Theses/Dissertations - Statistical Sciences
Permanent URI for this collectionhttps://hdl.handle.net/2104/4798
Browse
Browsing Theses/Dissertations - Statistical Sciences by Subject "Bayesian statistics."
Now showing 1 - 3 of 3
- Results Per Page
- Sort Options
Item Bayesian topics in biostatistics : treatment selection, sample size, power, and misclassification.(2011-12-19) Doty, Tave Parker.; Tubbs, Jack Dale.; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Bayesian methodology is implemented to investigate three problems in biostatistics. The first problem considers using biomarkers to select optimal treatments for individual patients. A Bayesian adaptation of the selection impact (SI) curve developed by Pepe and Song (2004) is investigated. The second problem considers a Bayesian approach for determining specific sample sizes to achieve a desired range of power for fixed-dose combination drug trials. Sidik and Jonkman (2003) developed a sample size formula using the intersection-union test for testing the efficacy of combination drugs. Our results are compared to their frequentist approach. The third problem considers response misclassification in fixed-dose combination drug trials under two scenarios: when the sensitivity and specificity are known, and when the sensitivity and specificity are unknown but have specified informative prior structures.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 Interval-censored negative binomial models : a Bayesian approach.(2012-11-29) Doherty, Stephanie Michelle.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Count data are quite common in many research areas. Interval-censored counts, in which an interval representing a range of counts is observed rather than the precise count, may arise in many situations, including survey data. In this dissertation we develop a model for accommodating interval-censored count data through the interval-censored negative binomial model, with an expansion to a regression model in which the interval count responses are regressed on covariate values. We employ both frequentist and Bayesian methods to arrive at point and interval estimates for the negative binomial parameters. We nd that many factors, including the interval-censored widths and the tendency of the precise counts toward either endpoint of the intervals, a ect parameter estimates based on interval-censored data as compared to estimates using only precise data. We perform simulation studies in the non-regression and regression contexts, which compare the interval-censored model to alternatives for accommodating interval-censored data. These methods are precise-count analyses based on the lower endpoints, upper endpoints, or means of the observed intervals. For the scenarios in our simulation experiments, we nd that the interval-censored model outperforms the lower endpoint and upper endpoint methods, and performs at least as well as, or better than, the mean method. We conclude with an extended example, in which we compare the interval-censored method to the lower and upper endpoint methods for health-related quality of life survey data that are interval-censored. We nd that the interval-censored method allows us to calculate parameter estimates and conduct posterior inferences, without the need to discard any information provided in the study.