Emerging Issues in Modeling Longitudinal Observations with Censoring

纵向研究-通常被称为流行病学中的队列研究或社会学中的小组研究-对于理解同一组学科中与时间有关的问题具有根本的重要性。在纵向研究中，可以在研究结束时、研究参与者脱落时或终末事件发生时停止收集信息。死亡是最常见的终末事件，常发生在老龄化队列研究和致死性疾病随访研究中，例如，器官衰竭或癌症研究。如果处理不当，终末事件的发生可能会导致统计推断出现严重偏倚，从而得出不正确的结论。 目前的文献主要集中在建模的纵向测量变量的终端事件尚未发生，因此观察到的重复测量“终止”的终端事件被隐含地视为不完整的数据。然而，这样的建模策略，是不合适的许多研究时，一些利益的影响是直接相关的终端事件的时间，如医疗费用数据。在本项目中，将实施条件建模策略，将重复测量直至终端事件视为完整数据，并直接对终端事件时间对响应变量的影响进行建模。一个相关的问题是回归分析中受检测限影响的一些预测变量，这经常发生在涉及测定测量的研究中，其中某些物质的测量（例如，激素、空气污染物或水污染物）由于技术限制而在其浓度低于一定水平时变得不可靠。目前的文献主要集中在特设插补或不可验证的模型假设的预测变量受检测限，但这些方法通常会产生偏倚的结果。本项目将使用稳健的统计方法来解决这个问题，该方法类似于终末事件的条件建模策略，并产生比现有方法更可靠的结果。本项目研究将终末事件时间视为纵向研究中的协变量，直接建模终末事件时间效应的建模策略。在这样的统计模型中，当数据收集时间远离终止事件时间时，保持纵向测量的响应变量和协变量之间的通常关系，并且当数据收集时间接近终止事件时，该关系变得与终止事件时间越来越相关。这样的模型提供了更直观和明智的解释，并可以应用于经常性事件的数据与存在的终端事件。将考虑参数和半参数模型。将研究所提出的模型中的参数估计方法。渐近理论的情况下，终端事件的时间是受右删失将是一个主要的焦点。本计画考虑的一组密切相关的具有截尾协变量的纵向回归问题是关于协变量的检测限问题。任何估计方法的有效性都取决于在检测限下对协变量的尾部分布进行建模和估计的可靠性。由于这类数据的特点，参数模型是不可验证的，非参数模型不能获得任何有用的信息，缺失的尾部分布。该项目研究半参数模型，它能够从观测数据中获得有用的信息，并且对缺失尾部概率的模型错误指定不敏感。

Longitudinal studies--commonly referred to as cohort studies in epidemiology or panel studies in sociology--are of fundamental importance in understanding time related issues within the same group of subjects. In longitudinal studies, the collection of information can be stopped at the end of the study, or at the time of dropout of a study participant, or at the time of the occurrence of a terminal event. Death, the most common terminal event, often occurs in aging cohort studies and fatal disease follow-up studies, e.g., organ failure or cancer studies. If not handled appropriately, the occurrence of terminal event can cause serious bias in statistical inference, leading to incorrect conclusions. The current literature has primarily focused on modeling the longitudinally measured variables given that the terminal event has not happened yet, hence the observed repeated measures "terminated" by a terminal event are implicitly treated as incomplete data. Such a modeling strategy, however, is inappropriate for many studies when some effect of interest is directly related to the terminal event time, such as the medical cost data. In this project, a conditional modeling strategy will be implemented, which treats repeated measures up to a terminal event as complete data and directly models the effect of terminal event time on a response variable. A related problem is some predictor variable subject to limit of detection in regression analysis, which occurs frequently in studies involving assay measures, where measures of certain substance (e.g., hormone, air pollutant, or water contaminant) become unreliable when their concentrations are below certain level due to technology limitation. The current literature has focused on primarily ad hoc imputation or unverifiable model assumptions for the predictor variable subject to limit of detection, but these methods generally yield biased results. This project will tackle this issue using robust statistical methods, which follow similarly the conditional modeling strategy for terminal events, and yield more reliable results than existing approaches.The project investigates modeling strategies that model the effect of terminal event time directly by treating it as a covariate in longitudinal studies. In such statistical models, the usual relationship of interest between the longitudinally measured response variable and covariates is kept when data collecting time is far from the terminal event time, and the relationship becomes increasingly related to the terminal event time when data collecting time is close to the terminal event. Such models provide much more intuitive and sensible interpretations, and can be applied to recurrent events data with the presence of a terminal event. Both parametric and semiparametric models will be considered. Estimating methods for parameters in the proposed models will be investigated. The asymptotic theory for the case that the terminal event time is subject to right censoring will be a major focus. A closely related set of longitudinal regression problems with censored covariates considered in this project is about the issue of detection limit for covariates. The validity of any estimating approach relies on how reliably one can model and estimate the tail distribution of the covariate subject to limit of detection. Due to the feature of this type of data, parametric models are not verifiable and nonparametric models are not able to gain any useful information about the missing tail distribution. The project investigates semiparametric models, which are able to gain useful information from observed data and are insensitive to model misspecification of the missing tail probabilities.