Applied Bayesian Biostatistics

应用贝叶斯生物统计学

• 批准号: RGPIN-2014-03918
• 负责人: Joseph, Lawrence
• 金额: $ 2.04万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=587495
• 关键词: Applied; Bayesian; Biostatistics

Three distinct themes will be investigated, some extensions of previous work, others new. Bayesian methods will be used throughout. (i) Bayesian design and analysis of diagnostic test data: It is common in the investigation of new diagnostic tests to have results from one or more tests for the same disease, none of which are error-free. It is nevertheless important to have the best possible estimates of disease prevalence and the properties of diagnostic tests. I have previously developed methods for both continuous and categorical diagnostic test data. The research area is especially interesting because it is typically non-identifiable, so that informative prior information is needed on at least a subset of the parameters in order to derive sensible inferences via Bayesian latent data models. Early methods were extended in several directions, including to correlated diagnostic tests, specific methods for rare diseases, inference for likelihood ratios, hierarchical models for diagnostic test data across several diseases, and various applications to cancer, and infectious and other diseases. I have also developed methods for the design of studies that will be based on diagnostic test data. In the next five years, I propose to continue to develop statistical methodology for related problems, including extensions to Polya tree models adjusted for covariates, and repeated measures of tests over time, including non-parametric longitudinal models. Latent class models have come under attack recently, with some authors showing that the correlational structure cannot be correctly identified, and the wrong choice of structure can lead to biased estimates. I will further investigate this issue, and expect to show that these concerns have been over-stated, and often the models work well. I will also investigate the impact of missing covariates that can cause correlations amongst tests. (ii) Sample size: Selection of the optimal number of subjects is an essential step in the planning of virtually every experiment. The choice of criterion is important, as different criteria can lead to very different sample size requirements. Ideally, the sample size criterion used should match the eventual analysis, but this is rarely the case in practice, in part from outdated traditions, and in part because of simplifications used to avoid complex models. One problem with Bayesian sample size methods is the dependence on the prior. It has been suggested to calculate posterior densities across a variety or family of prior distributions, but no sample size methods are available to match these analyses. In the next five years, I propose to introduce completely new Bayesian criteria for sample size problems. I will develop and investigate the properties of a novel "consensus-based" sample size criterion. This criterion is designed to match a Bayesian analysis which derives posteriors from a family of priors, to ensure posterior robustness to the prior. I will also develop Bayesian sample size methods for regression models, as well as sample size for agreement statistics such as Kappa. In regression, the methods will compare sample sizes in the presence and absence of correlations among independent variables and with and without measurement error. Little Bayes work exists in this area. (iii) Bayesian inference in music research. I was recently appointed to the Center for Interdisciplinary Research in Music, Media and Technology. There is close to no Bayesian activity in music technology with the exception of some simple models in cognitive science. Potential for new statistical work here is enormous, and I have already identified a project to work on: Nonparametric agreement models for instrument evaluation, in collaboration with Gary Scavone.

将调查三个不同的主题，一些是对以前工作的扩展，另一些是新的。贝叶斯方法将贯穿始终。 (1)诊断测试数据的贝叶斯设计和分析：在调查新的诊断测试时，常见的是同一疾病的一项或多项测试的结果，其中没有一项是没有错误的。尽管如此，重要的是对疾病流行率和诊断试验的性质有最好的估计。我之前已经为连续诊断测试数据和分类诊断测试数据开发了方法。这一研究领域特别有趣，因为它通常是不可识别的，因此需要关于至少一个参数子集的信息先验信息，以便通过贝叶斯潜在数据模型得出合理的推断。早期的方法被扩展到几个方向，包括相关的诊断测试，罕见疾病的特定方法，似然比的推断，几种疾病的诊断测试数据的分层模型，以及对癌症、传染病和其他疾病的各种应用。我还开发了基于诊断测试数据的研究设计方法。在接下来的五年里，我建议继续开发相关问题的统计方法，包括对协变量进行调整的Polya树模型的扩展，以及随着时间的推移对测试的重复测量，包括非参数纵向模型。潜在类模型最近受到了攻击，一些作者表明，相关结构不能被正确识别，错误的结构选择可能会导致有偏差的估计。我将进一步调查这个问题，并期望证明这些担忧被夸大了，而且通常模型运行得很好。我还将调查缺失协变量的影响，这些协变量可能会导致测试之间的相关性。 (2)样本量：选择最合适的受试者数量是规划几乎每一项实验的重要步骤。标准的选择很重要，因为不同的标准可能导致非常不同的样本量要求。理想情况下，使用的样本量标准应该与最终分析相匹配，但在实践中很少出现这种情况，部分原因是过时的传统，部分原因是为了避免复杂模型而使用的简化。贝叶斯样本量方法的一个问题是对先验的依赖。有人建议计算各种或一系列先验分布的后验密度，但没有样本量方法可以与这些分析相匹配。在接下来的五年里，我提议为样本量问题引入全新的贝叶斯标准。我将开发和研究一种新的“基于共识的”样本量标准的性质。这一标准被设计成与贝叶斯分析相匹配，贝叶斯分析从先验家族中得出后验，以确保后验对先验的稳健性。我还将开发回归模型的贝叶斯样本量方法，以及Kappa等协议统计的样本量。在回归中，这些方法将在自变量之间存在和不存在相关性以及有和没有测量误差的情况下比较样本大小。这方面的贝叶斯研究很少。 (3)音乐研究中的贝叶斯推理。我最近被任命为音乐、媒体和技术跨学科研究中心的成员。除了认知科学中的一些简单模型外，音乐技术中几乎没有贝叶斯活动。新的统计工作的潜力是巨大的，我已经确定了一个要研究的项目：与加里·斯卡沃内合作的工具评估的非参数协议模型。