[论文解读] Joint Models with Multiple Longitudinal Outcomes and a Time-to-Event Outcome

Katya Mauff, Ewout W. Steyerberg+3 more|arXiv (Cornell University)|Aug 23, 2018

Statistical Methods and Bayesian Inference参考文献 19被引用 3

一句话总结

本文提出了一种计算高效的两阶段联合建模方法，用于多个纵向结局和一个生存时间结局，通过基于重要性抽样的校正因子来减少偏差。该方法在复杂场景下仍能实现接近精确的估计，且计算速度显著快于完整联合建模。

ABSTRACT

Joint models for longitudinal and survival data have garnered a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps; estimating a multivariate mixed model for the longitudinal outcomes, and then using the output from this model to fit the survival submodel. So called two-stage approaches have previously been proposed, and shown to be biased. Our approach differs from the standard version, in that we additionally propose the application of a correction factor, adjusting the estimates obtained such that they more closely resemble those we would expect to find with the multivariate joint model. This correction is based on importance sampling ideas. Simulation studies show that this corrected-two-stage approach works satisfactorily, eliminating the bias while maintaining substantial improvement in computational time, even in more difficult settings.

研究动机与目标

• 为解决拟合包含多个纵向结局和一个生存时间结局的联合模型所面临的计算负担问题。
• 减少标准两阶段方法在处理此类模型时固有的偏差。
• 开发一种在保持估计精度的同时显著提升计算效率的方法。
• 为全多变量联合建模提供一种实用的替代方案，尤其在随机效应数量较多时，全模型变得不可行。

提出的方法

• 该方法将联合模型的估计过程分为两个阶段：首先对纵向结局拟合多变量混合效应模型。
• 其次，将第一阶段估计得到的随机效应作为协变量，纳入生存子模型中。
• 通过重要性抽样计算校正因子，对生存模型的估计结果进行调整，以校正因对随机效应进行条件化处理而引入的选择偏差。
• 校正因子考虑了真实联合模型与两阶段近似模型之间的分布不匹配问题。
• 该方法在保持单独建模计算简便性的同时，保留了接近完整联合模型的渐近性质。

实验结果

研究问题

• RQ1 基于校正因子的两阶段方法能否在多个纵向结局和生存时间结局的估计精度上达到与完整联合建模相当的水平？
• RQ2 与标准两阶段方法相比，所提出的方法在偏差和效率方面表现如何？
• RQ3 该方法在不牺牲估计精度的前提下，能在多大程度上减少计算时间？
• RQ4 基于重要性抽样的校正是否能有效缓解因忽略随机效应不确定性而引入的偏差？

主要发现

• 经校正的两阶段方法相比标准两阶段方法显著降低了偏差，其表现接近完整联合建模。
• 即使在随机效应数量较多或相关结构复杂的情况下，该方法仍能保持显著的计算加速。
• 模拟研究证实，校正因子能有效调整因对估计随机效应进行条件化处理而引起的偏差。
• 该方法在中等及以上样本量下，估计精度接近全多变量联合模型。