Applied Bayesian Biostatistics

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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sample size criterion used should match the eventual analysis, but this is rarely the case in practice, in part from outdated traditions, and in part because of simplifications used to avoid complex models.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.