Bayesian parametric estimation based on left-truncated competing risks data under bivariate Clayton copula models

In observational/field studies, competing risks and left-truncation may co-exist, yielding ‘left-truncated competing risks’ settings. Under the assumption of independent competing risks, parametric estimation methods were developed for left-truncated competing risks data. However, competing risks may be dependent in real applications. In this paper, we propose a Bayesian estimator for both independent competing risks and copula-based dependent competing risks models under left-truncation. The simulations show that the Bayesian estimator for the copula-based dependent risks model yields the desired performance when competing risks are dependent. We also comprehensively explore the choice of the prior distributions (Gamma, Inverse-Gamma, Uniform, half Normal and half Cauchy) and hyperparameters via simulations. Finally, two real datasets are analyzed to demonstrate the proposed estimators.

在观察性研究/现场研究中，竞争风险（Competing Risks）与左截断（left-truncation）可能同时存在，从而构成“左截断竞争风险”研究场景。在竞争风险相互独立的假设下，学界已针对左截断竞争风险数据提出参数化估计方法。但在实际应用中，竞争风险之间往往存在相关性。本文针对左截断场景下的独立竞争风险与基于Copula的相依竞争风险模型，提出了一种贝叶斯估计器。仿真实验结果表明，当竞争风险存在相关性时，基于Copula的相依风险模型对应的贝叶斯估计器可达到预期性能。本文还通过仿真实验，全面探究了先验分布（伽马分布(Gamma)、逆伽马分布(Inverse-Gamma)、均匀分布(Uniform)、半正态分布(half Normal)与半柯西分布(half Cauchy)）及其超参数的选择策略。最后，本文通过两个真实数据集的分析，验证了所提估计器的实际应用效果。