Bayesian approach for joint longitudinal and time-to-event data with survival fraction

• Main Authors: Abu Bakar, Mohd Rizam, Salah, Khalid Ali, Ibrahim, Noor Akma, Haron, Kassim
• Format: Article
• Language: English
• Published: Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2009
• Online Access: http://psasir.upm.edu.my/id/eprint/13373/1/Bayesian%20approach%20for%20joint%20longitudinal%20and%20time.pdf; http://psasir.upm.edu.my/id/eprint/13373/; http://www.emis.de/journals/BMMSS/vol32_1.htm

Many medical investigations generate both repeatedly-measured(longitudinal) biomarker and survival data. One of complex issue arises when investigating the association between longitudinal and time-to-event data when there are cured patients in the population, which leads to a plateau in the survival function S(t) after sufficient follow-up. Thus, usual Cox proportional hazard model [11] is not applicable since the proportional hazard assumption is violated. An alternative is to consider survival models incorporating a cure fraction. In this paper, we present a new class of joint model for univariate longitudinal and survival data in presence of cure fraction. For the longitudinal model, a stochastic Integrated Ornstein-Uhlenbeck process will present, and for the survival model a semiparametric survival function will be considered which accommodate both zero and non-zero cure fractions of the dynamic disease progression. Moreover, we consider a Bayesian approach which is motivated by the complexity of the model. Posterior and prior specification needs to accommodate parameter constraints due to the non-negativity of the survival function. A simulation study is presented to evaluate the performance of the proposed joint model.