Bayesian Methods for Latent Class Models

对于许多常见疾病，如肺炎，没有完美的测试。这使得估计疾病流行率（即人群中疾病的概率）或在灵敏度（真阳性概率）和特异性（真阴性概率）方面评估新测试的问题变得复杂。LCM提供了一种现实的方法来量化这些问题中的不确定性。在最简单的形式中，LCM假设观察到的变量与潜伏疾病状态无关，即测试误差不相关。 这些模型的应用一直很慢，因为仍然存在一些有趣的理论挑战。我的研究计划的长期目标是使潜在类模型的贝叶斯方法更强大，计算速度更快，更容易获得。目标目前的提案提出了三大主题下的项目：1）在一个单一的研究背景下的潜在类分析，2）潜在类分析的样本量确定，3）潜在类分析的荟萃分析的背景下。在每个主题下分别介绍了文献综述。* 方法：在第一个主题下，我将探索比较竞争潜在类模型的方法，基于随机效应定义更简单的模型，LCM先验分布的规范以及改进的计算方法。在第二个主题下，我将考虑使用近似估计方法来提高样本量计算的速度，并开发在样本量计算中考虑成本和条件依赖性的方法。在第三个主题下，我将扩展我以前的工作，使用I-squared统计量在荟萃分析中量化异质性。我还将介绍使用个体患者数据分析开发临床预测模型的挑战。*在整个过程中，贝叶斯方法将用于估计和推断。这种方法在潜在类模型的上下文中特别有价值，因为即使观察到许多测试，它们也可能是不可识别的，并且样本量很大。然后，只有当使用具有信息先验分布的贝叶斯方法时，才可能估计未知参数。* 研究计划的意义：在过去18年中，在NSERC的持续支持下，我支持了许多硕士和博士生在这一领域开发新方法，为加拿大劳动力的高素质专业人才库做出了贡献。我们开发的方法已被应用于支持重要的医疗保健研究项目和与诊断测试相关的政策制定。

Introduction: There is no perfect test for many common diseases like pneumonia. This complicates the problem of estimating disease prevalence (i.e. probability of disease in a population) or the problem of evaluating a new test in terms of sensitivity (true positive probability) and specificity (true negative probability). LCMs provide a realistic way to quantify the uncertainty in these problems. In its simplest form LCM assumes the observed variables are independent conditional on the latent disease status, i.e. errors on the tests are not correlated. Applications of these models have been slow to catch on because a number of interesting theoretical challenges remain. The long-term goal of my research program is to make Bayesian methods for Latent Class Models more robust, computationally fast and widely accessible.***Objectives The current proposal proposes projects under three broad themes: 1) Latent class analysis in the context of a single study, 2) Sample size determination for latent class analysis, 3) Latent class analysis in the context of a meta-analysis. A literature review is presented separately under each theme. ***Methods: Under the first theme, I will explore methods for comparing competing latent class models, defining simpler models based on random effects, specification of prior distributions for LCMs as well as improved computational methods. Under the second theme, I will consider the use of approximate estimation methods to improve the speed of sample size calculations and the development of methods that consider cost and conditional dependence in sample size calculations. Under the third theme, I will extend my previous work on quantifying heterogeneity in a meta-analysis setting using the I-squared statistic. I will also cover the challenges in developing a clinical prediction model using individual-patient data analysis.***Throughout a Bayesian approach will be used for estimation and inference. This approach is particularly valuable in the context of latent class models as they can be non-identifiable even when many tests are observed, and the sample size is large. Estimation of the unknown parameters is then only possible when using a Bayesian approach with informative prior distributions. ******Significance of research program: With continuous support from NSERC over the last 18 years I have supported numerous MSc and PhD students to develop new methods in this area, contributing to the pool of highly-qualified professionals for the Canadian workforce. Methods we have developed have been applied to support important health care research projects and policy making related to diagnostic tests.