Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. In this work, a Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation-maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.

中文翻译：

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双变量区间删失数据的 Gamma-failty 比例风险模型

相关的生存数据自然来自许多临床和流行病学研究。对于此类数据的分析，Gamma-failty 比例风险 (PH) 模型是一种流行的选择，因为回归参数具有边际解释，并且故障时间之间的统计关联可以通过 Kendall tau 明确量化。尽管它们很受欢迎，但用于相关区间删失数据的 Gamma-frailty PH 模型并没有像右删失数据的类似模型那样受到关注。在这项工作中，提出了用于双变量区间删失数据的 Gamma-frailty PH 模型，并开发了一种易于实现的用于模型拟合的期望最大化 (EM) 算法。所提出的模型采用单调样条表示法来逼近未知条件累积基线危险函数，在保持建模灵活性的同时显着减少未知参数的数量。EM 算法源自涉及潜在泊松随机变量的数据增强程序。大量的数值研究表明，所提出的方法可以提供可靠的估计和有效的推理，而且对脆弱性分布的错误指定具有鲁棒性。为了进一步说明其用途，建议的方法用于分析性传播感染流行病学研究的数据。EM 算法源自涉及潜在泊松随机变量的数据增强程序。大量的数值研究表明，所提出的方法可以提供可靠的估计和有效的推理，而且对脆弱性分布的错误指定具有鲁棒性。为了进一步说明其用途，建议的方法用于分析性传播感染流行病学研究的数据。EM 算法源自涉及潜在泊松随机变量的数据增强程序。大量的数值研究表明，所提出的方法可以提供可靠的估计和有效的推理，而且对脆弱性分布的错误指定具有鲁棒性。为了进一步说明其用途，建议的方法用于分析性传播感染流行病学研究的数据。