Bayesian Methods for Longitudinal Cancer Data

描述(申请人提供)：纵向数据经常出现在癌症研究的分析中。这项提案的目标将是开发新的贝叶斯模型和方法，以帮助分析纵向癌症研究并从中推断。这些新的发展可以归类为四个目标。第一个目标是开发新的(贝叶斯)模型，用于分析离散的多变量纵向数据。这一目标将建立在Heagerty和其他人最近针对单变量纵向二进制数据所做的创新工作的基础上，通过开发多变量离散纵向数据模型，直接对边际协变量效应进行建模，并提供自然的方法来对时间相关性和多变量相关性进行建模。第二个目标是开发灵活和自动化的方法，在分层模型中使用自由结样条线进行特定对象和整体曲线的拟合。将提出至少以三种方式扩展和改进当前方法的方法和RJMCMC算法：1)允许对象特定曲线的固定和随机分量的不同结点，2)适当地考虑对象之间协方差矩阵的可变性，以及3)为对象特定曲线的随机分量提供降维的自然设置。将开发这些方法的几个应用，包括使用这种方法通过联合纵向/生存模型来评估癌症生物标记物。第三个目标将解决跨群体的建模依赖问题，这些想法将与目标1中的想法相结合，以构建混合多变量纵向数据的模型。在存在随机丢失和/或不可忽略的丢失数据的情况下，正确地建模依赖关系对于推理非常重要。第四个目标是为具有不可忽略缺失的纵向数据开发灵活的贝叶斯半参数选择模型。这将建立在首席调查员最近的工作基础上，他在没有协变量的非纵向环境中构建了这种模型。这些模型的一个重要特点是保留了观测数据的边际分布。这里提出的许多方法在一定程度上是受到最近完成的两项癌症临床试验的推动：一项大型结直肠癌临床试验和一项大型乳腺癌预防试验。这些方法将在这些试验的数据上得到说明，并将允许回答这些试验中的具体问题，包括比较两个试验中不同治疗方法的生活质量纵向轨迹，乳腺癌试验提供了额外的复杂性，即有大量辍学，被认为是信息量大的。

DESCRIPTION (provided by applicant): Longitudinal data arise frequently in the analysis of cancer studies. The goal of this proposal will be to develop new Bayesian models and methods to assist in the analysis of, and inference from, longitudinal cancer studies. These new developments can be categorized into four aims. The first aim will be to develop new (Bayesian) models for the analysis of discrete multivariate longitudinal data. This aim will build on recent innovative work by Heagerty and others for univariate longitudinal binary data by developing models for multivariate discrete longitudinal data that model marginal covariate effects directly and provide natural ways to model both temporal and multivariate dependence. The second aim will be to develop flexible and automated methods for subject specific and overall curve fitting in hierarchical models using free knots splines. Methods and RJMCMC algorithms will be proposed that extend and improve current methods in at least three ways: 1) allow different knots for the fixed and random components of the subject-specific curves, 2) properly account for the variability of the between subject covariance matrix, and 3) provide a natural setup for dimension reduction for the random components of the subject-specific curves. Several applications of these methods will be developed, including using this methodology to evaluate cancer biomarkers through joint longitudinal/survival models. The third aim will address modeling dependence across groups and these ideas will be combined with those in aim 1 to construct models for mixed multivariate longitudinal data. Modeling dependence correctly is very important for inference in the presence of missing data that is missing at random and/or non-ignorable. The fourth aim will develop flexible Bayesian semi-parametric selection models for longitudinal data with non-ignorable missingness. This will build on recent work by the Principal Investigator's who constructed such models in the non-longitudinal setting without covariates. An important feature of these models will be the preservation of the marginal distribution of the observed data. Many of the methods proposed here are partially motivated by two recently completed cancer clinical trials; a large colorectal cancer clinical trial and a large breast cancer prevention trial. These methods will be illustrated on the data from these trials and will allow specific questions from these trials to be answered, including a comparison of the longitudinal trajectories of quality of life across treatments in both trials, with the breast cancer trial offering the additional complication of having a lot of dropout, thought to be informative.