Dynamic Prediction Using Landmark Historical Functional Cox Regression

Dynamic prediction of survival data in the presence of time-varying covariates is an area of active research. Two common analytic approaches for this type of data are joint modeling of the longitudinal and survival processes and landmarking. However, there has been little work dedicated to densely measured time-varying covariates using either approach. Moreover, the software for joint modeling is slow, especially for large datasets, and rather limited for landmarking. We propose a landmark approach for dynamic prediction of survival outcomes using densely measured longitudinal predictors, which treats the past of the time-varying covariate at each landmark point as a functional predictor. This approach is orders of magnitude faster than existing software for simpler joint models. Our extensive comparative simulation study required 8.4 computation-years, over 99% of which was devoted to fitting and predicting from two joint models. Our landmark approach performs similarly to joint modeling when the joint model is correctly specified and substantially out-performs it when it is not. Methods are motivated by an application predicting time to recovery of Multiple Sclerosis lesions in a large neuroimaging dataset. Supplementary materials for this article are available online.

存在时变协变量的生存数据动态预测是当前的活跃研究领域。针对此类数据的两种常用分析方法为纵向过程与生存过程联合建模，以及地标分析法（landmarking）。然而，现有研究极少针对两种方法下的密集测量时变协变量展开相关工作。此外，现有联合建模软件运行速度较慢，尤其针对大型数据集时；且地标分析法的配套软件功能亦较为受限。我们提出一种基于密集测量纵向预测变量的生存结局动态预测地标分析法，该方法将每个地标时点处的时变协变量历史序列视作函数型预测变量。该方法的运行速度较现有简易联合建模软件快数个数量级。我们开展的大规模对比模拟研究总计消耗8.4个计算年，其中超过99%的时间用于两个联合模型的拟合与预测。当联合模型设定正确时，我们提出的地标分析法性能与联合建模相当；而当联合模型设定有误时，其性能则显著优于联合建模。本方法的提出源于一项应用研究：针对大型神经影像数据集预测多发性硬化（Multiple Sclerosis）病灶的恢复时间。本文的补充材料可在线获取。