Unified Dynamic Modeling of Event Time Data with Semiparametric Profile Estimating Functions: Theory, Computing, and Applications

各种审查方案下的事件时间数据出现在各种领域。在事件时间定义的时间过程均值函数的部分函数回归模型中，可以灵活地研究协变量对事件发生影响的时间动力学，其中一些协变量系数是时变的，而另一些协变量系数是时间无关的。在存在多个时变分量的情况下，统计推断是具有挑战性的，特别是当事件时间不是连续而是离散地观察时，例如在间隔审查下。研究了一种统一的半参数轮廓估计函数方法及其在事件时间仅离散观测时的估计形式。对于连续观测数据，通过交替更新用于时变系数的估计方程和用于时间无关系数的估计方程之间的当前估计的算法来估计模型参数。对于区间截尾或双截尾数据，估计函数先用多重插补估计，然后交替求解。该方法将在R项目的质量保证计划下的R包中实施。该方法为事件时间动态回归模型提供了一个统一的理论框架，使得对计算算法和统计推断的综合研究成为可能。它使协变量效应的有效估计和连续假设检验成为可能。将该方法应用于囊性纤维化疾病登记数据，将产生关于营养不良和肺部疾病进展之间关联的时间性质的新知识。例如，感兴趣的事件可以是一些慢性病症状的复发，例如囊性纤维化患者的肺部感染，或者一些工程或电子系统的故障，例如计算机磁盘的访问故障。时变效应和时间无关效应的混合使得在评估一种疾病的治疗或随着时间推移的新系统设计的有效性方面具有最大的灵活性。当协变量效应的时间性质是重要的影响因素时，该方法对事件时间数据分析的实践有影响。一个公开可用的软件将使那些将从使用这些方法中受益的人手中掌握这种方法，因此，有助于理解协变量对事件发生的影响的时间动力学。

Event time data under various censoring schemes arise in a variety of fields. The temporal dynamics of covariate effects on the occurrence of events can be flexibly studied in a partly functional regression model on the mean function of temporal processes defined by event times, with some covariate coefficients time-varying while others time-independent. Statistical inferences are challenging with the presence of multiple time-varying components, particularly when event times are not continuously but discretely observed, as under interval censoring. The investigator studies a unified semiparametric profile estimating function approach and an estimated version of it when the event times are only discretely observed. For continuously observed data, the model parameters are estimated from an algorithm that alternately updates the current estimate between an estimating equation for time-varying coefficients and an estimating equation for time-independent coefficients. For interval censored or doubly censored data, estimating functions will be estimated first using multiple imputation and then solved alternately. The methodology will be implemented in an R package under the quality assurance scheme of the R Project. The proposed approach provides a unified theoretical framework of dynamic regression models for event times, enabling a synthesized investigation of computingalgorithms and statistical inferences. It allows efficient estimation and successive hypotheses test of covariate effects. Application of the method to a cystic fibrosis disease registry data will generate new knowledge on the temporal nature of the association between malnutrition and pulmonary disease progression.The proposed method is motivated by the need of modeling temporal dynamics of covariate effects on the occurrence of certain events. Events of interests can be, for example, the recurrences of some chronic disease symptoms such as lung infection in cystic fibrosis patients, or the breakdowns of some engineering or electronic systems such as access failure of computer disks. A blend of time-varying effects and time-independent effects allows most flexibility in assessing the efficacy of a treatment of a disease or a design of new system over time. The method has an impact on the practice of event time data analysis when the temporal nature of covariate effects are of important interests. A publicly available software will get the methodology into the hands of those who will profit from using them, and, therefore, help to understand the temporal dynamics of covariate effects on event occurrences.