Theses/Dissertations - Statistical Scienceshttp://hdl.handle.net/2104/47982018-02-20T07:57:14Z2018-02-20T07:57:14ZBayesian inference for bivariate Poisson data with zero-inflation.http://hdl.handle.net/2104/101252017-09-29T08:00:55Z2017-07-27T00:00:00ZBayesian inference for bivariate Poisson data with zero-inflation.
Multivariate count data with zero-inflation is common throughout pure and applied science. Such count data often includes excess zeros. Zero-inflated Poisson regression models have been used in several applications to model bivariate count data with excess zeros. In this dissertation, we explore a Bayesian approach to bivariate Poisson models where either one or both counts is zero-inflated, with a primary focus on informative prior structures for these models. Bayesian treatments of zero-inflated Poisson models have focused on diffuse prior structures for model parameters. Nevertheless, we demonstrate that such an approach can be problematic with respect to convergence. We offer an informative prior approach, and propose methods of prior elicitation from a subject-matter expert. This includes exploration of methods for informative prior construction for an association parameter, and a multivariate distribution. We demonstrate our proposed methods within the context of a clinical example.
2017-07-27T00:00:00ZGraphical methods in prior elicitation.http://hdl.handle.net/2104/101112017-09-29T08:00:20Z2017-07-16T00:00:00ZGraphical methods in prior elicitation.
Prior elicitation is the process of quantifying an expert's belief in the form of a probability distribution on a parameter(s) to be used in a Bayesian data analysis. Existing methods require experts to quantify their belief by specifying multiple distribution summaries, which are then converted into the parameters of a given prior family. The resulting priors, however, may not accurately represent the expert's opinion, which in turn can undermine the accuracy of an analysis. In this dissertation we propose two interactive graphical strategies for prior elicitation, along with web-based Shiny implementations for each, that do not rely on an expert's ability to reliably quantify thier beliefs. Instead, the expert moves through a series of tests where they are tasked with selecting hypothetical future datasets they believe to be most likely from a collection of candidate datasets that are presented in graphical form. The algorithms then convert these selections into a prior distribution on the parameter(s) of interest. After discussing each elicitation method, we propose a variation on the Metropolis-Hastings algorithm that provides support for the underlying stochastic scheme in the second of the two elicitation strategies. We apply the methods to data models that are commonly employed in practice, such as Bernoulli, Poisson, and Normal, though the methods can be more generally applied to other univariate data models.
2017-07-16T00:00:00ZBinomial and Poisson regression with misclassified outcomes and binary covariates : a Bayesian approach.http://hdl.handle.net/2104/101102017-09-29T08:00:15Z2017-07-20T00:00:00ZBinomial and Poisson regression with misclassified outcomes and binary covariates : a Bayesian approach.
Misclassification of an outcome and/or covariate is present in many regression applications due to the inability to have a "gold standard''. Therefore, fallible measurement methods are used when infallible tests are unavailable or too expensive. Ignoring misclassification results in biased regression estimates that can ultimately lead to an incorrect conclusion. In this dissertation we present a Bayesian approach to sample size determination for multilevel logistic regression models with misclassified outcomes to correct for the bias in the regression coefficients in order to obtain a more accurate sample size estimate. We explore a situation in which we only have one fallible test and also a situation in which we have two independent fallible tests. Further, we examine the influence of prior information on the posterior estimates of the coefficients for both of these situations. Secondly, we consider a multilevel generalized linear regression model for a Poisson response with a misclassified binary covariate. We again consider the situations in which one fallible test and two independent fallible tests are available to model the misclassified binary covariate. We conclude this section with a case study examining an India National health survey inspecting if being raised in a household with spousal abuse significantly impacts the number of children the child exposed has in their lifetime. Finally, the new FDA guidelines are requiring pharmaceutical companies to periodically monitor adverse events that are deemed ``anticipated'' throughout the life of a clinical trial. The event is only reported to the FDA before conclusion of the trial if it is determined that the rate of occurrence of the event is considerably higher than expected. We construct a two step Bayesian procedure to model the anticipated adverse events during a clinical trial that utilizes prior information to make a more informed decision. In the first step, for a blinded trial, the information remains blinded and is only unblinded (second step) when the overall rate of occurrence of the event is higher than a historical rate. In contrast to widely used methods, our proposed method controls for the Type I error rate and power.
2017-07-20T00:00:00ZBayesian models for unmeasured confounder in the analysis of time-to-event data.http://hdl.handle.net/2104/96482016-09-01T16:32:27Z2016-03-23T00:00:00ZBayesian models for unmeasured confounder in the analysis of time-to-event data.
Observational studies that omit confounders are subject to bias. In this dissertation we consider the specific case of time-to-event data. We also provide both the Bayesian parametric and the semi-parametric “twin regression” approaches with distributional assumptions of an unmeasured confounding variable, and then we compare them with the naive model. This assumes we ignore the effect of the unmeasured confounder. To explore the ability of bias adjustment from different sources of information, we offer a Bayesian parametric regression with a normal unmeasured confounder. We also develop a Bayesian semi-parametric proportional hazards model accounting for unmeasured confoundings with binary and normal distributions. We can see that the approaches adequately decrease the bias, even with a small validation size. Furthermore, we offer a novel Bayesian bias adjustment model when only summary statistics are available in the external validation data. Finally, we discuss and obtain several sets of solutions for different sources of validation data, censoring rates and sample sizes through simulation studies.
2016-03-23T00:00:00Z