Robust and efficient methods for analyzing complex longitudinal and survival data

在临床研究中，我们经常遇到包含许多复杂问题的多变量数据，包括生存结果中的脆弱性、纵向结果中的相关性、生物标记物中的左删失、协变量中的测量误差以及反应变量中的异常值。当焦点是个体的生存时间，并且希望研究内生的时间依赖的协变量或生物标志物对生存时间的影响时，通常使用纵向和生存数据的联合建模。通常，临床协变量或生物标记物的值未被观察到，但已知低于一个称为检测极限(LOD)的阈值。忽略LOD导致的左删失问题的幼稚方法，例如用LOD或LOD的一半替换未检测到的值，通常会导致协变量效应的有偏估计。对于有效的统计推断，重要的是使用适当的统计工具，在拟合联合模型时对左删失协变量进行调整。此外，临床和调查数据经常包含异常值，这可能会对普通的最大似然估计或假设检验产生深远影响。在估计模型参数时，需要用稳健的方法来限制离群点的影响。该建议的目的是开发高效、稳健的方法，在联合分析纵向数据和事件间隔时间数据时，可以同时限制离群值的影响并针对LOD进行调整。此外，在实践中，参数排序或约束可能会自然发生，在这种情况下，通过将参数约束纳入估计和假设检验中，可以提高统计方法的效率。本研究将考虑线性不等约束下的联合模型推理。在某些情况下，协变量被观测到带有测量误差，其中通过对观测到的协变量进行回归而得到的普通估计是渐近有偏的。这项研究将在分析多变量结果的联合模型的框架内，通过校正协变量中的LOD和测量误差来引入偏差调整估计器。这项研究还将开发和探索灵活的方法，可以解决潜在随机效应分布中的不确定性，并可以在错误指定的潜在过程下提供稳健的估计。上述发展将使健康科学研究人员能够通过解决许多实际问题，包括协变量的左删减、潜在过程的错误指定、不可忽视的遗漏反应、生物标志物中的测量误差和反应变量中的异常值，对他们用于分析调查和临床试验数据的假设模型进行可靠的估计和评估，因此将极大地有利于临床从业者根据现有的风险因素准确地预测健康结果。

In clinical studies, we often encounter multivariate data featuring many complex issues including frailties in survival outcomes, correlations in longitudinal outcomes, left-censoring in biomarkers, measurement errors in covariates, and outliers in response variables. Joint modeling of longitudinal and survival data is often used when the focus is on the survival times of individuals and one wishes to study the effect of endogenous time-dependent covariates or biomarkers on the survival times. Often values of a clinical covariate or biomarker are unobserved but known to be below a threshold called the limit of detection (LOD). Naive approaches that ignore the problem of left-censoring due to the LOD, such as replacing the undetected value by the LOD or by half of the LOD, typically lead to biased estimators of the covariate effects. For a valid statistical inference, it is important to use proper statistical tools that adjust for the left-censored covariates when fitting the joint model. Also, clinical and survey data often contain outliers that can have profound influence on the ordinary maximum likelihood estimation or hypothesis testing. Robust methods are needed to bound the influence of outliers when estimating the model parameters. The aim of this proposal is to develop efficient robust methods that can simultaneously bound the influence of outliers and adjust for the LOD when jointly analyzing longitudinal and time-to-event data. Also, parameter orderings or constraints may naturally occur in practice, and in such cases, the efficiency of a statistical method can be improved by incorporating the parameter constraints into the estimation and hypothesis testing. This research will consider inference with joint models under linear inequality constraints. In some situations, covariates are observed with measurement error, where an ordinary estimator obtained by regressing on the observed covariates is asymptotically biased. This research will introduce a bias-adjusted estimator by correcting for both the LOD and measurement error in covariates in the framework of the joint model for analyzing multivariate outcomes. This research will also develop and explore flexible methods that can address uncertainties in the latent random effects distributions and can provide robust estimates under a misspecified latent process. The aforementioned developments will enable researchers in health sciences to engage in reliable estimation and assessment of their hypothesized models for analyzing data from surveys and clinical trials by addressing many practical issues including left-censoring in covariates, misspecification of latent processes, nonignorable missing responses, measurement errors in biomarkers and outliers in response variables, and hence will greatly benefit clinical practitioners for accurately predicting health outcomes on the basis of available risk factors.