Multivariate Bayesian Modelling of Skewness and Kurtosis With Applications in Biostatistics

偏度和峰度的多元贝叶斯建模及其在生物统计学中的应用

• 批准号: EP/K007521/1
• 负责人: Mark Steel
• 金额: $ 39.27万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK007521%2F1
• 关键词: Multivariate; Bayesian; Modelling; Skewness; Kurtosis

We will study, from a Bayesian point of view, joint models for mixed responses such as continuous and discrete responses. Many of these models are motivated by longitudinal measurements obtained from clinical trials. A specific example of this is the longitudinal study of CD4 cell counts on individuals infected by the Human Immunodeficiency Virus (HIV) under a treatment with antiretroviral drugs. One of the interests in this context is the time elapsed from the infection to the presence of Acquired Immune Deficiency Syndrome (AIDS) and its relationship with the time evolution of some key biomedical indicators. This requires joint modelling of longitudinal and survival processes, which is the main area of application of this research proposal. Firstly, we will explore copulas for jointly modelling mixed responses, and compare various options by formal model comparison methods. Alternative approaches, based on designing new classes of flexible multivariate distributions will then be developed in detail. In addition, we need to propose priors for the model parameters. We will explore both informative and noninformative priors, and for the improper priors we will derive conditions for the existence of the posterior distribution. The use of appropriate MCMC methods will be necessary for efficiently conducting inference. Such methods will be developed and computer code will be made available freely. Most of these advances (developing classes of flexible multivariate distribution, formulating appropriate priors for constructing Bayesian models, proving posterior existence in these models, dealing with model uncertainty and with censored, missing or rounded observations, and implementing MCMC samplers for inference with such models) will be of substantial interest in themselves for the development of statistical methodology and have a much wider applicability as they could be used in a wide variety of applied fields. Nevertheless, in this project, we will focus specifically on applications in biostatistics. The aim is to substantially increase our understanding of disease progression and our methodology will also allow for the modelling of indicators of quality of life.

我们将从贝叶斯的角度研究混合响应的联合模型，如连续响应和离散响应。这些模型中的许多都是由临床试验中获得的纵向测量数据驱动的。这方面的一个具体例子是对接受抗逆转录病毒药物治疗的人类免疫缺陷病毒（HIV）感染者CD4细胞计数的纵向研究。在这方面的兴趣之一是从感染到出现获得性免疫缺陷综合征（艾滋病）的时间及其与一些关键生物医学指标的时间演变的关系。这需要纵向和生存过程的联合建模，这是本研究计划的主要应用领域。首先，我们将探索联合建模混合响应的copula，并通过形式模型比较方法比较各种选项。然后将详细开发基于设计灵活的多变量分布的新类的替代方法。此外，我们需要为模型参数提出先验。我们将探讨信息先验和非信息先验，对于不适当的先验，我们将推导后验分布存在的条件。为了有效地进行推理，使用适当的MCMC方法是必要的。这些方法将得到发展，计算机代码将免费提供。这些进步(开发灵活的多元分布类，为构建贝叶斯模型制定适当的先验，证明这些模型中的后验存在性，处理模型不确定性以及剔除，缺失或舍入观察值，以及使用这些模型进行推理的MCMC采样器)将对统计方法的发展具有实质性的兴趣，并且具有更广泛的适用性，因为它们可以用于各种应用领域。然而，在这个项目中，我们将特别关注生物统计学的应用。其目的是大大增加我们对疾病进展的了解，我们的方法也将允许对生活质量指标进行建模。

项目成果

On the propriety of the posterior of hierarchical linear mixed models with flexible random effects distributions

• DOI: 10.1016/j.spl.2014.09.023
• 发表时间: 2014-09
• 期刊: arXiv: Statistics Theory
• 作者: F. Rubio

Survival and lifetime data analysis with a flexible class of distributions

使用灵活的分布类别进行生存和寿命数据分析

• DOI: 10.48550/arxiv.1511.01855
• 发表时间: 2015
• 期刊: arXiv e-prints
• 作者: Rubio Francisco J.

Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis

具有偏斜对称误差分布的贝叶斯线性回归及其在生存分析中的应用

• DOI: 10.48550/arxiv.1601.02224
• 发表时间: 2016
• 期刊: arXiv e-prints
• 作者: Rubio Francisco J.

Flexible linear mixed models with improper priors for longitudinal and survival data

• DOI: 10.1214/18-ejs1401
• 发表时间: 2018-01-01
• 期刊: ELECTRONIC JOURNAL OF STATISTICS
• 影响因子: 1.1
• 作者: Rubio, F. J.;Steel, M. F. J.
• 通讯作者: Steel, M. F. J.

On modelling asymmetric data using two-piece sinh-arcsinh distributions

使用两部分 sinh-arcsinh 分布对非对称数据进行建模

• DOI: 10.48550/arxiv.1307.6021
• 发表时间: 2013
• 期刊: arXiv e-prints
• 作者: Rubio F. J.