Bayesian methods for (incomplete) longitudinal Cancer data

描述（由申请人提供）：我们继续我们之前的建议，开发新的贝叶斯方法纵向癌症数据缺失。在与观测到的或未观测到的响应相关的数据缺失的情况下，众所周知，错误地指定相关性通常会导致对平均参数的有偏估计。此外，在这种情况下，灵活、简洁的依赖关系模型通常是必要的。这种模型目前还不能用于相关矩阵（这是许多纵向模型的组成部分）。本建议的第一个目的是为纵向响应的相关矩阵引入一种新的参数化方法，该方法相对于先前的规范和建模提供了相当大的好处。我们将探讨几个模型和先验及其相关属性，计算问题和策略，包括自动简约建模，后验抽样和高维问题，以及它们在广泛的纵向模型应用中的实现。第二个目标将探索这些模型的扩展到多变量纵向数据。特别是，我们将探讨多元纵向响应向量的“排序”与简约模型和先验规范以及相关/协方差结构有关，其中这种排序不是问题。在第三个目标中，我们将开发新的贝叶斯方法用于纵向癌症研究的因果推断，在这些研究中，由于随访或协议定义的事件（进展或死亡）的丢失，反复测量的结果可能会丢失信息。在试图得出因果估计的推论时，需要不可识别的假设。我们将引入这些假设的低维、可解释的参数化，并从科学专家那里得到这些参数的先验。这些方法将用于回答最近几个癌症临床试验中感兴趣的问题，包括评估潜在的替代标志物（特定目标1），探索患者报告的（生活质量）和医生报告的（毒性）结果之间的关系（特定目标2），并在受试者因癌症进展或死亡而退出生活质量研究时做出推断（特定目标3）。公共卫生相关性：本应用中提出的新方法将具有重要的公共卫生效益。它们将有助于从晚期癌症的生活质量研究中得出正确的推论，理解医生报告的结果和患者报告的结果之间的关系，并更早地确定治疗效果。

DESCRIPTION (provided by applicant): We continue work from our previous proposal in developing new Bayesian methodology for longitudinal cancer data with missingness. In the presence of missing data that is related to observed or unobserved responses, it is known that mis-specifying the dependence will most often result in biased estimates of mean parameters. In addition, in such settings, flexible, parsimonious dependence models are often necessary. Such models are not currently available for correlation matrices (which form an integral part of many longitudinal models). The first aim of this proposal will introduce a new parameterization for a correlation matrix for longitudinal responses that offers considerable benefits with respect to prior specification and modeling. We will explore several models and priors and their associated properties, computational issues and strategies both with respect to automated parsimonious modeling, posterior sampling, and high-dimensional problems, and their implementation in a wide array of longitudinal models with applications. The second aim will explore the extension of these models to multivariate longitudinal data. In particular, we will explore the 'ordering' of the multivariate longitudinal response vector with regards to parsimonious models and prior specification and correlation/covariance structures for which this ordering is not an issue. In the third aim, we will develop new Bayesian approaches for causal inference in longitudinal cancer studies in which repeatedly measured outcomes may be informatively missing due to loss to follow-up or protocol-defined events (progression or death). In seeking to draw inference about causal estimands, non-identifiable assumptions are required. We will introduce low-dimensional, interpretable parameterizations of these assumptions and elicit priors for these parameters from scientific experts. These methods will be used to answer questions of interest from several recent cancer clinical trials including assessing potential surrogate markers (Specific Aim 1), exploring the relationship between patient reported (quality of life) and physician reported (toxicity) outcomes (Specific Aim 2), and making inference at the end of quality of life studies when subjects have dropped out due to cancer progression or death (Specific Aim 3). PUBLIC HEALTH RELEVANCE: The new methods proposed in this application will have important public health benefits. They will facilitate drawing correct inferences from quality of life studies for late stage cancers, understanding the relationship between physician reported and patient reported outcomes, and making earlier determinations of treatment effects.