Genitourinary surgeons and oncologists are particularly interested in whether a robotic surgery improves times to Prostate Specific Antigen (PSA) recurrence compared to a non-robotic surgery for removing the cancerous prostate. Time to PSA recurrence is an example of a survival time that is typically interval-censored between two consecutive clinical inspections with opposite test results. In addition, success of medical devices and technologies often depends on factors such as experience and skill level of the medical service providers, thus leading to clustering of these survival times. For analyzing the effects of surgery types and other covariates on median of clustered interval-censored time to post-surgery PSA recurrence, we present three competing novel models and associated frequentist and Bayesian analyses. The first model is based on a transform-both-sides of survival time with Gaussian random effects to account for the within-cluster association. Our second model assumes an approximate marginal Laplace distribution for the transformed log-survival times with a Gaussian copula to accommodate clustering. Our third model is a special case of the second model with Laplace distribution for the marginal log-survival times and Gaussian copula for the within-cluster association. Simulation studies establish the second model to be highly robust against extreme observations while estimating median regression coefficients. We provide a comprehensive comparison among these three competing models based on the model properties and the computational ease of their Frequentist and Bayesian analysis. We also illustrate the practical implementations and uses of these methods via analysis of a simulated clustered interval-censored data-set similar in design to a post-surgery PSA recurrence study.

泌尿生殖外科医生和肿瘤学家特别感兴趣的是，与去除癌性前列腺的非机器人手术相比，机器人手术是否能提高前列腺特异性抗原 (PSA) 复发的时间。PSA 复发时间是生存时间的一个例子，通常在两次连续临床检查之间进行间隔审查，但测试结果相反。此外，医疗设备和技术的成功往往取决于医疗服务提供者的经验和技能水平等因素，从而导致这些生存时间的聚集。为了分析手术类型和其他协变量对术后 PSA 复发的聚集间隔截断时间中位数的影响，我们提出了三个相互竞争的新模型以及相关的频率学和贝叶斯分析。第一个模型基于具有高斯随机效应的生存时间两侧的变换，以解释集群内关联。我们的第二个模型假设转换后的对数生存时间具有近似的边际拉普拉斯分布，并使用高斯 copula 来适应聚类。我们的第三个模型是第二个模型的特例，其中拉普拉斯分布用于边际对数生存时间，高斯 copula 用于集群内关联。模拟研究建立了第二个模型，在估计中值回归系数时对极端观察具有高度鲁棒性。我们基于模型属性及其频率学和贝叶斯分析的计算简便性，对这三个竞争模型进行了全面比较。