Theses/Dissertations - Statistical Scienceshttp://hdl.handle.net/2104/47982018-06-18T05:28:59Z2018-06-18T05:28:59ZBayesian propensity score analysis for clustered observational studies.http://hdl.handle.net/2104/103812018-06-06T16:22:09Z2018-04-12T00:00:00ZBayesian propensity score analysis for clustered observational studies.
There is increasing demand to investigate questions in observational study. The propensity score is a popular confounding adjustment technique to ensure valid causal inference for observational study. Observational data often has multilevel structure that would lead to one or more levels of confounding. Multilevel models are employed in Bayesian propensity score analysis to account for cluster and individual level confounding in the estimation of both propensity score an in turn exposure effect. In an extensive simulation study, several propensity score nalaysis approches with varing complexity of multilevel modelling structures are examined in terms of absolute mean bias and mean squared error. The Bayesian propensity score analysis for multilevel data is further developed to accomodate misclassified binary responses. Errors in response would distort the exposure to response relationship. The true exposure-response surface can be recovered through two classification probabilities: sensitivity and specificity that links observed misclassified response and unobserved true response. Incorpating misclassification greatly reduces bias in exposure effect estimation and yields coverage rate of 95% creditable set close to nomial level. The strong ignorability is the fundamental assumption for propensity score. Few literature discuss this important but untestable assumption. Without the confidence that there are no unmeasured confounders, we assmue the existence of unmeasured confounding and assess the sensitivity of exposure effect estimation to unmeasured confounding through two sensitivity parameters which characterize the associations of the unmeasured confounder with the exposure status and response variable. The influence of unmeasured confounding can be examined by possible change in exposure effect estimation with hypothetical values of sensitivity parameters.
2018-04-12T00:00:00ZBeta regression for modeling a covariate-adjusted ROC.http://hdl.handle.net/2104/103772018-06-06T16:08:06Z2018-03-12T00:00:00ZBeta regression for modeling a covariate-adjusted ROC.
The receiver operating characteristic (ROC) curve is a well-accepted measure of accuracy for diagnostic tests. In many applications, test performance is affected by covariates. As a result, several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. We present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. These methods utilize GLMs for binary data with an expected value equal to the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Given that the ROC is the cumulative distribution of the placement values, we propose a new method that directly models the placement values through beta regression. We compare the beta regression method to the existing parametric and semiparametric approaches with simulation and a clinical study. Bayesian extensions for the parametric and the beta methods are developed and the performance of these extensions is evaluated through simulation study. We apply the proposed beta regression approach and its Bayesian extension to a simple network meta-analysis problem using a Bayesian indicator model selection method.
2018-03-12T00:00:00ZApplications of Bayesian quantile regression and sample size determination.http://hdl.handle.net/2104/103722018-06-06T16:10:17Z2018-03-21T00:00:00ZApplications of Bayesian quantile regression and sample size determination.
Bayesian statistical methods reverse the philosophy of traditional statistical practice by treating parameters as random, rather than fixed. In so doing, Bayesian methods are able to incorporate uncertainty about parameter values and offer new approaches to problems traditionally viewed through only one lens. One technique that was introduced forty years ago but has only been considered from the Bayesian perspective within the last twenty years is quantile regression (QR). Similarly, sample size determination is a staple of both introductory coursework in statistics and upper-level clinical trial design, but it has historically been presented with little to no mention of its construction under the Bayesian paradigm. With Bayesian research now rapidly building in both of these arenas, we offer two distinct applications of Bayesian QR to count data and present a Bayesian sample size determination scheme for a cost-effectiveness model.
2018-03-21T00:00:00ZBayesian inference for bivariate Poisson data with zero-inflation.http://hdl.handle.net/2104/101252018-05-22T15:28:29Z2017-07-27T00:00:00ZBayesian 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.
2017-07-27T00:00:00Z