Department of Biostatistics (BIOS)

MICHAEL R. KOSOROK, *Chair*

Jianwen Cai, *Vice Chair*

Amy Herring, *Associate Chair*

*Professors*

Michael R. Kosorok (88)

Jianwen Cai (93) Survival Analysis and Regression Models, Clinical Trials, Analysis of Correlated Responses

Jason P. Fine (54)

Joseph G. Ibrahim (11) Bayesian Inference, Missing Data Problems, Bayesian Survival Analysis, Generalized Linear Models, Genomics

Amy H. Herring (25) Survival Analysis, Missing Data Methods, Environmental Statistics

Alan F. Karr, Inference for Stochastic Processes, Image Analysis (Joint with Statistics and Operations Research)

Gary G. Koch (14) Categorical Data Analysis, Nonparametric Methods

Danyu Lin (31) Survival Analysis, Semiparametric Statistical Methods, Clinical Trials

Yufeng Liu (joint with Statistics and Operations Research)

James Stephen Marron, High Dimension Low Sample Size (HDLSS) Data and/or Data, Exotic Data Types Such as Manifold and Tree-Structural Data (joint with Statistics and Operations Research)

Andrew Nobel, Data Mining, Statistical Data of Genomic Data, Machine Learning (joint with Statistics and Operations Research)

Pranab K. Sen (10) Statistical Inference, Clinical Trials, Multivariate Analysis (Joint with Statistics)

Richard Smith, Spatial Statistics, Time Series Analysis, Extreme Value Theory, Bayesian Statistics (joint with Statistics and Operations Research)

Chirayath M. Suchindran (29) Statistical Demography

Kinh N. Truong (90) Time Series Analysis, Nonparametric Regression, Bootstrap Methods, Hazard Regression, Splines

Donglin Zeng (5) High Dimensional Data, Survival Analysis

Haibo Zhou (40) Missing/Auxiliary Data, Survival Analysis, Human Fertility

Hongtu Zhu (48)

Fei Zou (4) Statistical Genetics

*Associate Professors*

Lloyd J. Edwards (95) Longitudinal Data Analysis, Measurement Error Models, Clinical Trials

Michael Hudgens (42) Nonparametric Estimation, Group Testing, Causal Inference, Infectious Diseases

Anastasia Ivanova (83) Clinical Trials Design, Sequential Design of Binary Response Experiments, Statistical Methodology in Biostatistics

Bahjat Qaqish (94) Generalized Linear Models, Survival Analysis, Statistical Computing

Wei Sun (53)

*Assistant Professors*

Yun Li (59) (joint with Genetics)

Michael Wu (60)

*Research Professors*

Richard E. Bilsborrow (30) Economic Demography, Demography, Economic Development, Environment

Shrikant I. Bangdiwala (80) Nonparametric Methods, Clinical Trials Methodology, International Health, Injury Prevention

Robert M. Hamer (28) Linear Models, Mixed Models, Clinical Trials (joint with Psychiatry)

John S. Preisser Jr. (89) Categorical Data, Longitudinal Data Analysis

Paul W. Stewart (84) Linear Models, Distribution Theory, Statistical Inference, Longitudinal Data

*Professor of the Practice*

Sonia M. Davis (70)

*Clinical Professor*

David J. Couper (77) Epidemiological Methods, Longitudinal Data, Data Quality

*Research Associate Professors*

Ethan Lange (44) (joint with Genetics)

Todd A. Schwartz (13) Categorical Data, Clinical Trials

*Research Assistant Professors*

Eric Bair (61) (joint with School of Dentistry)

Jamie B. Crandell (64) (joint with School of Nursing)

Daniela T. Sotres-Alvarez

Mark A. Weaver (46)

*Clinical Assistant Professors*

Jane Monaco (43) Survival Analysis, Correlated Failure Time Data

*Clinical Assistant Professors*

Lisa M. Wruck

*Research Instructor*

Katherine J. Roggenkamp (3) Statistical Computing

*Adjunct Professors*

Herman E. Mitchell, Clinical Trials, Health Care Research, Clinical Epidemiology

Shyamal D. Peddada

Ibrahim A. Salama (38) Nonparametric Statistics, Order Statistics, Ergodic Theory

Clarice R. Weinberg, Statistical Methods in Epidemiology and in Environmental Health, Reproductive Epidemiology

Robert L. Obenchain

Fred A. Wright

*Adjunct Associate Professors*

Georgiy Bobashev

Matthew R. Nelson

Maura E. Stokes, Categorical Data Analysis

*Adjunct Assistant Professors*

Jacqueline L. Johnson (67)

Karen L. Kesler

Jean Orelien

Sean L. Simpson

William Valdar

*Professors Emeriti*

Clarence E. Davis (27)

James E. Grizzle

Ronald W. Helms (15)

Lawrence L. Kupper (19) Regression Analysis, Statistical Applications in Epidemiology and in Environmental Health

Keith E. Muller (76) Linear and Nonlinear Repeated Measures Models, Study Design

Dana E. Quade (6)

Michael J. Symons (17) Consulting, Bayesian Applications, Statistical Education

Craig D. Turnbull (26) Public Health Statistics, Research on Perinatal Outcomes and Behavioral Sciences

Lloyd Chambless

Courses for Graduate and Advanced Undergraduate Students

**BIOS**

**500H Introduction to Biostatistics (3). **Prerequisites, MATH 231 and 232; corequisite, BIOS 511. Access to SAS, Excel required. Permission of instructor for nonmajors. Introductory course in probability, data analysis, and statistical inference designed for BSPH biostatistics students. Topics include sampling, descriptive statistics, probability, confidence intervals, tests of hypotheses, chi-square distribution, two-way tables, power, sample size, ANOVA, nonparametric tests, correlation, regression, survival analysis.

**511 Introduction to Statistical Computing and Data Management (4). **Required preparation, previous or concurrent course in applied statistics. Permission of instructor for nonmajors. Introduction to use of computers to process and analyze data, concepts and techniques of research data management, and use of statistical programming packages and interpretation. Focus is on use of SAS for data management and reporting.

**540 Problems in Biostatistics (1–21). **Arrangements to be made with the faculty in each case. A course for students of public health who wish to make a study of some special problem in the statistics of the life sciences and public health.

**543 Biostatistical Seminar for Clinical and Translational Investigators (1). **Prerequisites, BIOS 541 and 542. Permission of the instructor for students lacking the prerequisites. This seminar provides clinical and translational researchers who have basic quantitative training in biostatistics with a more in-depth understanding of selected topics and introduces them to more advanced methods. Pass/Fail only.

**545 Principles of Experimental Analysis (3). **Permission of the instructor for nonmajors. Required preparation, basic familiarity with statistical software (preferably SAS able to do multiple linear regression) and introductory biostatistics, such as BIOS 600. Continuation of BIOS 600. Analysis of experimental and observational data, including multiple regression and analysis of variance and covariance.

**550 Basic Elements of Probability and Statistical Inference I (GNET 636) (4). **Required preparation, two semesters of calculus (such as MATH 231, 232). Fundamentals of probability; discrete and continuous distributions; functions of random variables; descriptive statistics; fundamentals of statistical inference, including estimation and hypothesis testing.

**551 Basic Elements of Probability and Statistical Inference II (3). **Prerequisite, BIOS 550. Permission of the instructor for students lacking the prerequisite. Required preparation, basic familiarity with statistical software (preferably SAS able to do multiple linear regression) or permission of the instructor. The theory and application of multiple linear regression and related analysis of variance including logistic regression and Poisson regression.

**600 Principles of Statistical Inference (3). **Required preparation, knowledge of basic descriptive statistics. Major topics include elementary probability theory, probability distributions, estimation, tests of hypotheses, chi-squared procedures, regression, and correlation.

**610 Biostatistics for Laboratory Scientists (3). **Required preparation, elementary calculus. This course introduces the basic concepts and methods of statistics, focusing on applications in the experimental biological sciences.

**660 Probability and Statistical Inference I (3). **Required preparation, three semesters of calculus (such as MATH 231, 232, 233). Introduction to probability; discrete and continuous random variables; expectation theory; bivariate and multivariate distribution theory; regression and correlation; linear functions of random variables; theory of sampling; introduction to estimation and hypothesis testing.

**661 Probability and Statistical Inference II (3). **Prerequisite, BIOS 660. Permission of the instructor for students lacking the prerequisite. Distribution of functions of random variables; Helmert transformation theory; central limit theorem and other asymptotic theory; estimation theory; maximum likelihood methods; hypothesis testing; power; Neyman-Pearson Theorem, likelihood ratio, score, and Wald tests; noncentral distributions.

**662 Intermediate Statistical Methods (4). **Pre- or corequisites, BIOS 511 and 550. Principles of study design, descriptive statistics, sampling from finite and infinite populations, inferences about location and scale. Both distribution-free and parametric approaches are considered. Gaussian, binomial, and Poisson models, one-way and two-way contingency tables.

**663 Intermediate Linear Models (4). **Required preparation, BIOS 662. Matrix-based treatment of regression, one-way and two-way ANOVA, and ANCOVA, emphasizing the general linear model and hypothesis, as well as diagnostics and model building. Reviews matrix algebra. Includes statistical power for linear models and binary response regression methods.

**664 Sample Survey Methodology (STOR 358) (4). **Prerequisite, BIOS 550. Permission of the instructor for students lacking the prerequisite. Fundamental principles and methods of sampling populations, with emphasis on simple, random, stratified, and cluster sampling. Sample weights, nonsampling error, and analysis of data from complex designs are covered. Practical experience through participation in the design, execution, and analysis of a sampling project.

**665 Analysis of Categorical Data (3). **Prerequisites, BIOS 545, 550, and 662. Permission of the instructor for students lacking the prerequisites. Introduction to the analysis of categorized data: rates, ratios, and proportions; relative risk and odds ratio; Cochran-Mantel-Haenszel procedure; survivorship and life table methods; linear models for categorical data. Applications in demography, epidemiology, and medicine.

**666 Applied Multivariate Analysis (3). **Prerequisite, BIOS 663. Application of multivariate techniques, with emphasis on the use of computer programs. Multivariate analysis of variance, multivariate multiple regression, weighted least squares, principal component analysis, canonical correlation, and related techniques.

**667 Applied Longitudinal Data Analysis (3). **Analysis of variance and multiple linear regression course at the level of BIOS 545 or 663 required. Familiarity with matrix algebra recommended. Univariate and multivariate repeated measures ANOVA, GLM for longitudinal data, linear mixed models. Estimation and inference, maximum and restricted maximum likelihood, fixed and random effects.

**668 Design of Public Health Studies (3). **Prerequisites, BIOS 545 and 550. Statistical concepts in basic public health study designs: cross-sectional, case-control, prospective, and experimental (including clinical trials). Validity, measurement of response, sample size determination, matching and random allocation methods.

**669 Working with Data in a Public Health Research Setting (3). **Prerequisite, BIOS 511 or EPID 700. Permission of the instructor for students lacking the prerequisite. Provides a foundation and training for working with data from clinical trials or research studies. Topics: issues in study design, collecting quality data, using SAS and SQL to transform data, typical reports, data closure and export, and working with big data.

**670 Demographic Techniques I (3). **Source and interpretation of demographic data; rates and ratios, standardization, complete and abridged life tables; estimation and projection of fertility, mortality, migration, and population composition.

**680 Introductory Survivorship Analysis (3). **Prerequisite, BIOS 661. Permission of the instructor for students lacking the prerequisite. Introduction to concepts and techniques used in the analysis of time to event data, including censoring, hazard rates, estimation of survival curves, regression techniques, applications to clinical trials.

**691 Field Observations in Biostatistics (1). **Field visits to, and evaluation of, major nonacademic biostatistical programs in the Research Triangle area. Field fee: $25.

**693H Honors Research in Biostatistics (3). **Directed research. Written and oral reports required.

**694H Honors Research in Biostatistics (3). **Directed research. Written and oral reports required.

Courses for Graduate Students

**BIOS**

**700 Research Skills in Biostatistics (1). **Prerequisites, BIOS 760, 761 or 758, 762, 763, and 767. Permission of the department for students with passing grade of either doctoral qualifying examination in biostatistics. BIOS 700 will introduce doctoral students in biostatistics to research skills necessary for writing a dissertation and for a career in research.

**735 Statistical Computing - Basic Principles and Applications (4). **Prerequisites, BIOS 660, 661, 662, and 663. Required preparation, one undergraduate-level programming class. Teaches important concepts and skills for statistical software development using case studies. After this course, students will have an understanding of the process of statistical software development, knowledge of existing resources for software development, and the ability to produce reliable and efficient statistical software.

**740 Specialized Methods in Health Statistics (1–21). **Permission of the instructor. Statistical theory applied to special problem areas of timely importance in the life sciences and public health. Lectures, seminars, and/or laboratory work, according to the nature of the special area under study.

**750 Advanced Techniques in Biometry (1–21). **Prerequisites, BIOS 661 and 663. Permission of the instructor. Up to three or four separate one-semester-hour modules presenting advanced techniques in biometry (topics covered usually vary at each offering). A knowledge of elementary computer programming is assumed.

**752 Design and Analysis of Clinical Trials (3). **Prerequisites, BIOS 600 and 661. This course will introduce the methods used in clinical. Topics include dose-finding trials, allocation to treatments in randomized trials, sample size calculation, interim monitoring, and non-inferiority trials.

**756 Advanced Nonparametric Methods in Biometric Research (3). **Prerequisite, BIOS 661. Theory and application of nonparametric methods for various problems in statistical analysis. Includes procedures based on randomization, ranks and U-statistics. A knowledge of elementary computer programming is assumed.

**758 Advanced Statistical Methods in Biometric and Public Health (4). **Prerequisites, BIOS 660 and 661. Introduction to probability theory, statistics, stochastic processes, and martingales. Finite sample methods. Basic statistical estimator properties. Stochastic convergence and central limit theorems. Transformation of variables and variance stabilization. Neyman-Pearson hypothesis testing methodology. Large sample inference methods, likelihood ratio, Rao's score, and Wald tests. Categorical data and regression models. Resampling plans.

**759 Applied Time Series Analysis (3). **Prerequisites, BIOS 661 and 663. Permission of the instructor. Topics include correlograms, periodograms, fast Fourier transforms, power spectra, cross-spectra, coherences, ARMA and transfer-function models, spectral-domain regression. Real and simulated data sets are discussed and analyzed using popular computer software packages.

**760 Advanced Probability and Statistical Inference I (4). **Prerequisite, BIOS 661. Permission of the instructor for students lacking the prerequisite. Measure space, sigma-field, measurable functions, integration, conditional probability, distribution functions, characteristic functions, convergence modes, SLLN, CLT, Cramer-Wold device, delta method, U-statistics, martingale central limit theorem, UMVUE, estimating function, MLE, Cramer-Rao lower bound, information bounds, LeCam's lemmas, consistency, efficiency, EM algorithm.

**761 Advanced Probability and Statistical Inference II (4). **Prerequisite, BIOS 760. Permission of the instructor for students lacking the prerequisite. Elementary decision theory: admissibility, minimaxity, loss functions, Bayesian approaches. Hypothesis testing: Neyman-Pearson theory, UMP and unbiased tests, invariance, confidence sets, contiguous alternatives. Elements of stochastic processes: Poisson processes, renewal theory, Markov chains, martingales, Brownian motion.

**762 Theory and Applications of Linear and Generalized Linear Models (4). **Prerequisites, BIOS 661 and 663, MATH 547, and 417 or 577. Corequisite, BIOS 760. Linear algebra, matrix decompositions, estimability, multivariate normal distributions, quadratic forms, Gauss-Markov theorem, hypothesis testing, experimental design, general likelihood theory and asymptotics, delta method, exponential families, generalized linear models for continuous and discrete data, categorical data, nuisance parameters, over-dispersion, multivariate linear model, generalized estimating equations, and regression diagnostics.

**763 Generalized Linear Model Theory and Applications (4). **Permission of the instructor for nonmajors. Introduction to the theory and applications of generalized linear models, quasi-likelihoods and generalized estimating equations. Topics include logistic regression, overdispersion, Poisson regression, log-linear models, conditional likelihoods, multivariate regression models, generalized mixed models, and regression diagnostics.

**764 Advanced Survey Sampling Methods (3). **Prerequisite, BIOS 664. Continuation of BIOS 664 for advanced students: stratification, special designs, multistage sampling, cost studies, nonsampling errors, complex survey designs, employing auxiliary information, and other miscellaneous topics.

**765 Models and Methodology in Categorical Data (3). **Prerequisites, BIOS 661, 663, 665, and 666. Theory of statistical methods for analyzing categorical data by means of linear models; multifactor and multiresponse situations; interpretation of interactions.

**767 Longitudinal Data Analysis (4). **Prerequisites, BIOS 661 and 762. Permission of the instructor for nonmajors. Presents modern approaches to the analysis of longitudinal data. Topics include linear mixed effects models, generalized linear models for correlated data (including generalized estimating equations), computational issues and methods for fitting models, and dropout or other missing data.

**771 Demographic Techniques II (3). **Prerequisite, BIOS 670. Required preparation, integral calculus. Life table techniques; methods of analysis when data are deficient; population projection methods; interrelations among demographic variables; migration analysis; uses of population models.

**772 Statistical Analysis of MRI Images (3). **The course will review major statistical methods for the analysis of MRI and its applications in various studies.

**773 Statistical Analysis with Missing Data (3). **Prerequisites, BIOS 761 and 762. Fundamental concepts, including classifications of missing data, missing covariate and/or response data in linear models, generalized linear models, longitudinal data models, and survival models. Maximum likelihood methods, multiple imputation, fully Bayesian methods, and weighted estimating equations. Focus on biomedical sciences case studies. Software packages include WinBUGS, SAS, and R.

**774 Statistical Learning and High Dimensional Data (3). **Prerequisite, BIOS 661. Permission of the instructor for students lacking the prerequisite. Introductory overview of statistical learning methods and high-dimensional data analysis. Involves three major components: supervised or unsupervised learning methods, statistical learning theory, and statistical methods for high-dimensional data including variable selection and multiple testing. Real examples are used.

775 Statistical Methods in Diagnostic Medicine (3) Statistical concepts and techniques for evaluating medical diagnostic tests and biomarkers for detecting disease. Measures for quantifying test accuracy. Statistical procedures for estimating and comparing these quantities, including regression modeling. Real data will be used to illustrate the methods. Developments in recent literature will be covered.

**776 Causal Inference in Biomedical Research (3). **Prerequisites, BIOS 661 and 663. Permission of the instructor for students lacking the prerequisites. This course will consider drawing inference about causal effects in a variety of settings using the potential outcomes framework. Topics covered include causal inference in randomized experiments and observational studies, bounds and sensitivity analysis, propensity scores, graphical models, and other areas.

**777 Mathematical Models in Demography (3). **Permission of the instructor. A detailed presentation of natality models, including necessary mathematical methods, and applications; deterministic and stochastic models for population growth, migration.

**779 Bayesian Statistics (4). **Prerequisite, BIOS 762. Permission of the instructor for students lacking the prerequisite. Topics include Bayes' theorem, the likelihood principle, prior distributions, posterior distributions, predictive distributions, Bayesian modeling, informative prior elicitation, model comparisons, Bayesian diagnostic methods, variable subset selection, and model uncertainty. Markov chain Monte Carlo methods for computation are discussed in detail.

**780 Theory and Methods for Survival Analysis (3). **Prerequisites, BIOS 760 and 761. Permission of the instructor for students lacking the prerequisites. Counting process-martingale theory, Kaplan-Meier estimator, weighted log-rank statistics, Cox proportional hazards model, nonproportional hazards models, multivariate failure time data.

**781 Statistical Methods in Human Genetics (4). **Prerequisites, BIOS 661 and 663. Permission of the instructor for students lacking the prerequisites. An introduction to statistical procedures in human genetics, Hardy-Weinberg equilibrium, linkage analysis (including use of genetic software packages), linkage disequilibrium and allelic association.

**782 Statistical Methods in Genetic Association Studies (3). **Prerequisite, BIOS 760. This course provides a comprehensive survey of the statistical methods for the designs and analysis of genetic association studies, including genome-wide association studies and next-generation sequencing studies. The students will learn the theoretical justifications for the methods as well as the skills to apply them to real studies.

**783 Statistical Methods in Quantitative Genetics (3). **Prerequisites, BIOS 661 and 663. Permission of the instructor for students lacking the prerequisites. An introduction to the statistical basis of variation in quantitative traits, with focus on experimental crosses and decomposition of trait variation, linkage map construction, statistical methodologies, and computer software for mapping quantitative trait loci. Issues involving whole-genome analysis will be highlighted.

**784 Introduction to Computational Biology (3). **Prerequisites, BIOS 661 and 663. Permission of the instructor for students lacking the prerequisites. Molecular biology, sequence alignment, sequence motifs identification by Monte Carlo Bayesian approaches, dynamic programming, hidden Markov models, computational algorithms, statistical software, high-throughput sequencing data and its application in computational biology.

**785 Analysis of Microarray Data (3). **Prerequisites, BIOS 661 and 663. Permission of the instructor for students lacking the prerequisites. Clustering algorithms, classification techniques, statistical techniques for analyzing multivariate data, analysis of high dimensional data, parametric and semiparametric models for DNA microarray data, measurement error models, Bayesian methods, statistical software, sample size determination in microarray studies, applications to cancer.

**791 Empirical Processes and Semiparametric Inference (3). **Prerequisite, BIOS 761. Permission of the instructor for students lacking the prerequisite. Theory and applications of empirical process methods to semiparametric estimation and inference for statistical models with both finite and infinite dimensional parameters. Topics include bootstrap, Z-estimators, M-estimators, semiparametric efficiency.

**841 Principles of Statistical Consulting (3). **Prerequisites, BIOS 545. Permission of the instructor for nonmajors. An introduction to the statistical consulting process, emphasizing its nontechnical aspects.

**842 Practice in Statistical Consulting (1–21). **Prerequisites, BIOS 511, 545, 550, and 841. Permission of the instructor. Under supervision of a faculty member, the student interacts with research workers in the health sciences, learning to abstract the statistical aspects of substantive problems, to provide appropriate technical assistance, and to communicate statistical results.

**843 Seminar in Biostatistics (1). **This seminar course is intended to give students exposure to cutting edge research topics and hopefully help them in their choice of a thesis topic. It also allows the student to meet and learn from major researchers in the field.

**844 Leadership in Biostatistics (3). **Prerequisite, BIOS 841. Using lectures and group exercises, students are taught where and how biostatisticians can offer leadership in both academic and nonacademic public health settings.

**850 Training in Statistical Teaching in the Health Sciences (1–21). **Required preparation, a minimum of one year of graduate work in statistics. Principles of statistical pedagogy. Students assist with teaching elementary statistics to students in the health sciences. Students work under the supervision of the faculty, with whom they have regular discussions of methods, content, and evaluation of performance.

**889 Research Seminar in Biostatistics (0.5–21). **Permission of the instructor. Seminar on new research developments in selected biostatistical topics.

**990 Research in Biostatistics (1–21). **Individual arrangements may be made by the advanced student to spend part or all of his or her time in supervised investigation of selected problems in statistics.

**992 Master's (Non-Thesis) (3). **

**994 Doctoral Research and Dissertation (3).**