Courses Offered and Class Schedule
BIOS 6221 Introduction to Biostatistics. 3 Credits
Three hours of lecture per week. General introduction to descriptive and inferential statistics: The role of biostatistics in the health sciences, techniques and principles for summarizing data, estimation, hypothesis testing and decision-making. Examples and problems from the health sciences are used. Non-majors only.
BIOS 6222 Biostatistics II. 3 Credits
Three hours of lecture per week. Continuation of BIOS 6221. Additional biostatistics techniques in health sciences: Hypothesis testing via the general linear model, including analysis of variance and linear regression, methods of correlation analysis, and multiple regression techniques. Examples and problems from the health sciences are used. Non-majors only.
BIOS 6223 Introduction to Theory of Probability. 3 Credits
Three hours of lecture per week. Elementary concepts of probability; conditional probability, Bayes’ theorem; random variables and probability distributions, transformations of random variables; moments and moment generating functions; discrete and continuous random variables, common families of distributions; essential inequalities and identities; multivariate distributions, joint, conditional and marginal distributions; covariance and correlation, conditional expectation; basic concepts of random samples; convergence concepts, convergence in probability and in distribution, the law of large numbers, and the central limit theorem. Prerequisite: Calculus I-III and linear algebra.
BIOS 6224 Introduction to Statistical Inference. 3 Credits
Three hours of lecture per week. Principles of data reduction, sufficiency and completeness, minimal sufficient statistics; the likelihood principle; point estimation, method of moments, maximum likelihood estimation; methods of evaluating estimators, unbiased estimation, Fisher information, hypotheses testing, likelihood ratio tests, methods of evaluating tests, most powerful tests; interval estimation, methods of evaluating interval estimators Prerequisite: BIOS 6223.
BIOS 6226 Survival Analysis. 3 Credits
Three hours of lecture per week. This course provides students with statistical methodology for the analysis of time-to-event data and trains students in the appropriate analysis of survival data, by both parametric and nonparametric methods. Emphasis will be placed on methods and models most useful in clinical research with attention to proper interpretation of statistical packages output. Prerequisite: BIOS 6222 or BIOS 6267.
BIOS 6227 Statistical Programming and Numerical Methods+. 3 Credits
Three hours of lecture per week, summer semester. An introductory programming course oriented toward statistical applications using SAS (including IML) and the R programming languages. Topics include data types, assignment statements, operators, sequential control, conditional control, iteration, subprograms, arrays, character manipulation, manipulating and processing SAS output from SAS procedures, Gibbs sampler, and Markoff Chain Monte-Carlo methods. Prerequisite: BIOS 6267 or permission of the instructor.
BIOS 6230* Applied Bayesian Analysis. 3 Credits
Three hours of lecture per week. Introduction to Bayesian approach to statistical inference. Application oriented, but such theory as is necessary for a proper understanding of the Bayesian methodology will be covered. Topics covered include Bayesian Inference – prior determination, point and interval estimation, hypothesis testing, prediction, model assessment and model choice; Bayesian Computation – Markov Chain Monte Carlo (MCMC) methods, Gibbs Sampling and extensions; and Bayesian applications on real data sets from the biological or medical fields. Prerequisite: BIOS 6224, BIOS 6227, BIOS 6267, or permission of the instructor.
BIOS 6231 Introduction to Stochastic Processes. 3 Credits
Three hours of lecture per week. Markov chains; birth-death processes; random walks; renewal theory; Poisson processes; Brownian motion; branching processes; martingales; with applications. Prerequisites: BIOS 6224.
BIOS 6241 Sampling Methods in the Health Sciences. 3 Credits
Three hours of lecture per week. Methods for conducting sample surveys in the health sciences: Biases and non-sampling errors, probability and non-probability samples, simple random sampling, stratification, varying probabilities of selection, multi-stage sampling, systematic sampling, cluster sampling, double sampling, and ratio estimation. Prerequisite: Permission of the instructor.
BIOS 6242 Design and Analysis of Experiments. 3 Credits
Three hours of lecture per week. Principles of experimentation. Completely randomized designs, randomized complete block designs, factorial designs, Latin squares, crossover designs, blocking, response surface designs. Applications are in the health sciences. Prerequisite: BIOS 6221 or BIOS 6266, or permission of the instructor.
BIOS 6243* Nonparametric Methods. 3 Credits.
Three hours of lecture per week. Broad coverage of statistical methods appropriate for data from distributions requiring minimal assumptions. Coverage include rank tests, permutation and randomization tests, bootstrap methods, analysis of categorical data, rank correlation methods, analysis of variance and regression methods for ranked data, and methods of nonparametric survival analysis. Prerequisite: Permission of the instructor.
BIOS 6244 Analysis of Categorical Data in the Health Sciences. 3 Credits
Three hours of lecture per week. Model formulation, parameter estimation, and hypothesis testing for categorical data from different types of experimental and survey research situations: Characterization of interaction in multidimensional contingency tables, stepwise regression procedures for proportions, and exact inference. Prerequisite: BIOS 6222 or BIOS 6267.
BIOS 6250 Multivariate Methods. 3 Credits
Three hours of lecture per week. Review of matrix algebra, multivariate normal distribution, multivariate general linear model, principal components, factor analysis, cluster analysis, discriminant analysis. Applications are in the health sciences. Prerequisites: BIOS 6224, BIOS 6267.
BIOS 6260 Longitudinal Data Analysis. 3 Credits
Three hours of lecture per week. This course will emphasize analysis and interpretation of data obtained from subjects measured repeatedly over time. Coverage will begin with traditional approaches to analysis of longitudinal data such as multivariate repeated measures and the univariate analysis of repeated measures as a split-plot model and will quickly lead into models for mean response such as the analysis of response profiles and parametric curve fitting including linear splines. Models for the covariance matrix will be then be considered. Linear mixed models and generalized estimation equations will be covered in detail. Other topics will be covered as time allows. Examples from the health and biomedical sciences will be presented to motivate the material. Prerequisites: BIOS 6222 or BIOS 6267.
BIOS 6264 Clinical Trials. 3 Credits
Three hours of lecture per week. Introduction to the conduct of clinical trials and clinical trials methodology. Topics covered include selection of primary and secondary research questions and hypotheses, use of surrogate variables, defining study population, generalizability of results, basic study design, randomization process, blinding, sample size estimation, using baseline assessments, recruitment of study participants, data collection and quality control, assessing and reporting adverse events, assessing quality of life, participant adherence, survival analysis techniques and issues, monitoring response variables, data analysis issues, study closeout, and reporting and interpreting results. Prerequisites: BIOS 6222 or BIOS 6267.
BIOS 6266 Principles of Applied Statistics. 3 Credits
Three hours lecture per week. Broad coverage of methods of applied statistics, designed for students who want to take advantage of their good math backgrounds for better understanding. Data description; elementary probability, random variables, distributions; principles of statistical inference; methods for one-, two-, and multi-sample settings, including ANOVA and multiple regression; methods for categorical responses. Use of SAS and other software for analysis, simulations, graphics, and report writing. Some cases will use large national databases, such as NHANES and CPS. Prerequisites: multi-variable calculus and linear algebra.
BIOS 6267 Applied General Linear Models. 3 Credits
Three hours of lecture per week. This is a practical course on the use of general linear models. Topics include a review of relevant matrix algebra; general linear models including multiple regression, analysis of variance, analysis of covariance, multivariate response, and logistic regression models; methods for estimation, hypothesis testing and diagnostics; model specification for designed experiments and for observational studies; applications are in the health sciences. Prerequisites: BIOS 6221 or BIOS 6266.
BIOS 6269 Theory of General Linear Models. 3 Credits
Three hours of lecture per week. This course presents the essentials of statistical inference theory for general linear models. Topics include a review of relevant matrix algebra; distributions of quadratic forms; theoretical aspects of estimation, hypothesis testing and diagnostics. Prerequisite: BIOS 6224, BIOS 6267 or permission of the instructor.
BIOS 6270* Theory of Mixed Models. 3 Credits
Three hours of lecture per week. Rigorous course on the theory of mixed models. Essentials of relevant matrix algebra; distribution of quadratic forms; models with variance-covariance components; one-way, two-way random and mixed models with fixed effects; methods of estimation of variance components; ML, REML, ANOVA; estimation of fixed effects; testing hypotheses about fixed effects; repeated measures design methods; choices of covariance structures; generalized linear mixed models. Prerequisites BIOS 6224, BIOS 6269.
BIOS 6272 Generalized Linear Models. 3 Credits
Three hours of lecture per week. Study of parametric models in the exponential family of distributions including the normal, binomial, Poisson, and gamma. Parameter estimation with Iterative re-weighted least squares and quasi-likelihood methods. Modeling of correlated data or data with non-constant variance via mixed models (e.g., GLIMMIX). In-depth coverage of generalized estimating equations (GEE1 and GEE2) and quadratic estimating equations (QEE). Applications with be presented from a variety of settings such as the basic sciences, medicine, dental, and public health. Prerequisite: BIOS 6224, BIOS 6267 or permission of the instructor.
BIOS 6275* Design and Analysis of Expression Studies. 3 Credits
Three hours of lecture per week. Design and analysis of differential gene expression studies using microarrays. Design and analysis of differential protein expression studies. Analysis of RT-PCR gene expression data. Design and analysis of tissue array studies. Current statistical issues. Applications in biomedical research, e.g. expression and survival times of patients by tumor grade. Data mining approaches for expression data: clustering and classification algorithms. Prerequisites: EPID 6219, BIOS 6267.
BIOS 6283 Advanced Theory of Inference. 3 Credits
Three hours of lecture per week. A mathematical study of the classical theory of statistical inference. Moment generating functions and characteristic functions, distributions of order statistics, exponential family of distributions, models of convergence, the Cramer-Rao inequality, efficiency, best unbiased estimation, completeness, minimal sufficiency, maximum likelihood estimators; monotone likelihood ratio, unbiased and invariant hypothesis tests, generalized likelihood ratio tests, Bayes' and minimax procedures. Prerequisite: BIOS 6224.
BIOS 6284 Advanced Theory of Inference. 3 Credits
Three hours of lecture per week. A mathematically rigorous survey of selected topics in the theory of statistical inference such as: Bayesian inference, decision theory, information theory, large sample theory, multivariate distributions, nonparametric inference, sequential analysis, stochastic processes, time series, components of variance. Prerequisite: BIOS 6283.
BIOS 6296 Statistical Consulting in the Health Sciences. 2 Credits
A practical course designed to expose students to real-life consulting situations and the statistical problems that arise in the health sciences. The student will work on a consulting project under the supervision of a faculty member and will present a progress report each week. Prerequisites: BIOS 6267.
BIOS 6298 Seminar in Biostatistics. 1 Credit
Reports on research progress in current literature. Students attend colloquium and give an oral presentation in their second year.
BIOS 6500 Special Topics in Biostatistics. 1-4 Credits
Hours and credits to be arranged depending on the particular topic. This course is designed, depending upon the students’ interest and staff availability, to cover advanced topics such as stochastic processes, time series analysis, analysis of survival distributions, experimental design, multivariate analysis, etc.
BIOS 6600* Capstone. 3-4 Credits
Registration by permission of the school. Amount of credit must be stated at time of registration.
BIOS 6900 Thesis Research. 1-6 Credits
Registration by permission of the school. Amount of credit must be stated at time of registration.
* Proposed new course to be added to curriculum for Fall 2007.
+ Name to be changed from Introduction to Computer Programming
