Bayesian Methods for Latent Class Models

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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.