Emerging Issues in Modeling Longitudinal Observations with Censoring

纵向研究——通常被称为流行病学的队列研究或社会学的小组研究——对于理解同一组受试者中与时间相关的问题至关重要。在纵向研究中，信息收集可以在研究结束时停止，或在研究参与者退出时停止，或在结束事件发生时停止。死亡是最常见的终末事件，经常发生在衰老队列研究和致命性疾病随访研究中，例如器官衰竭或癌症研究。如果处理不当，终端事件的发生会导致统计推断出现严重偏差，从而得出错误的结论。目前的文献主要集中于纵向测量变量的建模，假设终端事件尚未发生，因此观察到的被终端事件“终止”的重复测量被隐式地视为不完整数据。然而，当一些感兴趣的效应与终端事件时间直接相关时，例如医疗费用数据，这种建模策略并不适合许多研究。在本项目中，将实施条件建模策略，该策略将重复测量直到终端事件作为完整数据，并直接建模终端事件时间对响应变量的影响。一个相关的问题是回归分析中一些受检测限制的预测变量，这在涉及测定措施的研究中经常发生，其中某些物质（例如，激素，空气污染物或水污染物）的测量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对受检测限制的预测变量进行临时推算或不可验证的模型假设，但这些方法通常产生有偏差的结果。本项目将使用稳健的统计方法来解决这个问题，这些方法与终端事件的条件建模策略类似，并产生比现有方法更可靠的结果。该项目通过将终端事件时间作为纵向研究中的协变量来直接研究其影响的建模策略。在这类统计模型中，当数据采集时间离终端事件时间较远时，纵向测量的响应变量与协变量之间保持通常的兴趣关系，当数据采集时间离终端事件时间较近时，这种关系与终端事件时间的关系越来越密切。这样的模型提供了更加直观和合理的解释，并且可以应用于具有终端事件存在的循环事件数据。参数模型和半参数模型都将被考虑。本文将研究所提出模型中参数的估计方法。对于终端事件时间受正确审查的情况，渐近理论将是一个主要的焦点。在这个项目中考虑的一组与删节协变量密切相关的纵向回归问题是关于协变量的检测极限问题。任何估计方法的有效性都依赖于对受检测限影响的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关于缺失尾部分布的任何有用信息。该项目研究了半参数模型，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.