Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

翻译：针对纵向半连续生物标志物与终点事件的两部分联合模型，近期已有基于频率学派估计方法的研究。该模型将生物标志物分布分解为阳性概率与阳性值条件期望两部分，通过共享随机效应表征生物标志物与终点事件间的关联结构。相较于采用单一回归模型的经典联合模型，此类方法的计算复杂度显著增加。在此背景下，R包frailtypack实现的频率学派估计在处理复杂模型（即参数数量庞大、随机效应维度较高的情况）时可能面临挑战。作为替代方案，我们提出基于集成嵌套拉普拉斯近似（INLA）算法的两部分联合模型贝叶斯估计方法，以减轻计算负担并实现更复杂模型的拟合。模拟研究证实，在考察场景下，INLA算法能够提供后验估计的精确近似，且相比frailtypack显著缩短了计算时间并降低了估计变异性。通过对两项随机癌症临床试验（GERCOR和PRIME研究）的分析，我们对比了贝叶斯与频率学派方法：INLA方法在估计生物标志物与事件风险关联性时展现出更低的变异性。此外，贝叶斯方法成功识别出PRIME研究中与不同治疗反应相关的患者亚群。本研究结果表明，采用INLA算法的贝叶斯估计方法能够实现复杂联合模型的拟合，在广泛临床应用中具有潜在价值。