Department of Statistical Sciences
https://hdl.handle.net/2104/4761
2020-07-04T07:17:25ZBayesian adjustment for misclassification bias and prior elicitation for dependent parameters.
https://hdl.handle.net/2104/10809
Bayesian adjustment for misclassification bias and prior elicitation for dependent parameters.
This research is motivated by problems in biopharmaceutical research. Prior elicitation is defined as formulating an expert's beliefs about one or more uncertain quantities into a joint probability distribution, and is often used in Bayesian statistics for specifying prior distributions for parameters in the data model. However, there is limited research on eliciting information about dependent random variables, which is often necessary in practice. We develop methods for constructing a prior distribution for the correlation coefficient using expert elicitation. Electronic health records are often used to assess potential adverse drug reaction risk, which may be misclassified for many reasons. Unbiased estimation with the presence of outcome misclassification requires additional information. Using internally validated data, we develop Bayesian models for analyzing misclassified data with a validation substudy and compare its performance to the existing frequentist approaches.
2019-11-25T00:00:00ZBayesian inference for vaccine efficacy and prediction of survival probability in prime-boost vaccination regimes.
https://hdl.handle.net/2104/10808
Bayesian inference for vaccine efficacy and prediction of survival probability in prime-boost vaccination regimes.
This dissertation consists of two major topics on applying Bayesian statistical methods in vaccine development. Chapter two concerns the estimation of vaccine efficacy from validation samples with selection bias. Since there exists a selection bias in the validated group, traditional assumptions about the non-validated group being missing at random do not hold. A selection bias parameter is introduced to handle this problem. Extending the methods of et al. scharfstein (2006), we construct and validate a data generating mechanism that simulates real-world data and allows evaluation of their model. We implement the Bayesian model in JAGS and assess its performance via simulation. Chapter three introduces a two-level Bayesian model which can be used in predicting survival probability from administrated dose concentrations. This research is motivated by the need to use limited information to infer the probability of survival for the next Ebola outbreak under a heterologous prime-boost vaccine regimen. The first level models the relationship between dose and induced antibody count. We use a two-stage response surface to model this relationship. The second level models the association between the antibody count and the probability of survival using a logistic regression. We combine these models to predict survival probability from administrated dosage. We illustrate application of the model with three examples in this chapter and evaluate its performance in Chapter four.
2019-11-08T00:00:00ZComputational Bayesian methods applied to complex problems in bio and astro statistics.
https://hdl.handle.net/2104/10803
Computational Bayesian methods applied to complex problems in bio and astro statistics.
In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in simulation to analyze how estimates of a parameter of interest change across sample sizes.
2019-09-05T00:00:00ZTopic on the statistical analysis of high-dimensional data.
https://hdl.handle.net/2104/10685
Topic on the statistical analysis of high-dimensional data.
High-dimensional genomic data can provide deep insight into biological processes. However, conventional statistical methods typically cannot be applied directly to genomic data sets because the high dimensionality of markers commonly exceeds sample size, rendering the sample covariance matrix to be singular. Here, we examine three scenarios involving high-dimensional genomic data: reordering of principle components of multi-class data based on alternative criteria, comparing tests for two population means on high-dimensional data, and correcting for systematic batch effects in microarray data. All three investigations overcome issues of dimensionality and use principal components for dimension-reduction, visualization, or statistical analysis. First we use alternatively ordered principal components to produce low-dimensional models for visualization; second, we compare five high-dimensional tests of two-means and describe a principal-component alternative to Hotelling's T2 test; and finally, we utilize principal component reduction of microarray data to visualize existing batch effects between cohorts. Overall, we explore solutions to the analysis of high-dimensional, genomic data through the use of principal components analysis or other adaptations to reach the desired analytic objectives.
2019-04-15T00:00:00Z