Course Descriptions

Issues involving whole-genome analysis, model selections for genetic architecture and advanced statistical pattern recognition tools. Topics: Bayesian modeling for genomic data; MCMC and non parametric linkage analysis in pedigree analysis, genetic mapping of complex traits by the EM algorithm; HMM for DNA sequence analysis; Time course models and neural networks for microarray data and so on.

3 Credits, Spring Semester

This graduate course is designed to extend the principles and techniques for designing and analyzing data from clinical trials presented in an introductory course on the subject, with a focus on selected topics in modern randomized designs. The latest methodology will be comprehensively presented and will be illustrated using examples from diverse therapeutic areas. Topics will include trials based on between-subject correlated outcomes, advanced issues in non-inferiority designs, and a wide variety of adaptive design methods. Much of that to be discussed will be in the context of applications in support of regulatory authority (ex., FDA) approval.

Presents useful methods for analyzing categorical data that are not covered in STA 517. Topics: Exact conditional inference, conditional logistic regression, models for matched pairs, repeated measures, and multinomial regression based on general response functions, latent class models analysis, and mixed models for categorical data.

This course provides students with an advanced theoretical foundation for statistical inference. Topics: Decision theory, methods of point estimation and properties, interval estimation, tests of hypotheses, and Bayesian inference.

STA 622 is a core course in the biostatistics PhD program. It is designed to provide students with tools to derive the asymptotic properties of estimators and, from them, large sample tests of hypotheses. Modes of convergence are defined and lemmas, theorems and corollaries are presented that are useful in proving the consistency of many estimators and in deriving their asymptotic distribution. Key theorems and results include Chebyshev’s Inequality and its corollaries, Central Limit Theorems, Taylor’s series expansions of functions of sequences of random variables and random vectors, Slutsky’s Theorems, and the Helly-Bray Theorem. Large sample distributions are derived and consistency proven for sample moments, Instrumental Variable estimators, nonlinear least squares estimators, the estimators of quantiles, and the empirical distribution function. The empirical distribution function is discussed as the basis for Bootstrap estimation and inference.

This is a core course in the biostatistics PhD program. It is designed to provide students with a detailed knowledge and rigorous understanding of statistical theory that underlies linear models analysis. A unified framework is presented for understanding statistical methods that students learn in the applied core courses of the Biostatistics master’s program; including simple and multiple linear regression, analysis of variance, analysis of covariance, and repeated measures and longitudinal data analysis. The purpose of the course is to provide students with a deep and unified understanding of these methods, and their proper uses, by demonstrating that they fit into the general linear model framework and by presenting theoretical underpinnings that are common to all. Students will learn that a wide range of statistical problems can be formulated in a general way through the specification of linear models, and that these problems can be solved by applying the theories of parameter estimation and general linear hypothesis testing learned in this course. The practical value of this theoretical knowledge is communicated through discussions of applied problems. As a preliminary to learning the theory of linear models students are taught prerequisite topics in basic and advanced matrix algebra and multivariate normal distribution theory.

This course covers advanced methods of modeling that are highly useful in practice but are not covered in earlier courses. Topics: Fitting of generalized linear models, diagnostics, asymptotic theory, over-dispersion, estimating equations, mixed models, generalized additive models, smoothing, and other topics chosen by the instructor.

The Bayesian approach to statistical design and analysis can be viewed as a philosophical approach or as a procedure-generator. The use of Bayesian design and analysis is burgeoning. In this introduction to Bayesian methods, we consider basic examples of Bayesian thinking and formalism on which more complicated and comprehensive approaches are built. These include adjusting estimates using related information, the use of Bayes Factors in testing of hypotheses, the relationship of the prior and posterior distributions, and the key steps in a Bayesian analysis. We consider the Bayesian approach that requires a data likelihood (the sampling distribution) and a prior distribution. From these, the posterior distribution can be computed and used to inform statistical design and analysis. Applications of this technique are presented.

Theoretical presentation of multivariate methods. Topics: Canonical correlation, principal components, distribution of the roots of a determinantal equation, classification and discrimination methods, and Bayesian approach to multivariate analysis.

3 Credits, Spring Semester

Prerequisite: This course is designed for PhD students who have passed both parts of the qualifying exams.

Evidence-generation methods from observational data will be studied. Topics include: concept of evidence, aspects of design and analysis of observational data, engaging the issue of bias—topics in quantitative bias analysis, uncertainty in clinical medicine, generalizing randomized clinical trial results to broader populations, detecting treatment effect heterogeneity and subgroup identification.