Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification
Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification
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DOI：
10.1002/sim.6779
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发表时间：
2016-03-30
影响因子：
2
通讯作者：
Humphreys, Keith
中科院分区：
文献类型：
--
作者：
Crowther, Michael J.;Andersson, Therese M-L.;Humphreys, Keith
现在医学研究的一个共同目标是调查重复测量的生物标志物（测量有误差）与感兴趣事件的时间之间的相互关系。这种形式的问题可以通过联合纵向生存模型来解决，最常见的方法是将纵向混合效应模型与比例风险生存模型相结合，其中模型通过共享随机效应联系起来。在本文中，我们将研究合并延迟输入（左截断），这一点受到的关注相对较少。延迟进入的扩展需要第二组数值积分，超出了标准联合模型所需的数值积分。因此，我们实现了两组完全自适应高斯-埃尔米特求积法和嵌套高斯-克朗罗德求积法（以允许时间相关的关联结构），同时进行，以评估可能性。我们通过模拟研究评估了完全自适应正交与之前提出的非自适应正交，在最小化偏差和减少计算时间方面显示出显着的改进。我们通过模拟进一步研究了错误指定纵向轨迹的后果及其对关联估计的影响。我们的场景显示，与我们发现的高度敏感的变化率相比，当前的价值关联结构非常稳健，这表明当事实更复杂时假设更简单的趋势可能会导致重大偏差。我们强调灵活的参数方法，通过建议使用多项式或样条来捕获纵向趋势，并使用限制三次样条来对基线对数风险函数进行建模，从而概括了以前的模型。这些方法在乳腺癌患者的数据集上进行了说明，将乳房X线照相密度与生存率联合建模，其中我们展示了如何在危险期之前合并密度测量，以利用所有可用信息。提供用户友好的Stata软件。 (C) 2015 年作者。医学统计由 JohnWiley & Sons Ltd 出版。
A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available information. User-friendly Stata software is provided. (C) 2015 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.