Robust and efficient methods for analyzing complex longitudinal and survival data

在临床研究中，我们经常遇到具有许多复杂问题的多变量数据，包括生存结果的脆弱性、纵向结果的相关性、生物标志物的左检、协变量的测量误差以及反应变量的异常值。当关注个体的生存时间，并且希望研究内源性时间相关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志物的值未被观察到，但已知低于称为检测限（LOD）的阈值。忽略由LOD引起的左审查问题的朴素方法，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偏估计。为了获得有效的统计推断，在拟合联合模型时，使用适当的统计工具来调整左删节协变量是很重要的。此外，临床和调查数据通常包含可能对普通最大似然估计或假设检验产生深远影响的异常值。在估计模型参数时，需要采用鲁棒方法来约束异常值的影响。本建议的目的是开发有效的鲁棒方法，在联合分析纵向和时间到事件数据时，可以同时约束异常值的影响并调整LOD。此外，参数排序或约束可能在实践中自然出现，在这种情况下，可以通过将参数约束合并到估计和假设检验中来提高统计方法的效率。本研究将考虑线性不等式约束下联合模型的推理。在某些情况下，观测到的协变量存在测量误差，通过对观测到的协变量进行回归得到的普通估计量是渐近偏的。本研究将在联合模型框架中引入一种偏差校正估计量，通过校正协变量的LOD和测量误差来分析多变量结果。本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估计。上述发展将使健康科学的研究人员能够通过解决许多实际问题，包括协变量的左审查、潜在过程的错误说明、不可忽视的缺失反应、生物标志物的测量误差和反应变量的异常值，对他们的假设模型进行可靠的估计和评估，以分析调查和临床试验的数据。因此，将极大地有利于临床从业人员在现有的风险因素的基础上准确预测健康结果。

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.