Search

This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a wrong parametric assumption. In this regard, we consider a robust experimental design which does not require any parametric assumption.

A 2009 report published by the National Research Council addressed the need for improvements in the field of forensic science. In the report emphasis was placed on the need for more rigorous scientific analysis within many forensic science disciplines and for established limitations and determination of error rates from statistical analysis. This research focused on multivariate statistical techniques for the analysis of spectral data obtained for multiple forensic applications which include samples from: automobile float glasses and paints, bones, metal transfers, ignitable liquids and fire debris, and organic compounds including explosives. The statistical techniques were used for two types of data analysis: classification and discrimination. Statistical methods including linear discriminant analysis and a novel soft classification method were used to provide classification of forensic samples based on a compiled library. The novel soft classification method combined three statistical steps: Principal Component Analysis (PCA), Target Factor Analysis (TFA), and Bayesian Decision Theory (BDT) to provide classification based on posterior probabilities of class membership. The posterior probabilities provide a statistical probability of classification which can aid a forensic analyst in reaching a conclusion. The second analytical approach applied nonparametric methods to provide the means for discrimination between samples. Nonparametric methods are performed as hypothesis test and do not assume normal distribution of the analytical figures of merit. The nonparametric iv permutation test was applied to forensic applications to determine the similarity between two samples and provide discrimination rates. Both the classification method and discrimination method were applied to data acquired from multiple instrumental methods. The instrumental methods included: Laser Induced-Breakdown Spectroscopy (LIBS), Fourier Transform Infrared Spectroscopy (FTIR), Raman spectroscopy, and Gas Chromatography-Mass Spectrometry (GC-MS). Some of these instrumental methods are currently applied to forensic applications, such as GC-MS for the analysis of ignitable liquid and fire debris samples; while others provide new instrumental methods to areas within forensic science which currently lack instrumental analysis techniques, such as LIBS for the analysis of metal transfers. The combination of the instrumental techniques and multivariate statistical techniques is investigated in new approaches to forensic applications in this research to assist in improving the field of forensic science.

Two-stage designs have been widely used in phase II clinical trials. Such designs are desirable because they allow a decision to be made on whether a treatment is effective or not after the accumulation of the data at the end of each stage. Optimal fixed two-stage designs, where the sample size at each stage is fixed in advance, were proposed by Simon when the primary outcome is a binary response. We propose an adaptive two-stage design which allows the sample size at the second stage to depend on the results at the first stage. Using a Bayesian decision theoretic construct, we derive optimal adaptive two-stage designs. The optimality criterion is to minimize the expected sample size under the null hypothesis value. We further explore optimal adaptive designs that minimize the expected sample size at the alternative hypothesis, at a probability mid-point between the null and alternative hypotheses and a weighted combination of the null, alternative and mid-point value. We also construct an envelope function that gives the lowest expected sample size for any possible value of the response probability. The different designs are compared to Simon's design as well as the envelope function. The designs that minimize the expected sample size at the mid-point between the null and alternative hypotheses and the design that minimizes a weighted average of the response probabilities are closer to the envelope function. Results show that these designs perform better across a range of the response probability values, and generally surpass Simon's design.