In survival studies it is important to record the values of key longitudinal covariates until the occurrence of event of a subject. For this reason, it is essential to study the association between longitudinal and time-to-event outcomes using the joint model. In this paper, profile likelihood approach has been used to estimate the cumulative hazard and regression parameters from the joint model of survival and longitudinal data. Moreover, we show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator. The estimators of the regression parameters from the joint model are shown to be semi-parametric efficient.

翻译：在生存研究中,必须记录关键纵向共变值,直到出现某一主题的事件。因此,必须使用联合模型研究纵向结果和时间与活动结果之间的联系。在本文件中,采用了剖析可能性方法,从生存和纵向数据联合模型中估算累积危险和回归参数。此外,我们通过剖面可能性的无反应扩展,显示了剖面概率估计器的无反应常态常态性,并获得了差异估计器的明确形式。联合模型回归参数的估测器显示半参数效率。