Theses/Dissertations - Statistical Scienceshttp://hdl.handle.net/2104/47982015-10-05T04:07:42Z2015-10-05T04:07:42ZLogistic regression models for short sequences of correlated binary variables possessing first-order Markov dependence.http://hdl.handle.net/2104/94962015-09-05T08:03:48Z2015-07-23T00:00:00ZLogistic 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/2104/94772015-09-05T08:02:59Z2015-06-30T00:00:00ZTopics 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).
2015-06-30T00:00:00ZNormal approximation for Bayesian models with non-sampling bias.Yuan, Jiang, 1984-http://hdl.handle.net/2104/89262015-02-18T09:05:50Z2014-01-28T00:00:00ZNormal approximation for Bayesian models with non-sampling bias.
Yuan, Jiang, 1984-
Bayesian sample size determination can be computationally intensive for mod-
els where Markov chain Monte Carlo (MCMC) methods are commonly used for in-
ference. It is also common in a large database where the unmeasured confounding
presents. We present a normal theory approximation as an alternative to the time
consuming MCMC simulations in sample size determination for a binary regression
with unmeasured confounding. Cheng et al. (2009) develop a Bayesian approach to
average power calculations in binary regression models. They then apply the model
to the common medical scenario where a patient's disease status is not known. In
this dissertation, we generate simulations based on their Bayesian model with both
binary and normal outcomes. We also use normal theory approximation to speed
up such sample size determination and compare power and computational time for
both.
2014-01-28T00:00:00ZSample size determination for two sample binomial and Poisson data models based on Bayesian decision theory.Sides, Ryan A.http://hdl.handle.net/2104/89222015-02-18T09:05:45Z2014-01-28T00:00:00ZSample size determination for two sample binomial and Poisson data models based on Bayesian decision theory.
Sides, Ryan A.
Sample size determination continues to be an important research area in statistical analysis due to the cost and time constraints that often exist in areas such as pharmaceuticals and public health. We begin by outlining the work of a previous article that attempted to find a minimum necessary sample size in order to reach a desired expected power for binomial data under the Bayesian paradigm. We make improvements to their efforts that allow us to specify not only a desired expected Bayesian power, but also a more generic loss function and a desired expected Bayesian significance level, the latter having never been considered previously. We then extend these methodologies to handle Poisson data and discuss challenges in the methodology. We cover a detailed example in both cases and display various results of interest.
We conclude by covering a mixed treatment comparisons meta-analysis problem when analyzing Poisson data. Traditional methods do not allow for the presence of underreporting. Here, we illustrate how a constant underreporting rate for all treatments has no effect on relative risk comparisons; however, when this rate changes per treatment, not accounting for it can lead to serious errors. Our method allows this to be taken into account so that correct analyses can be made.
2014-01-28T00:00:00Z