Applied Bayesian Biostatistics

将研究三个不同的主题，一些是以前工作的延伸，另一些是新的。贝叶斯方法将贯穿始终。**(i)诊断测试数据的贝叶斯设计和分析：在对新的诊断测试的调查中，对同一疾病进行一项或多项测试的结果是常见的，其中没有一项是没有错误的。然而，对疾病流行率和诊断测试的特性进行尽可能最佳的估计是很重要的。我以前开发了连续和分类诊断测试数据的方法。该研究领域特别有趣，因为它通常是不可识别的，因此至少需要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。早期的方法在几个方面得到了扩展，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，包括扩展到根据协变量调整的Polya树模型，以及随着时间的推移重复测量测试，包括非参数纵向模型。最近，潜在类模型受到了攻击，一些作者表明，相关结构不能正确识别，错误的结构选择可能导致有偏差的估计。我将进一步调查这个问题，并希望表明这些担忧被夸大了，而且模型通常工作得很好。我还将研究缺失协变量的影响，这些协变量可能导致测试之间的相关性。**(ii)样本量：选择最优的受试者数量是几乎每个实验计划的重要步骤。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，所使用的样本量标准应该与最终的分析相匹配，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使用复杂的模型而进行了简化。贝叶斯样本大小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，但没有可用的样本量方法来匹配这些分析。在接下来的五年里，我建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”的样本大小标准的性质。该准则旨在匹配贝叶斯分析，该分析从一系列先验中获得后验，以确保对先验的后验鲁棒性。我还将开发回归模型的贝叶斯样本量方法，以及协议统计（如Kappa）的样本量。在回归中，这些方法将比较独立变量之间存在和不存在相关性以及有无测量误差的样本量。贝叶斯在这个领域有一些研究。**(iii)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一员。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。在这里，新的统计工作的潜力是巨大的，我已经确定了一个项目：用于工具评估的非参数协议模型，与Gary Scavone合作。

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.