Joint modelling of longitudinal binary data and survival data

The medical costs in an ageing society substantially increase when the incidences of chronic diseases, disabilities and inability to live independently are high. Healthy lifestyles not only affect elderly individuals but also influence the entire community. When assessing treatment efficacy, survival and quality of life should be considered simultaneously. This paper proposes the joint likelihood approach for modelling survival and longitudinal binary covariates simultaneously. Because some unobservable information is present in the model, the Monte Carlo EM algorithm and Metropolis-Hastings algorithm are used to find the estimators. Monte Carlo simulations are performed to evaluate the performance of the proposed model based on the accuracy and precision of the estimates. Real data are used to demonstrate the feasibility of the proposed model.

当慢性病、残疾以及无法独立生活的发生率居高不下时，老龄化社会（ageing society）的医疗成本会大幅攀升。健康的生活方式不仅对老年个体产生影响，亦会作用于整个社区。在评估治疗疗效时，应同时兼顾生存状况与生活质量。本文提出了联合似然法（joint likelihood approach），可同时对生存数据与纵向二元协变量（longitudinal binary covariates）进行建模。由于该模型中存在部分不可观测信息，故采用蒙特卡洛EM算法（Monte Carlo EM algorithm）与梅特罗波利斯-黑斯廷斯算法（Metropolis-Hastings algorithm）求解估计量（estimators）。本文通过蒙特卡洛模拟（Monte Carlo simulations），基于估计值的准确性与精确性对所提模型的性能进行评估，并采用真实数据集验证该模型的可行性。