Theses/Dissertations - Statistical Sciences
Permanent URI for this collectionhttps://hdl.handle.net/2104/4798
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Browsing Theses/Dissertations - Statistical Sciences by Subject "Bayesian sample size determination."
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Item A bivariate regression model with correlated mixed responses.(2013-09-16) Bray, Ross A.; Seaman, John Weldon, 1956-; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.In the dissertation we consider a bivariate model for associated binary and continuous responses such as those in a clinical trial where both safety and efficacy are observed. We designate a marginal and conditional model that allows for the association between the responses by including the marginal response as an additional predictor of the conditional response. We use a Bayesian approach to model the bivariate regression model using a hierarchical prior structure. Simulation studies indicate that the model provides good point and interval estimates of regression parameters across a variety of parameter configurations, with smaller binary event probabilities offering particular challenges. For example, as the probability of an adverse event decreases, we find that the marginal posterior variances increase for the binary safety response regression coefficients, but not for the conditional efficacy response coefficients. Potential problems with induced priors are briefly considered. We implement an asymptotic higher order approximation in order to obtain parameter estimates and confidence intervals via a simulation study. In comparison, the frequentist intervals are slightly more narrow than the Bayesian intervals (using vague priors), but the latter have far superior coverage. Finally, we implement a Bayesian sample size determination method while controlling an operating characteristic of the model, the family-wise error rate. We find that there is a savings in power afforded by use of the multiplicity adjustment when simultaneously testing multiple hypotheses. Simulation results indicate that multiplicity adjustments improve the power of the model when compared to the overly conservative Bonferroni adjustment. We also see an improvement in power through the effective use of prior information.Item Sample size determination for two sample binomial and Poisson data models based on Bayesian decision theory.(2014-01-28) Sides, Ryan A.; Stamey, James D.; Kahle, David J.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.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.