Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, CB#7420, Chapel Hill, NC 27599, United States.
Statistics and Data Science Innovation Hub, GlaxoSmithKline, Philadelphia, PA 19426, United States.
Biostatistics. 2024 Oct 1;25(4):962-977. doi: 10.1093/biostatistics/kxae009.
There is an increasing interest in the use of joint models for the analysis of longitudinal and survival data. While random effects models have been extensively studied, these models can be hard to implement and the fixed effect regression parameters must be interpreted conditional on the random effects. Copulas provide a useful alternative framework for joint modeling. One advantage of using copulas is that practitioners can directly specify marginal models for the outcomes of interest. We develop a joint model using a Gaussian copula to characterize the association between multivariate longitudinal and survival outcomes. Rather than using an unstructured correlation matrix in the copula model to characterize dependence structure as is common, we propose a novel decomposition that allows practitioners to impose structure (e.g., auto-regressive) which provides efficiency gains in small to moderate sample sizes and reduces computational complexity. We develop a Markov chain Monte Carlo model fitting procedure for estimation. We illustrate the method's value using a simulation study and present a real data analysis of longitudinal quality of life and disease-free survival data from an International Breast Cancer Study Group trial.
人们对联合模型在分析纵向和生存数据中的应用越来越感兴趣。虽然随机效应模型已经得到了广泛的研究，但这些模型可能难以实现，并且固定效应回归参数必须根据随机效应进行解释。Copulas 为联合建模提供了一个有用的替代框架。使用 Copulas 的一个优点是，从业者可以直接为感兴趣的结果指定边际模型。我们使用高斯 Copula 开发了一个联合模型，以描述多维纵向和生存结果之间的关联。我们提出了一种新颖的分解方法，而不是在 Copula 模型中使用非结构化相关矩阵来描述依赖性结构（例如，自回归），这在小到中等样本量下提供了效率增益，并降低了计算复杂度。我们开发了一种用于估计的马尔可夫链蒙特卡罗模型拟合过程。我们使用模拟研究说明了该方法的价值，并展示了来自国际乳腺癌研究小组试验的纵向生活质量和无病生存数据的实际数据分析。
