Browsing by Subject "Bayesian."
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Item Bayesian methods to estimate the accuracy of diagnostic tests in meta-analysis models.(2014-09-05) Knorr, Jack S.; Seaman, John Weldon, 1956-; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.With the growing number of studies looking at the performance of diagnostic tests, combining the studies into a meta-analysis becomes an important and increasingly viable area of statistics, especially within the medical field. We begin by developing a hierarchical Bayesian prior structure to estimate prevalences and misclassi cation rates for a single diagnostic test. We provide the results from a simulation study which shows that this model has desirable operating characteristics. We then adapt the model to analyze a scenario in which the collected studies come from two populations, one of which having a known higher prevalence of the trait of interest. Next, we adapt the model from a previous article which constructs an estimate to the summary receiver operating characteristics curve for a diagnostic test. We develop a procedure to elicit prior distributions from an expert and to provide feedback once the priors are obtained. The model is demonstrated in detail and results are reported. We conclude by finding the necessary sample size to compare two diagnostic tests while using a meta-analysis to help power the study. Here we consider a brand new diagnostic test being compared to two established tests in a network meta-analysis. We present a model that provides a sample size needed to compare sensitivities and specificities in a reasonable computing time.Item Bayesian sample-size determination and adaptive design for clinical trials with Poisson outcomes.(Elsevier., 2010) Hand, Austin L.; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Because of the high cost and time constraints for clinical trials, researchers often need to determine the smallest sample size that provides accurate inferences for a parameter of interest or need to adaptive design elements during the course of the trial based on information that is initially unknown. Although most experimenters have employed frequentist methods, the Bayesian paradigm offers a wide variety of methodologies and are becoming increasingly more popular in clinical trials because of their flexibility and their ease of interpretation. Recently, Bayesian approaches have been used to determine the sample size of a single Poisson rate parameter in a clinical trial setting. We extend these results to the comparison of two Poisson rates and develop methods for sample-size determination for hypothesis testing in a Bayesian context. Also, we propose a Bayesian predictive adaptive two-stage design for Poisson data that allows for sample-size adjustments by basing the second-stage sample size on the first-stage results. Lastly, we present a new Bayesian meta-analytic non-inferiority method for binomial data that allows researchers a more direct interpretation of their results. Our method uses MCMC methods to approximate the posterior distribution of the new treatment compared to a placebo rather than indirectly inferring a conclusion from the comparison of the new treatment to an active control.