Random effect models for time-to-event data, also known as frailty models, provide a conceptually appealing way of quantifying association between survival times and of representing heterogeneities resulting from factors which may be difficult or impossible to measure. In the literature, the random effect is usually assumed to have a continuous distribution. However, in some areas of application, discrete frailty distributions may be more appropriate. The present paper is about the implementation and interpretation of the Addams family of discrete frailty distributions. We propose methods of estimation for this family of densities in the context of shared frailty models for the hazard rates for case I interval-censored data. Our optimization framework allows for stratification of random effect distributions by covariates. We highlight interpretational advantages of the Addams family of discrete frailty distributions and the K-point distribution as compared to other frailty distributions. A unique feature of the Addams family and the K-point distribution is that the support of the frailty distribution depends on its parameters. This feature is best exploited by imposing a model on the distributional parameters, resulting in a model with non-homogeneous covariate effects that can be analysed using standard measures such as the hazard ratio. Our methods are illustrated with applications to multivariate case I interval-censored infection data.

翻译：针对时间-事件数据的随机效应模型，亦称脆弱度模型，为量化生存时间之间的关联性及表征由难以或无法测量的因素导致的异质性提供了一种概念上具有吸引力的方法。在现有文献中，随机效应通常被假定服从连续分布。然而，在某些应用领域中，离散脆弱度分布可能更为适用。本文重点探讨离散脆弱度分布Addams族的实现与解释。针对I型区间删失数据的风险率，我们在共享脆弱度模型框架下提出了该密度族参数的估计方法。我们的优化框架允许通过协变量对随机效应分布进行分层处理。相较于其他脆弱度分布，我们着重阐述了Addams族离散脆弱度分布与K点分布在解释性方面的优势。Addams族与K点分布的一个独特特征在于其脆弱度分布的支撑集依赖于参数本身。通过对分布参数建立模型可充分发挥这一特性，从而构建具有非齐次协变量效应的模型，并可采用风险比等标准度量进行分析。我们通过多元I型区间删失感染数据的应用实例来演示所提方法。