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

各种滤波方案下的事件时间数据出现在不同的领域。在由事件时间定义的时间过程平均函数的部分泛函回归模型中，一些协变量系数时变而另一些协变量系数时独立，可以灵活地研究协变量影响事件发生的时间动态。随着多个时变分量的存在，统计推断是具有挑战性的，特别是当事件时间不是连续的，而是离散的观察时，如在区间审查下。研究者研究了一种统一的半参数剖面估计函数方法及其在事件时间仅被离散观察时的估计版本。对于连续观测数据，模型参数由一种算法估计，该算法交替更新时变系数估计方程和时变系数估计方程之间的当前估计。对于区间截短或双截短的数据，先用多次插值估计估计函数，然后交替求解。该方法将在“R计划”的质素保证计划下，以一个R程式包的形式推行。提出的方法为事件时间的动态回归模型提供了统一的理论框架，使计算算法和统计推断的综合研究成为可能。它允许协变量效应的有效估计和连续假设检验。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与肺部疾病进展之间关联的时间性质的新知识。提出的方法的动机是需要对某些事件发生的协变量效应的时间动力学进行建模。例如，感兴趣的事件可以是某些慢性疾病症状的复发，例如囊性纤维化患者的肺部感染，或者某些工程或电子系统的故障，例如计算机磁盘的访问失败。时变效应和时变无关效应的混合，在评估一种疾病的治疗效果或设计一种新系统时，具有最大的灵活性。当协变量效应的时间性质具有重要意义时，该方法对事件时间数据分析的实践产生了影响。一个公开可用的软件将使方法论进入那些将从使用它们中获利的人手中，并且，因此，有助于理解事件发生的协变量效应的时间动态。

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.