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 a simulation to analyze how estimates of a parameter of interest change across sample sizes

Bayesian Subset Selection of Binomial Parameters Using Possibly Misclassified Data

Three Bayesian approaches are considered for the selection of binomial proportion parameters when data is subject to misclassification. The cases where the misclassification is non-differential and differential were considered, thus extending previous work which considered only non-differential misclassification. In this article, various selection criteria are applied to a simulated data set and a real data set

A Bayesian approach to correct for unmeasured or semi-unmeasured confounding in survival data using multiple validation data sets

Purpose: The existence of unmeasured confounding can clearly undermine the validity of an observational study. Methods of conducting sensitivity analyses to evaluate the impact of unmeasured confounding are well established. However, application of such methods to survival data (“time-to-event” outcomes) have received little attention in the literature. The purpose of this study is to propose a novel Bayesian method to account for unmeasured confounding for survival data.   Methods: The Bayesian method is proposed under an assumption that the supplementary information on unmeasured confounding in the form of internal validation data, external validation data or expert elicited prior distributions is available. The method for incorporating such information to Cox proportional hazard model is described.  Simulation studies are performed based on the recently published instrumental variable method to assess the impact of unmeasured confounding and to illustrate the improvement of the proposed method over the naïve model which ignores unmeasured confounding.   Results: Simulation studies illustrate the impact of ignoring the unmeasured confounding and the effectiveness of our Bayesian approach. The corrected model had significantly less bias and coverage of 95% intervals much closer to nominal.   Conclusion: The proposed Bayesian method provides a useful and flexible tool in incorporating different types of supplemental information on unmeasured confounding to adjust the treatment estimates when the outcome is survival data.  It out-performed the naïve model in simulation studies based on a real world study. &nbsp

The Effect of Specific Gravity and Growth Rate on Bending Strength of Finger-Jointed Southern Pine

In this study, the effect of specific gravity and rings per inch on the bending strength of 11 mill-run batches of finger-jointed southern pine lumber was examined. The bending test specimens were prepared according to the Glued Lumber Standard for Southern Pine as outlined by the SPIB. For each fingerjointed board, 8 wood properties were calculated. The 8 wood properties were maximum, minimum, average, and differential specific gravity; and maximum, minimum, average, and differential rings per inch. Multiple linear regression analysis was used to examine the effect of these wood properties on the bending strength (MOR) of the lumber. This relationship was examined for test specimens subjected to an accelerated aging cycle and those not subjected to the cycle. Coefficients of determination (r2) ranged from 0.06 to 37. For both specific gravity and rings per inch, the differential specimens had the lowest r2 values, and the average specimens had the highest r2 values. The relationships found in this study are consistent with strength-wood property relationships for finger-jointed and solid wood specimens reported in previous literature

A Faith Practices Scale for the Church

Recent studies demonstrate an overlapping relationship between faith practices of individuals, family functioning, and the corporate faith of congregations This study reports on the psychometric properties of the Christian Faith Practices Scale (CFPS), which was created to empirically measure Dykstrasfaith behaviors or practices Analysis of a krge purposive sample (N=7,403) indicates initial evidence of reliability and validity for the instrument We conclude that the CFPS is a useful tool for empowering faith practices through practical measurement and offer specific recommendations for using the scale with congregations, small groups, and family meeting

A double-sampling approach for maximum likelihood estimation for a Poisson rate parameter with visibility-biased data

We propose a Poisson-based model that uses both infallible data and fallible data subject to misclassification in the form of false negatives that yield visibility bias. We than derive maximum likelihood estimators for the Poisson rate parameter of interest and the misclassification parameter under two different sampling scenarios. We also derive expressions for the information matrices and the asymptotic variances of the maximum likelihood estimators for the rate parameter and the maximum likelihood estimators for the false-negative parameter. Finally, we also study our new models via a simulation experiment and then apply our new estimation procedures to a real data set

A Bayesian Hierarchical Spatial Model to Correct for Misreporting in Count Data: Application to State-Level COVID-19 Data in the United States

The COVID-19 pandemic that began at the end of 2019 has caused hundreds of millions of infections and millions of deaths worldwide. COVID-19 posed a threat to human health and profoundly impacted the global economy and people’s lifestyles. The United States is one of the countries severely affected by the disease. Evidence shows that the spread of COVID-19 was significantly underestimated in the early stages, which prevented governments from adopting effective interventions promptly to curb the spread of the disease. This paper adopts a Bayesian hierarchical model to study the under-reporting of COVID-19 at the state level in the United States as of the end of April 2020. The model examines the effects of different covariates on the under-reporting and accurate incidence rates and considers spatial dependency. In addition to under-reporting (false negatives), we also explore the impact of over-reporting (false positives). Adjusting for misclassification requires adding additional parameters that are not directly identified by the observed data. Informative priors are required. We discuss prior elicitation and include R functions that convert expert information into the appropriate prior distribution

Bayesian sample size determination for cost-effectiveness studies with censored data

<div><p>Cost-effectiveness models are commonly utilized to determine the combined clinical and economic impact of one treatment compared to another. However, most methods for sample size determination of cost-effectiveness studies assume fully observed costs and effectiveness outcomes, which presents challenges for survival-based studies in which censoring exists. We propose a Bayesian method for the design and analysis of cost-effectiveness data in which costs and effectiveness may be censored, and the sample size is approximated for both power and assurance. We explore two parametric models and demonstrate the flexibility of the approach to accommodate a variety of modifications to study assumptions.</p></div

Bayesian Analysis and Design for Joint Modeling of Two Binary Responses With Misclassification

Survey data are often subject to various types of errors such as misclassification. In this article, we consider a model where interest is simultaneously in two correlated response variables and one is potentially subject to misclassification. A motivating example of a recent study of the impact of a sexual education course for adolescents is considered. A simulation-based sample size determination scheme is applied to illustrate the impact of misclassification on power and bias for the parameters of interest