fitting JLCM can significantly improve the accuracy of the risk prediction. Therefore, this model is preferred for these populations.


1. Joint United Nations Programme on HIV/AIDS (UNAIDS) [Internet]. 2018. Available from:
2. Hickey GL, Philipson P, Jorgensen A, Kolamunnage-Dona R (2016). Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Med Res Methodol,16(1):117.
3. Pawitan Y, Self S (1993). Modeling Disease Marker Processes in AIDS. J Am Stat Assoc, 88(423):719–26.
4. Gruttola V De, Tu XM (1994). Modelling Progression of CD4-Lymphocyte Count and Its Relationship to Survival Time. Biometrics ,50(4):1003–14.
5. Alimohamadi Y, Tabatabaee H, Afsarkazerooni P et al (2014). Epidemiologic characteristics of HIV-positive patients referring to behavioral diseases consultation center in Shiraz , Iran. Med J Islam Repub Iran, 28:147.
6. Rizopoulos D (2011). Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time-to-Event Data. Biometrics, 67(3):819-29.
7. Ibrahim JG, Chu H, Chen LM (2010). Basic concepts and methods for joint models of longitudinal and survival data. J Clin Oncol, 28(16):2796–801.
8. Hogan JW, Laird NM (1998). Increasing efficiency from censored survival data by using random effects to model longitudinal covariates. Stat Methods Med Res,7(1):28–48.
9. Rizopoulos D, Hatfield L, Carlin B, Takkenberg JM (2014). Combining Dynamic Predictions from Joint Models for Longitudinal and Time-to-Event Data using Bayesian Model Averaging. J Am Stat Assoc, 109(508):1385–97.
10. Lim HJ, Mondal P, Skinner S (2013). Joint modeling of longitudinal and event time data: application to HIV study. J Med Stat Infect,1(1):1.
11. Rizopoulos D, Lesaffre E (2014). Introduction to the special issue on joint modelling techniques. Stat Methods Med Res, 23(1):3–10.
12. Vonesh EF, Greene T, Schluchter MD (2006). Shared parameter models for the joint analysis of longitudinal data and event times. Stat Med, 25(1):143–63.
13. Cowling BJ, Hutton JL, Shaw JEH (2006). Joint Modelling of Event Counts and Survival Times. Appl Statist, 55(1):31–39.
14. Henderson R, Diggle P, Dobson A (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics,1(4):465–80.
15. Lin H, McCulloch CE, Turnbull BW et al (2000). A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations. Stat Med, 19(10):1303-18.
16. Andrinopoulou E-R, Nasserinejad K, Szczesniak R et al (2018). Integrating Latent Classes in the Bayesian Shared Parameter Joint Model of Longitudinal and Survival Outcomes,1–20.
17. Proust-Lima C, Séne M, Taylor JMG et al (2014). Joint latent class models for longitudinal and time-to-event data: A review. Stat Methods Med Res ,23(1):74–90.
18. Liu Y, Liu L, Zhou J (2015). Joint latent class model of survival and longitudinal data: An application to CPCRA study. Comput Stat Data Anal ,91:40–50.
19. Gueorguieva R, Rosenheck R, Lin H (2012). Joint modelling of longitudinal outcome and interval-censored competing risk dropout in a schizophrenia clinical trial. J R Stat Soc Ser A Stat Soc,175(2):417–33.
20. World Health Organization (2009). Guidelines for Using HIV Testing Technologies in Surveillance. Geneva, Switzerland: UNAIDS.
21. Wulfsohn MS, Tsiatis AA (1997). A Joint Model for Survival and Longitudinal Data Measured with Error. Biometrics, 53(1):330-9.
22. R.Brown E, G.Ibrahim J (2003). Bayesian approaches to joint cure-rate and longitudinal models with applications to cancer vaccine trials. Biometrics,59(3):686–93.
23. Rizopoulos D, Ghosh P (2011). A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Stat Med, 30(12):1366-80.
24. Rizopoulos D (2012). Joint Models for Longitudinal and Time-to-Event Data: With Applications in R. 1st ed. CRC Press, 275 p. (Chapman & Hall/CRC Biostatistics Series).
25. Andrinopoulou ER, Rizopoulos D, Takkenbergb JJM et al (2014). Joint modeling of two longitudinal outcomes and competing risk data. Stat Med, 33(18):3167-78.
26. Faucett CL, Thomas DC (1996). Simultaneously modelling censored survival data and repeatedly measured covariates: a gibbs sampling approach. Stat Med, 15(15):1663-85.
27. Schwarz G (1978). Estimating the Dimension of a Model. Ann Statist, 6(2):461–4.
28. Wang J, Luo S, Li L (2017). Dynamic prediction for multiple repeated measures and event time data: an application to parkinson’s disease. Ann Appl Stat,11(3):1787–1809.
29. Król A, Mauguen A, Mazroui Y et al (2017). Tutorial in Joint Modeling and Prediction: a Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event.
30. Guo X, Carlin BP (2004). Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages. Am Stat,58(1):16–24.
31. Liu L, Huang X (2009). Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome. J R Stat Soc Ser C (Appl Stat), 58(1):65–81.
32. Mauguen A, Rachet B, Mathoulin-Pélissier S et al (2013). Dynamic prediction of risk of death using history of cancer recurrences in joint frailty models. Stat Med,32(30):5366–80.
33. Proust-Lima C, Taylor JMG (2009). Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach. Biostatistics,10(3):535–49.
34. Futoma J, Sendak M, Cameron CB, Heller K (2016). Predicting Disease Progression with a Model for Multivariate Longitudinal Clinical Data. Proceedings of Machine Learning for Healthcare, 56:42–54.
35. Harrell Jr FE., Lee KL, Mark DB (1996). Multivariable prognostic models : issues in developing models , evaluating assumptions and adequacy , and measuring and reducing errors. Stat Med, 15(4):361–87.
How to Cite
KHORASHADIZADEH F, TABESH H, PARSAEIAN M, ESMAILY H, RAHIMI FOROUSHANI A. Predicting the Survival of AIDS Patients Using Two Frameworks of Statistical Joint Modeling and Comparing Their Predictive Accuracy. Iran J Public Health. 49(5):949-958.
Original Article(s)