Theses/Dissertations - Statistical Scienceshttp://hdl.handle.net/2104/47982017-03-29T03:25:11Z2017-03-29T03:25:11ZBayesian 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.
2016-03-23T00:00:00ZBayesian methods to estimate the accuracy of a binary measurement system.http://hdl.handle.net/2104/96452016-09-01T18:26:09Z2016-04-19T00:00:00ZBayesian methods to estimate the accuracy of a binary measurement system.
Binary Measurement Systems (BMS) are frequently used in such applications as quality control. They are important enough that their operating characteristics, the repeatability and reproducibility are important because of the clues that provide engineers in improving the BMS. We have developed a Bayesian single inspector model that incorporates baseline information. Simulation studies show that this can cut credible set width of the misclassification parameters in half. We have also developed Bayesian fixed effects and random effects models for BMS's with multiple inspectors. Simulation studies that demonstrated acceptable performance characteristics. Several applications are also worked out included sample size determination for the fixed effects model, and superior subset selection with the random effects model.
2016-04-19T00:00:00ZLogistic regression models for short sequences of correlated binary variables possessing first-order Markov dependence.http://hdl.handle.net/2104/94962016-09-09T15:05:02Z2015-07-23T00:00:00ZLogistic regression models for short sequences of correlated binary variables possessing first-order Markov dependence.
In this dissertation we consider a first-order Markov dependence model for a short sequence of correlated Bernoulli random variables. Specifically, we offer logistic regression models with first-order Markov dependency, using preceding responses as covariates. We develop maximum likelihood and Bayesian methods for inference using these models, and compare them in simulation studies. We develop methods for obtaining informative priors for the Bayesian models, including a modified conditional means prior approach, which we refer to as the Markov dependent priors approach. Due to the implicit dependence of transition probabilities on the value of the marginal probability, elicitation of priors for transition probabilities from experts is problematic. With our approach, however, we can induce priors on regression coefficients from prior distributions on the marginal probability and the transition probabilities. We also give details for constructing informative priors when historical data is available, using power priors. Finally, we considered sample size determination for first-order Markov dependence probabilities using the Bayesian two-priors method.
2015-07-23T00:00:00ZTopics in Bayesian models with ordered parameters : response misclassification, covariate misclassification, and sample size determination.http://hdl.handle.net/2104/94772016-09-07T18:16:48Z2015-06-30T00:00:00ZTopics in Bayesian models with ordered parameters : response misclassification, covariate misclassification, and sample size determination.
Researchers often analyze data assuming models with constrained parameters. Order constrained parameters are of particular interest. In this dissertation, we examine three Bayesian models which incorporate ordered parameters. We investigate ordered differential response misclassification in a logistic regression model and provide an adjustment for it using a conditional prior structure. We examine a parametric Bayesian Weibull proportional hazards model with ordered covariate misclassification and provide an adjustment for it. Finally, we consider informative hypotheses (Hoijtink, 2012) and perform sample size determination for this problem using the two priors approach of Brutti et al. (2008).
2015-06-30T00:00:00Z