School of Management, University of Science and Technology of China, Anhui, China.
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China.
Stat Med. 2024 Oct 15;43(23):4595-4613. doi: 10.1002/sim.10193. Epub 2024 Aug 15.
Joint models for longitudinal and time-to-event data are receiving increasing attention owing to its capability of capturing the possible association between these two types of data. Typically, a joint model consists of a longitudinal submodel for longitudinal processes and a survival submodel for the time-to-event response, and links two submodels by common covariates that may carry both fixed and random effects. However, research gaps still remain on how to simultaneously select fixed and random effects from the two submodels under the joint modeling framework efficiently and effectively. In this article, we propose a novel block-coordinate gradient descent (BCGD) algorithm to simultaneously select multiple longitudinal covariates that may carry fixed and random effects in the joint model. Specifically, for the multiple longitudinal processes, a linear mixed effect model is adopted where random intercepts and slopes serve as essential covariates of the trajectories, and for the survival submodel, the popular proportional hazard model is employed. A penalized likelihood estimation is used to control the dimensionality of covariates in the joint model and estimate the unknown parameters, especially when estimating the covariance matrix of random effects. The proposed BCGD method can successfully capture the useful covariates of both fixed and random effects with excellent selection power, and efficiently provide a relatively accurate estimate of fixed and random effects empirically. The simulation results show excellent performance of the proposed method and support its effectiveness. The proposed BCGD method is further applied on two real data sets, and we examine the risk factors for the effects of different heart valves, differing on type of tissue, implanted in the aortic position and the risk factors for the diagnosis of primary biliary cholangitis.
由于联合模型能够捕捉到这两种类型数据之间的可能关联，因此越来越受到关注。通常，联合模型由纵向过程的纵向子模型和时间事件响应的生存子模型组成，并通过可能具有固定和随机效应的共同协变量将两个子模型联系起来。然而，在联合建模框架下，如何有效地同时从两个子模型中选择固定和随机效应，仍存在研究空白。在本文中，我们提出了一种新的块坐标梯度下降（BCGD）算法，用于同时选择联合模型中可能具有固定和随机效应的多个纵向协变量。具体来说，对于多个纵向过程，采用线性混合效应模型，其中随机截距和斜率作为轨迹的基本协变量，对于生存子模型，采用流行的比例风险模型。惩罚似然估计用于控制联合模型中协变量的维度，并估计未知参数，特别是在估计随机效应的协方差矩阵时。所提出的 BCGD 方法可以成功地捕获固定和随机效应的有用协变量，具有出色的选择能力，并在实践中有效地提供固定和随机效应的相对准确估计。模拟结果表明了该方法的出色性能，并支持其有效性。所提出的 BCGD 方法进一步应用于两个真实数据集，我们检查了不同类型组织植入主动脉位置的不同心脏瓣膜的影响的风险因素，以及原发性胆汁性胆管炎的诊断风险因素。
