Phil D. Young

A comparison of regularization methods applied to the linear discriminant function with high-dimensional microarray data

Classification of gene expression microarray data is important in the diagnosis of diseases such as cancer, but often the analysis of microarray data presents difficult challenges because the gene expression dimension is typically much larger than the sample size. Consequently, classification methods for microarray data often rely on regularization techniques to stabilize the classifier for improved classification performance. In particular, numerous regularization techniques, such as covariance-matrix regularization, are available, which, in practice, lead to a difficult choice of regularization methods. In this paper, we compare the classification performance of five covariance-matrix regularization methods applied to the linear discriminant function using two simulated high-dimensional data sets and five well-known, high-dimensional microarray data sets. In our simulation study, we found the minimum distance empirical Bayes method reported in Srivastava and Kubokawa [Comparison of discrimination methods for high dimensional data, J. Japan Statist. Soc. 37(1) (2007), pp. 123–134], and the new linear discriminant analysis reported in Thomaz, Kitani, and Gillies [A Maximum Uncertainty LDA-based approach for Limited Sample Size problems – with application to Face Recognition, J. Braz. Comput. Soc. 12(1) (2006), pp. 1–12], to perform consistently well and often outperform three other prominent regularization methods. Finally, we conclude with some recommendations for practitioners.

Bayesian adaptive two-stage design for determining person-time in Phase II clinical trials with Poisson data

ABSTRACT Adaptive clinical trial designs can often improve drug-study efficiency by utilizing data obtained during the course of the trial. We present a novel Bayesian two-stage adaptive design for Phase II clinical trials with Poisson-distributed outcomes that allows for person-observation-time adjustments for early termination due to either futility or efficacy. Our design is motivated by the adaptive trial from [9], which uses binomial data. Although many frequentist and Bayesian two-stage adaptive designs for count data have been proposed in the literature, many designs do not allow for person-time adjustments after the first stage. This restriction limits flexibility in the study design. However, our proposed design allows for such flexibility by basing the second-stage person-time on the first-stage observed-count data. We demonstrate the implementation of our Bayesian predictive adaptive two-stage design using a hypothetical Phase II trial of Immune Globulin (Intravenous).

Estimation-Equivalent and Dispersion-Equivalent Error Covariance Matrices for the General Linear Model

SYNOPTIC ABSTRACT We give a new, very concise derivation of an explicit characterization representation of the general nonnegative-definite error covariance matrix for a Gauss-Markov model, such that the best linear unbiased estimator is identical to the least-squares estimator. Our characterization derivation is very concise, and we use only elementary matrix properties in the proof. We also characterize the general symmetric nonnegative-definite error covariance matrix of a Gauss-Markov model, such that the covariance matrices of the best linear unbiased estimator, the least squares estimator, and the independently and identically-distributed least-squares estimator have identical covariance structures.

Bayesian Assessment of a Binary Measurement System with Baseline Data

SYNOPTIC ABSTRACT Binary measurement systems that classify parts as either pass or fail are widely used. In industrial settings, many previously passed and failed parts are often available. We develop a Bayesian model to incorporate baseline information to determine whether a part originated from the stream of previously passed or failed parts as well as the overall pass rate of the inspection system. Simulation studies demonstrate the viability of our proposed method, and we compare our model to simpler models that do not incorporate all baseline information. We show that in some cases incorporation of baseline data can result in the reduction of posterior standard deviations by a factor of two. Additionally, our Bayesian approach has the advantages of allowing the incorporation of expert opinion and not relying on the assumption of normality.