Bayesian approaches to parameter estimation and variable selection for misclassified binary data.

Binary misclassification is a common occurrence in statistical studies that, when ignored, induces bias in parameter estimates. The development of statistical methods to adjust for misclassification is necessary to allow for consistent estimation of parameters. In this work we develop a Bayesian framework for adjusting statistical models when fallible data collection methods produce misclassification of binary observations. In Chapter 2, we develop an approach for Bayesian variable selection for logistic regression models in which there exists a misclassified binary covariate. In this case, we require a subsample of gold standard validation data to estimate the sensitivity and specificity of the fallible classifier. In Chapter 3, we propose a Bayesian approach for the estimation of population prevalence of a biomarker in repeated diagnostic testing studies. In such situations, it is necessary to account for interindividual variability which we achieve through both the inclusion of random effects within logistic regression models and Bayesian hierarchical modeling. Our examples focus on applications for both reliability studies and biostatistical studies. Finally, we develop an approach to attempt to detect conditional dependence parameters between two fallible diagnostic tests for a binary logistic regression covariate in the absence of a gold standard test in Chapter 4. We compare the performance of the proposed procedure to previously published means assessing model fit.