Bayesian Methods for Longitudinal Cancer Data

描述（由申请人提供）：纵向数据经常出现在癌症研究的分析中。该提案的目标是开发新的贝叶斯模型和方法，以帮助分析和推断纵向癌症研究。这些新的发展可以分为四个目标。第一个目标是开发新的（贝叶斯）模型，用于分析离散多变量纵向数据。这一目标将建立在最近的创新工作，Heageland和其他单变量纵向二进制数据，通过开发模型的多变量离散纵向数据，模型的边际协变量的影响，直接提供自然的方式来模拟时间和多变量的依赖。第二个目标将是开发灵活和自动化的方法，用于使用自由节点样条的分层模型中的特定主题和整体曲线拟合。将提出以至少三种方式扩展和改进当前方法的方法和RJMCMC算法：1）允许针对受试者特异性曲线的固定和随机分量的不同结，2）适当地考虑受试者之间协方差矩阵的可变性，以及3）提供针对受试者特异性曲线的随机分量的降维的自然设置。将开发这些方法的几种应用，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志物。第三个目标将解决跨组建模依赖性，这些想法将与目标1中的想法相结合，构建混合多变量纵向数据的模型。在随机和/或不可验证的缺失数据存在的情况下，正确建模依赖性对于推理非常重要。第四个目标将开发灵活的贝叶斯半参数选择模型的纵向数据与非可重复的缺失。这将建立在主要研究者最近的工作基础上，主要研究者在无协变量的非纵向环境中构建了此类模型。这些模型的一个重要特点是保持观测数据的边际分布。这里提出的许多方法部分是由两个最近完成的癌症临床试验的动机;一个大型的结直肠癌临床试验和一个大型的乳腺癌预防试验。这些方法将在这些试验的数据上进行说明，并将回答这些试验的具体问题，包括比较两项试验中治疗的生活质量纵向轨迹，乳腺癌试验提供了大量脱落的额外并发症，被认为是信息丰富的。

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.