Background and objective: With the recent surge in availability of large biomedical databases mostly derived from electronic health records, the need for the development of scalable marginal survival models with faster implementation cannot be more timely. The presence of clustering renders computational complexity, especially when the number of clusters is high. Marginalizing conditional survival models can violate the proportional hazards assumption for some frailty distributions, disrupting the connection to a conditional model. While theoretical connections between proportional hazard and accelerated failure time models exist, a computational framework to produce both for either marginal or conditional perspectives is lacking. Our objective is to provide fast, scalable bridged-survival models contained in a unified framework from which the effects and standard errors for the conditional hazard ratio, the marginal hazard ratio, the conditional acceleration factor, and the marginal acceleration factor can be estimated, and related to one another in a transparent fashion. Methods We formulate a Weibull parametric frailty likelihood for clustered survival times that can directly estimate the four estimands. Under a nonlinear mixed model specification with positive stable frailties powered by Gaussian quadrature, we put forth a novel closed form of the integrated likelihood that lowered the computational threshold for fitting these models. The method is illustrated on a real dataset generated from electronic health records examining tooth-loss. Results: Our novel closed form of the integrated likelihood significantly lowered the computational threshold for fitting these models by a factor of 12 (36 compared to 3 min) for the R package parfm, and a factor of 2400 for Gaussian Quadrature (4.6 days compared to 3 min) in SAS. Moreover, each of these estimands are connected by simple relationships of the parameters and the proportional hazards assumption is preserved for the marginal model. Our framework provides a flow of analysis enabling the fit of any/all of the 4 perspective-parameterization combinations. Conclusions We see the potential usefulness of our framework of bridged parametric survival models fitted with the Static-Stirling closed form likelihood. Bridged-survival models provide insights on subject-specific and population-level survival effects when their relation is transparent. SAS and R codes, along with implementation details on a pseudo data are provided.

背景和目的：随着最近主要来自电子健康记录的大型生物医学数据库的可用性激增，开发具有更快实施速度的可扩展边际生存模型的需求再及时不过了。聚类的存在会导致计算复杂性，尤其是在聚类数量很高的情况下。将条件生存模型边缘化可能会违反某些脆弱分布的比例风险假设，从而破坏与条件模型的连接。虽然存在比例风险和加速故障时间模型之间的理论联系，但缺乏用于产生边际或条件视角的计算框架。我们的目标是提供快速、方法我们制定了聚类生存时间的 Weibull 参数脆弱似然，可以直接估计四个估计值。在由高斯正交驱动的具有正稳定弱点的非线性混合模型规范下，我们提出了一种新颖的集成似然封闭形式，降低了拟合这些模型的计算阈值。该方法在从检查牙齿缺失的电子健康记录生成的真实数据集上进行了说明。结果：对于 R 包 parfm，我们新颖的集成似然封闭形式将拟合这些模型的计算阈值显着降低了 12 倍（36 比 3 分钟），高斯正交降低了 2400 倍（4.6 天比 3 分钟） ) 在 SAS 中。此外，这些估计中的每一个都通过参数的简单关系连接起来，并且为边际模型保留了比例风险假设。我们的框架提供了一个分析流程，可以拟合任何/所有 4 种透视参数化组合。结论我们看到了我们的桥接参数生存模型框架的潜在有用性，该模型配备了静态斯特林封闭形式似然性。当它们的关系是透明的时，桥接生存模型提供了关于特定主题和人口水平生存效应的见解。提供了 SAS 和 R 代码，以及伪数据的实现细节。