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有关的问题至关重要。在纵向研究中，信息收集可以在研究结束时、研究参与者退学时、或终末期事件发生时停止。死亡是最常见的终末期事件，通常发生在老龄化队列研究和致命疾病后续研究中，例如器官衰竭或癌症研究。如果处理不当，终端事件的发生可能会造成统计推断的严重偏差，导致错误的结论。目前的文献主要集中于在终端事件尚未发生的情况下对纵向测量的变量进行建模，因此被终端事件“终止”的观测到的重复测量被隐含地视为不完整数据。然而，当一些感兴趣的影响与最终事件时间直接相关时，例如医疗成本数据，这种建模策略对于许多研究是不合适的。在本项目中，将实施条件建模策略，将直到终端事件的重复测量视为完整数据，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的一些受检测限度限制的预测变量，这种情况经常出现在涉及分析措施的研究中，其中某些物质(例如激素、空气污染物或水污染物)的测量因技术限制而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极限限制的预测变量的临时补偿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。这个项目将使用稳健的统计方法来解决这个问题，这种方法类似于对终端事件的条件建模策略，并且比现有的方法产生更可靠的结果。该项目研究建模策略，通过在纵向研究中将其作为协变量来直接建模终端事件时间的影响。在这种统计模型中，当数据采集时间远离终端事件时间时，纵向测量的响应变量与协变量之间保持通常的关注关系，而当数据采集时间接近终端事件时，这种关系变得与终端事件时间越来越相关。这样的模型提供了更直观和合理的解释，并且可以应用于存在终端事件的重复事件数据。参数模型和半参数模型都将被考虑。将研究所提出的模型中参数的估计方法。关于终端事件时间服从右删失情形的渐近理论将是一个主要的焦点。这个项目中考虑的一组密切相关的带有删失协变量的纵向回归问题是关于协变量的检测限的问题。任何估计方法的有效性取决于一个人在检测极限下建模和估计协变量的尾部分布的可靠性有多高。由于这类数据的特点，参数模型是不可验证的，非参数模型无法获得关于缺失尾部分布的任何有用信息。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，并且对模型错误指定的丢失尾部概率不敏感。

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.