The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We propose a model in which the number of recurrences before termination is a random variable of interest, enabling inference and prediction on it. Then, conditionally on this number, we specify a joint distribution for recurrence and survival. This novel conditional approach induces dependence between recurrence and survival, which is often present, for instance due to frailty that affects both. Additional dependence between recurrence and survival is introduced by the specification of a joint distribution on their respective frailty terms. Moreover, through the introduction of an autoregressive model, our approach is able to capture the temporal dependence in the recurrent events trajectory. A non-parametric random effects distribution for the frailty terms accommodates population heterogeneity and allows for data-driven clustering of the subjects. A tailored Gibbs sampler involving reversible jump and slice sampling steps implements posterior inference. We illustrate our model on colorectal cancer data, compare its performance with existing approaches and provide appropriate inference on the number of recurrent events.
翻译:终止事件之前经常发生事件的次数往往引起兴趣。例如,死亡终止了一个人的复发过程和复发次数,这是经济成本的一个重要指标。我们提出了一个模型,在模型中,终止前复发次数是一个随机的利息变量,从而可以推断和预测它。然后,以这个数字为条件,我们指定了复发和生存的联合分配。这种新的有条件方法往往引起复发和生存之间的依赖性,这经常存在,例如由于既影响又影响两方面的弱点。复发和存活之间的额外依赖性是通过按其各自脆弱条件联合分发的规格而引入的。此外,通过采用自动递增模式,我们的方法能够捕捉到复发事件轨迹中的时间依赖性。对疲软性术语的非参数随机性分布适应了人口的异性,并允许以数据驱动的组合。一个定制的Gibs取样器,包括可逆跳动和切片采样步骤,用于后推推推。我们用关于经常癌症的模型,我们用现有数据比较了当前情况。