COURSE INFORMATION
Biostatistics

BEP 233d. Research Synthesis and Meta-Analysis Applications in Public Health and Clinical Medicine (Department of Biostatistics and Epidemiology)
Dr. G. Colditz
2.5 credits
Seminars. One 3-hour session each week.

Concerned with the use of existing data to inform clinical decision making and health care policy, the course focuses on research synthesis (meta-analysis). The principles of meta-analytic statistical methods are reviewed, and the application of these to data sets is explored. Application of methods includes considerations for clinical trials and observational studies. The use of meta-analysis to explore data and identify sources of variation among studies is emphasized, as is the use of meta-analysis to identify future research questions.
Course Activities: Students prepare a protocol to conduct a meta-analysis and use existing meta-analysis software to apply principles outlined in the course to data sets provided for this purpose.

BEP 233t. Research Synthesis and Meta-Analysis Applications in Public Health and Clinical Medicine (Departments of Biostatistics and Epidemiology)
Dr. M. Stoto
2.5 credits
Lectures. Five 2-hour sessions each week.

Concerned with the use of existing data to inform clinical decision making and health care policy, the course focuses on research synthesis (meta-analysis). The principles of meta-analytic statistical methods are reviewed, and the application of these to data sets is explored. Application of methods includes considerations for clinical trials and observational studies. The use of meta-analysis to explore data and identify sources of variation among studies is emphasized, as is the use of meta-analysis to identify future research questions.
Course Activities: Students prepare a protocol to conduct a meta-analysis and use existing meta-analysis software to apply principles outlined in the course to data sets provided for this purpose.

BIO 113a. Introduction to SAS
Ms. L. Allred (P), Dr. M. Pagano (S)
2.5 credits
Lectures, laboratories. Two 1.5 hour-sessions each week. One 1.5-hour lab each week.

Provides intensive instruction in the use of SAS to prepare data for statistical analysis. The focus is on database management and programming problems. Basic issues in each of these areas are discussed in the context of teaching the specific skills required to use SAS effectively.
Course Note: Credit is given for only one section of BIO 113a, e or s; labtime to be announced at first meeting.

BIO 113e. Introduction to SAS
Dr. T. Fenton (P), Dr. M. Pagano (S)
1.25 credits
Lectures. Four 2.5-hour sessions. Four 3.75-hour lab sessions.

Provides intensive instruction in the use of SAS to prepare data for statistical analysis. The focus is on database management and programming problems. Basic issues in each of these areas are discussed in the context of teaching the specific skills required to use SAS effectively.
Course Note: Credits is give only for one section of BIO 113a, e or s; lab time to be announced at first meeting.

BIO 113s. Introduction to SAS
Ms. L. Allred (P), Dr. M. Pagano (S)
2.5 credits
Lectures. Five 2-hour sessions each week (including laboratory sessions).

Provides intensive instruction in the use of SAS to prepare data for statistical analysis. The focus is on database management and programming problems. Basic issues in each of these areas are discussed in the context of teaching the specific skills required to use SAS effectively.
Course Note: Credit is given for only one section of BIO 113a, e or s; lab time to be announced at first meeting.

BIO 200ab. Principles of Biostatistics
Dr. M. Pagano
5 credits
Lectures, laboratories. Two 1-hour sessions each week. One 2-hour lab each week.

Lectures and laboratory exercises acquaint the student with the basic concepts of biostatistics and their applications and interpretation. The computer is used throughout the course. Topics include descriptive statistics, graphics, diagnostic tests, probability distributions, inference, tests of significance, association, linear and logistic regression, life tables, and survival analysis.
Course Note: Credit is given for only one of these courses: BIO 200ab, BIO 201ab; this course cannot be counted as part of the credit requirement for a major or minor doctoral field course; course enrollment is limited to 150 students; lab or section time to be announced at first meeting.

BIO 201ab. Introduction to Statistical Methods
Dr. K. Gauvreau
5 credits
Lectures, laboratories. Two 1.5-hour sessions each week. One 2-hour lab each week.

Covers basic statistical techniques that are important for analyzing data arising from epidemiology, environmental health, biomedical and other public health-related research. Major topics include descriptive statistics, elements of probability, introduction to estimation and hypothesis testing, nonparametric methods, techniques for categorical data, regression analysis, analysis of variance, and elements of study design. Applications are stressed. Designed as an alternate to BIO 200ab, for students desiring more emphasis on theoretical developments or those having had an introductory statistics course at the level of BIO 200ab.
Course Note: Courses in algebra and calculus strongly recommended; credit is not given for both BIO 200ab and BIO 201ab; lab or section time to be announced at first meeting.

BIO 202s. Principles of Biostatistics, Part I
Dr. M. Testa
2.5 credits
Lectures, laboratories. Five 2-hour sessions and five 2-hour labs each week.

This course is the first part of introductory biostatistics and acquaints the student with the basic concepts and methods of biostatistics, their applications, and their interpretation. The material covered includes data presentation, numerical summary measures, rates and standardization, and life tables. Probability is introduced to quantify uncertainty, especially as it pertains to diagnostic and screening methods. Also covered are sampling distributions so that students may be introduced to confidence intervals and hypothesis testing. The computer is used throughout the course, and the student will gain familiarity with the software package STATA.
Course Note: Requires a basic knowledge of mathematics and familiarity with use of personal computers. Students taking BIO202 and BIO203 will be given credit for BIO200 or BIO201.

BIO 203t. Principles of Biostatistics, Part II
Dr. C. Yiannoutsos (P), Dr. S. Lagakos (S)
2.5 credits
Lectures, laboratories. Five 2-hour sessions each week and five 2-hour labs each week.

This course is the second part of introductory biostatistics; it continues to explore inference in greater depth. Lectures and laboratory exercises will emphasize applied data analysis, building upon the fundamentals emphasized in BIO 200s. Topics covered include the comparison of two means, analysis of variance, non-parametric methods, inference on proportions, contingency tables, multiple 2 * 2 tables, correlation, simple regression, multiple regression and logistic regression, analysis of survival data, and sampling theory. The computer is used throughout the course, and the student will gain more familiarity with STATA.
Course Note: BIO 202 is required; students who successfully completed BIO 200t in 2001 are eligible to take BIO 203 in the 2002 Summer Institute.
Students who take BIO202 and BIO 203 will not be given credit for BIO200 or BIO201.

BIO 206s.Introductory Statistics for Medical Research
Dr. E. J. Orav
2.5 credits
Lectures. Five 2-hour sessions each week.

Introduces basic biostatistical techniques with an emphasis on applications to clinical research. Topics include probability and statistics, hypothesis testing, confidence intervals, non-parametrics, and power calculations.
Course Note: Designed primarily for participants in the Program in Clinical Effectiveness; no auditors.

BIO 207t. Statistics for Medical Research II
Dr. G. Reed, Dr. E.J. Orav
2.5 credits
Lectures. Five 1.75-hour sessions each week.

Presents additional biostatistical techniques that commonly appear in the analysis of clinical databases and trials. Topics include contingency table analyses, log-rank tests, paired and matched analyses, analysis of variance and multiple comparisons procedures.
Course Note: BIO 206s required; no auditors.

BIO 208t. Statistics for Medical Research, Advanced
Dr. E. J. Orav
2.5 credits
Lectures. Five 2-hour sessions each week.

Presents additional biostatistical techniques that commonly appear in the analysis of clinical databases and trials. This course will move at a faster pace than the alternative BIO 207t while covering all of the same topics (contingency tables, log-rank tests, paired and matched analyses, analysis of variance and multiple comparisons procedures). In addition, linear and logistic regression will be introduced.
Course Note: BIO 206s required; no auditors.

BIO 209t Statistics for Medical Research, Translational
Dr. L. Sleeper (P), Dr. E. J. Orav (S)
2.5 credits
Lectures. Five 2-hour sessions each week.

Presents additional biostatistical techniques that are most relevant to researchers involved with designed experiments. Topics include contingency tables, paired analyses, simple analysis of variance, multiple comparisons procedures, two-way analysis of variance, and simple repeated measures analysis of variance.
Course Note: BIO 206s required; no auditors.

BIO 210cd. The Analysis of Rates and Proportions
Dr. R. Glynn
5 credits
Lectures, laboratories. Two 1.5-hour sessions each week. One 1.5-hour lab each week.

Emphasizes concepts and methods for analysis of data which are categorical, rate-of-occurrence (e.g., incidence rate), and time-to-event (survival duration). Stresses applications in epidemiology, clinical trials, and other public health research. Topics include measures of association, 2x2 tables, stratification, matched pairs, logistic regression, model building, analysis of rates, and survival data analysis using proportional hazards models.
Course Note: BIO 200ab, BIO 201ab or BIO 200s and BIO 200t or signature of instructor required; lab or section times to be announced at first meeting.

BIO 211cd. Regression and Analysis of Variance in Experimental Research
Dr. J. Ibrahim
5 credits
Lectures, laboratories. Two 1.5-hour sessions each week; one 1-hour lab each week.

Covers analysis of variance and regression, including details of data-analytic techniques and implications for study design. Also included are probability models and computing. Students learn to formulate a scientific question in terms of a statistical model, leading to objective and quantitative answers.
Course Note: BIO 200ab, BIO 201ab, or signature of instructor required; lab or section time will be announced at first meeting.

BIO 212cd. Survey Research Methods in Community Health
Dr. T. Mangione (P), Dr. S. Lagakos (S)
2.5 credits
Lectures. One 2-hour session each week.

Covers research design, sample selection, questionnaire construction, interviewing techniques, the reduction and interpretation of data, and related facets of population survey investigations. Focuses primarily on the application of survey methods to problems of health program planning and evaluation. Treatment of methodology is sufficiently broad to be suitable for students who are concerned with epidemiological, nutritional, or other types of survey research.

BIO 213ab. Applied Regression for Clinical Research
Dr. E. J. Orav
5 credits
Lectures. Two 1.5-hour sessions each week. One 1.5-hour lab each week.

This course will introduce students involved with clinical research to the practical application of multiple regression analysis. Linear regression, logistic regression and proportional hazards survival models will be covered, as well as general concepts in model selection, goodness-of-fit, and testing procedures. Each lecture will be accompanied by a data analysis using SAS and a classroom discussion of the results. The course will introduce, but will not attempt to develop the underlying likelihood theory.
Course Note: Previous introductory level statistics course and SAS programming ability required; lab or section time will be announced at first meeting.

BIO 214c. Principles of Clinical Trials
Dr. J. Ware
2.5 credits
Lectures. Two 2-hour sessions each week.

Designed for individuals interested in the scientific, policy, and management aspects of clinical trials. Topics include types of clinical research, study design, treatment allocation, randomization and stratification, quality control, sample size requirements, patient consent, and interpretation of results. Students design a clinical investigation in their own field of interest, write a protocol for it, and critique recently published medical literature.
Course Note: BIO 200ab, BIO 201ab, BIO 206s, BIO 207t, or BIO 200s and BIO 200t or signature of instructor required.

BIO 214t. Principles of Clinical Trials
Dr. K. Stanley, Dr. R. Gelber
2.5 credits
Lectures. Five 2-hour sessions each week.

Designed for individuals interested in the scientific, policy, and management aspects of clinical trials. Topics include types of clinical research, study design, treatment allocation, randomization and stratification, quality control, sample size requirements, patient consent, and interpretation of results. Students design a clinical investigation in their own field of interest, write a proposal for it, and critique recently published medical literature.
Course Note: BIO 200ab, BIO 201ab, BIO 206s, BIO 207t, BIO 200s or BIO 200t or signature of instructor required.

BIO 222ab. Basics of Statistical Inference
Dr. P. Catalano
5 credits
Lectures, laboratories. Two 1.5 hour-sessions each week. One 2-hour lab each week.

This course will provide a basic, yet thorough introduction to the probability theory and mathematical statistics that underlie many of the commonly used techniques in public health research. Topics to be covered include probability distributions (normal, binomial, Poisson), means, variances and expected values, finite sampling distributions, parameter estimation (method of moments, maximum likelihood), confidence intervals, hypothesis testing (likelihood ratio, Wald and score tests). All theoretical material will be motivated with problems from epidemiology, biostatistics, environmental health and other public health areas. This course is aimed towards second year doctoral students in fields other than Biostatistics.
Course Note: One intermediate level biostatistics course such as BIO 210cd, BIO 211cd, or permission of the instructor required; some elementary calculus and algebra skills; lab or section time to be announced at first meeting.

BIO 223cd. Applied Survival Analysis and Discrete Data Analysis
Dr. R. Xu
5 credits
Lectures. Two 2-hour sessions each week. One 1-hour optional lab each week.

This course will cover topics in both discrete data analysis (25% of class) and applied survival analysis (75% of class). The course will begin with a review of sampling plans and contingency table for discrete data. Further topics in discrete data analysis will include logistic regression, exact inference, and conditional logistic regression. This short survey of discrete data topics will provide a natural transition to analysis of survival data. Survival topics include: hazard, survivor, and cumulative hazard functions, Kaplan-Meier and actuarial estimation of the survival distribution, comparison of survival using log rank and other tests, regression models including the Cox proportional hazards model and accelerated failure time model, adjustment for time-varying covariates, and use of parametric distributions (exponential, Weibull) in survival analysis. Class material will include presentation of statistical methods for estimation and testing, along with current software (SAS, Stata, Splus) for implementing analyses of discrete data and survival data. Applications to real data will be emphasized.
Course Note: BIO 210cd, BIO 213ab, or BIO230ab required, or permission of instructor.

BIO 224t. Survival Methods in Clinical Research
Dr. R. Davis
2.5 credits
Lectures. Five 2-hour sessions each week.

This course will cover the common approaches to the display and analysis of survival data, including Kaplan-Meier curves, log rank tests, and Cox proportional hazards regression. Computing, using SAS, will be an integral component of the course.
Course Note: BIO 210cd, BIO 211cd, BIO 213ab or signature of instructor required.

BIO 226ab. Applied Longitudinal Analysis
Dr. B. Coull
5 credits
Lectures, laboratories. Two 2-hour sessions each week.

This course covers modern methods for the analysis of repeated measures, correlated outcomes and longitudinal data, including the unbalanced and incomplete data sets characteristic of biomedical research. Topics include an introduction to the analysis of correlated data, repeated measures ANOVA, random effects and growth curve models, and generalized linear models for correlated data, including generalized estimating equations (GEE).
Course Activities: Homework assignments will focus on data analysis in SAS using PROC GLM, PROC MIXED, and PROC GENMOD.
Course Note: BIO 211cd, BIO 213ab, or BIO 232ab, or signature of instructor required; lab or section time will be announced at first meeting.

BIO 227a. Fundamental Concepts in Gene Mapping
Dr. J. Rogus, Dr. A. Doria
2.5 credits
Lectures, laboratories. Two 2-hour sessions each week.

This course will introduce students to the basic concepts of genetics and molecular biology that are necessary for an understanding of the genetic basis of disease. The course material consists of two main topics, molecular biology and genetic epidemiology, plus case studies. Specific areas to be covered include 1) the structure and characteristics of the human genome, the Human Genome Project, and laboratory methods in molecular biology, and 2) heritability, gene mapping, simple and complex genetic traits, linkage, and linkage disequilibrium.

BIO 228b. Statistical Genetics in Complex Human Disease
Dr. L. Palmer (P), Dr. N. Laird (S)
2.5 credits
To be given 2001-2002; offered alternate years.
Lectures: Two 2-hour sessions each week.

This is an introductory course covering statistical methods for the
analysis of family data, with emphasis on gene mapping. Topics covered
will include: allele frequency estimation, classical segregation and
linkage analysis, multipoint linkage tests, model-free linkage analysis, general pedigree analysis, family-based association analysis and study
design for complex genetic traits. Students will gain exposure to some
of the methods and computer tools available for gene mapping and genetic analysis, and begin to read and evaluate statistical human genetics
literature.
Course Note: BIO227a or signature of instructor required.

BIO 230ab. Probability Theory and Applications I
Dr. M. Bonetti
5 credits
Lectures, laboratories. Two 2-hour sessions each week. One 2-hour lab each week.

A first course in probability fundamental to the biostatistics program. Topics include axiomatic foundations, frequency and personal concepts of probability, combinatorics, discrete and continuous sample spaces, independence and conditional probability, random variables, expectation operator, moments, generating functions and characteristic functions, standard distributions, transformations, sampling distributions related to the normal distribution, convergence concepts, weak and strong laws of large numbers, the central limit theorem, and elements of stochastic processes.
Course Note: Multi-variable calculus (one or two semesters beyond elementary calculus) suggested; signature of instructor required; lab or section time to be announced at first meeting.

BIO 231cd. Statistical Inference I
Dr. M. Zelen
5 credits
Lectures, laboratories. Two 2-hour sessions each week. One 1.5-hour lab each week.

A fundamental course in statistical inference. Discusses general principles of data reduction: exponential families, sufficiency, ancillarity and completeness. Describes general methods of point and interval parameter estimation and the small and large sample properties of estimators: method of moments, maximum likelihood, unbiased estimation, Rao-Blackwell and Lehmann-Scheffe theorems, information inequality, asymptotic relative efficiency of estimators. Describes general methods of hypothesis testing and optimality properties of tests: Neyman-Pearson theory, likelihood ratio tests, score and Wald tests, uniformly and locally most powerful tests, asymptotic relative efficiency of tests.
Course Note: BIO 230ab or signature of instructor required; lab or section time to be announced at first meeting.

BIO 232ab. Methods I
Dr. M. Wand
5 credits
Lectures. Two 2-hour sessions each week.

Introductory methods course aimed at first year Biostatistics students. Topics cover introduction of common statistical models and methods for data analysis. Concepts of populations and samples, contingency tables and distributional models such as Bernoulli, Poisson and normal models and related ones will be introduced. Methods for data analysis include chi-square tests, one- and two-sample t-tests, linear rank tests, correlation, ANOVA, and simple linear regression. Methods of exploratory data analysis and robust estimation will be discussed. The application of methods to the analysis of data using SAS and Splus statistical software packages will be emphasized.
Course Note: A working knowledge of calculus and linear algebra and one introductory statistics course are required. For non-Biostatistics degree candidates, BIO 222ab or equivalent is also required. Lab or section time will be announced at first meeting.

BIO 233cd. Methods II
Dr. D. Wypij
5 credits
Lectures, laboratories (optional). Two 2-hour sessions each week. One 1.5-hour lab each week.

This course focuses on the analysis of categorical data and count data, and provides an introduction to methods for analysis of survival data. Topics include a review of sampling plans, analysis of contingency tables, large sample and exact methods for constructing confidence intervals and hypothesis tests, measures of association, logistic regression, and log-linear analysis. Survival topics will include estimation of survival distributions, comparison of groups, and regression models such as the Cox proportional hazards model and the accelerated failure time models.
Course Note: BIO 210cd and BIO 222ab or BIO 232ab, or signature of instructor required. Lab or section time to be announced at first meeting.

BIO 235cd. Regression and Analysis of Variance
Dr. F. Vaida
5 credits
Lectures, laboratories. Two 2-hour sessions each week. One 2-hour lab each week.

This is an advanced course in data analysis for linear models - regression and analysis of variance. Estimation methods (maximum likelihood and least squares) and issues of inference (confidence intervals, hypothesis testing, analysis of residuals) are presented from a theoretical and data analysis perspective.
Course Note: BIO 232ab and BIO 231cd, or signature of instructor required; familiarity with matrix algebra and BIO 211cd or equivalent recommended. Lab or section time to be announced at first meeting.

BIO 240d. Sample Surveys
Dr. A. Zaslavsky, Dr. S. Lagakos
2.5 credits
To be given 2001-2002; offered alternate years.
Lectures. One 2-hour session each week.

Methods for design and analysis of sample surveys. A brief introduction to questionnaire design and evaluation will be followed by a discussion of sample design techniques. Estimation methods, including calculation and use of sampling weights, and variance estimation methods.
Course Note: BIO 210cd, BIO 211cd or BIO 222ab or equivalent required.

BIO 243c. Nonparametric Methods
Dr. M. Hughes
2.5 credits
To be offered 2001-2002; offered alternate years.
Lectures. Two 2-hour sessions each week.

Presents the theory and application of nonparametric methods. Topics include permutation tests, permutation limit theorems, 2-sample rank tests and their asymptotic efficiency, k-sample rank tests, 1-sample tests of location, paired comparsions, rank tests for symmetry and independence, and analogues of linear modeling based on ranks.
Course Note: BIO231cd required.

BIO 244ab. Analysis of Failure Time Data
Dr. L.J. Wei
5 credits
Lectures. Two 2-hour sessions each week.

Discusses the theoretical basis of concepts and methodologies associated with survival data and censoring, nonparametric tests, and competing risk models. Much of the theory is developed using counting processes and martingale methods. Material is drawn from recent literature.
Course Note: BIO 231cd and BIO 233cd required.

BIO 245ab. Analysis of Multivariate and Longitudinal Data
Dr. N. Laird
5 credits
Lectures. Two 2-hour sessions each week.

Presents classical and modern approaches to the analysis of multivariate observations, repeated measures, and longitudinal data. Topics include the multivariate normal distribution, Hotelling's T2, MANOVA, the multivariate linear model, random effects and growth curve models, generalized estimating equations, statistical analysis of multivariate categorical outcomes, and estimation with missing data. Discusses computational issues for both traditional and new methodologies.
Course Note: BIO 231cd, BIO 235ab or BIO235cd required.

[BIO 247cd.] Design of Scientific Investigations
Dr. V. De Gruttola
5 credits
Not to be given 2001-2002; offered alternate years.
Lectures. Two 2-hour sessions and one 2-hour lab each week.

Discusses those aspects of statistical theory and practice relevant to the design of scientific investigations in the health sciences. Topics include sample size considerations, basic principles of experimental design (randomization, replication, and balance), block designs, factorial experiments, response surface modeling, clinical trials, adaptive designs, cohort studies, early detection trials, and double sampling techniques.
Course Note: BIO 235ab, BIO235cd or signature of instructor required; minimum enrollment of 10 students required.

BIO 248cd. Advanced Statistical Computing
Dr. R. Gray
5 credits
Lectures. Two 2-hour sessions each week.

A course in computing algorithms useful in statistical research and advanced statistical applications. Topics include computer arithmetic, matrix algebra, numerical optimization methods with application to maximum likelihood estimation and GEEs, spline smoothing and penalized likelihood, numerical integration, random number generation and simulation methods, Gibbs sampling, bootstrap methods, missing data problems and EM, imputation, data augmentation algorithms, and Fourier transforms.
Course Note: BIO 235ab, BIO235cd or consent of instructor and proficiency with C or Fortran programming required.

BIO 249ab. Bayesian Methodology in Biostatistics
Dr. S. Normand
5 credits
Lectures. Two 2-hour sessions each week.

This course examines basic aspects of the Bayesian paradigm including Bayes’ theorem, the likelihood principle, prior distributions, posterior distributions, and predictive distributions. General topics include Bayesian analysis of linear models, generalized linear models, survival models, and random effects models. Computations using Markov chain Monte Carlo methods are discussed. Bayesian methods in meta-analysis and the design and analysis of clinical trials will be examined.
Course Note: BIO 230ab, BIO 231cd and BIO 232ab or signature of instructor required.

BIO 250ab. Probability II
Dr. S. Lagakos, Dr. Y. Li
5 credits
Lectures. Two 2-hour sessions each week.

A sequel to BIO 230ab, covering a variety of more advanced topics in probability theory. Topics include a brief overview of measure theory integration, convergence on sequences of random variables and stochastic processes, limit theorems, projections, and conditional expectation.
Course Note: BIO 230ab, BIO 231cd, and BIO 232ab or signature of instructor required.

BIO 251cd. Statistical Inference II
Dr. L. Ryan
5 credits
Lectures. Two 2-hour sessions each week.

Sequel to BIO 231cd. Considers several advanced topics in statistical inference. Topics include limit theorems, multivariate delta method, properties of maximum likelihood estimators, saddlepoint approximations, asymptotic relative efficiency, robust and rank-based procedures, resampling methods, and nonparametric curve estimation.
Course Note: BIO 231cd required.

[BIO 262ab.] Statistical Problems in Drug Development
Dr. M. Testa
2.5 credits
Not to be given 2001-2002; offered alternate years.
Lectures. One 2-hour session each week.

This course will introduce the student to the "real life" applications of statistical methodology required for pharmaceutical drug development and will feature guest lecturers from the pharmaceutical industry. Weekly seminars will cover statistical techniques used in the various phases of drug development, including assessment of pharmacologic activity; preclinical animal models and toxicology studies; clinical trials (Phase I dose ranging through Phase III comparative efficacy trials); and post-surveillance, pharmacoepidemiologic and pharmacoeconomic studies. Statistical techniques and examples include applications of optimum screening designs, use of non-parametric estimators, problems of multiplicity, tests for monotonicity, parametric and nonparametric regression, ordered categorical data analysis, survival methods, issues of power and sample size, bioequivalence studies, longitudinal data analysis, univariate and multivariate general linear models, multiple endpoint problems and quality-of-life measurement models.
Course Note: BIO210, BIO211 or BIO213 or written permission of the instructor required. Exposure to linear models and non-parametric statistics recommended.

BIO 263d. Computational Methods for Categorical Data Analysis
Dr. C. Mehta
2.5 credits
To be given 2001-2002; offered alternate years.
Lectures. Two 2-hour sessions each week.

This course deals with exact nonparametric methods of inference. These methods use fast numerical algorithms to permute the observed data in all possible ways, and thereby derive exact distributions for the test statistics of interest without making any distributional or large-sample assumptions. In contrast, standard parametric methods of inference make distributional assumptions about the data, while standard nonparametric methods of inference rely on asymptotic theory to derive approximate distributions for the test statistics. Exact nonparametric methods are particularly important for small, sparse or unbalanced data where the usual asymptotic theory breaks down. This course will cover exact inference for one, two and K-sample problems, ordered and unordered RxC contingency tables, 2x2 and 2xC contingency tables with or without stratification, and logistic regression. A unified view, encompassing both continuous and categorical data, will be presented based on the permutation principle. Modern algorithmic advances that make exact permutational inference computationally feasible will be treated in depth. The methods will be illustrated by several biomedical data sets. This course will use StatXact and LogXact statistical packages.

[BIO 268ab]. Statistical Methods in Human Genetics
Dr. K. Lunetta
2.5 credits
Not to be given 2001-2002; offered alternate years.
Lectures. One 2-hour session each week.

This course will introduce students to statistical procedures for investigating inheritance in humans. Methods for human gene mapping, such as family-based tests of association and linkage, will be emphasized. Readings from selected texts and current literature. A brief introduction to human genetics will be provided.
Course Note: BIO 230ab and BIO 231cd required.

BIO 270cd. Statistical Science Outreach
Dr. R. Gelman, Dr. V. DeGruttola
2.5 credits
To be given 2001-2002; offered alternate years.
Seminars. One 2-hour session each week.

This is a seminar aimed at broadening the background of students in probability and statistics. Students will be expected to give short presentations from expository articles and papers. Articles will be chosen on the basis of ideas rather than technical content. There will be some emphasis on historical developments. This course is suitable for students in any year of the Biostatistics program.
Course Note: Enrollment in a biostatistics degree program required; this class cannot be used to satisfy the intermediate requirement for doctoral students in the Department of Biostatistics; minimum enrollment of 10 students required; signature of instructor required.

BIO 271ab. Statistical Computing Environments
Dr. R. Gentleman
2.5 credits
Lectures, laboratories. One 2-hour session each week.

Acquaints the students with the modern computing environments (hardware and software) needed for careers in biostatistics. Course will consist of lectures and computer labs, with several guest lecturers. Specific topics include, programming environments in statistics, algorithmic and symbolic mathematics, source language programming and its tools, editors, typesetters, Internet tools, UNIX and other tools that have great potential for research in and practice of statistics.
Course Note: Enrollment in a biostatistics degree program required; this class cannot be used to satisfy the intermediate requirement for doctoral students in the Department of Biostatistics; signature of instructor required; no auditors.

BIO 274cd. Applied Stochastic Processes and Models in Public Health
Dr. A. Rotnitzky
5 credits
To be given 2001-2002; offered alternate years.
Lectures. Two 2-hour sessions each week.

The aim of this course is to develop those aspects of stochastic processes that are relevant for modeling important problems in public health. Among the topics to be covered are: Poisson processes, birth and death processes, Markov chains and processes, semi-Markov processes. Applications will be made to models of prevalence and incidence of disease, therapeutic clinical trials, clinical trials for prevention of disease, length biased sampling, models for early detection of disease, cell kinetics and family history problems.
Course Note: BIO 230ab required.

BIO 275ab Operational Mathematics
Dr. R. Betensky
2.5 credits
Lectures. One 2-hour sessions each week.

The aim of this course is to strengthen students' background in analysis and operational use of mathematics. The course will emphasize the application of several fundamental results, and not the proofs of these results. Students will work several problems which illustrate fundamental mathematical operations. Topics include concepts of convergence (e.g., power series, Taylor's series), functions (limits, continuity, step functions, L'Hopital's rule, differentiability), integration (Riemann, Stieltjes, Lebesque), operations convergence theorem, complex variables (e.g., Laplace transforms, Fourier transforms, inversion formulas).
Course Note: BIO 230ab required; no auditors.

BIO 277cd. Computational Biology
Dr. W. Wong
5.0 credits
Lectures. One 4-hour session each week.

With the rapid advances in molecular biology over the past decade, the need for quantitative methods to analyze the vast amounts of information that are being generated is enormous. This course will present and discuss quantitative methods used in the analysis of several types of data bases. Topics may include restriction maps, cloning, genome mapping, sequence assembly, sequency alignment, and trees and sequences.
Course Note: BIO 230ab, BIO 231, or equivalent required; ordinal grading option only.

[BIO 279d.] Smoothing in Biostatistical Modeling
Dr. M. Wand
2.5 credits
Not to be given 2001-2002; offered alternate years.
Lectures. Two 2-hour sessions each week.

Smoothing is means by which non-linear structure can be incorporated into a statistical model without the need for parametric modeling. This course will describe some of the main smoothing techniques and illustrate their use in biostatistical modeling. Computational and some theoretical issues will also be discussed. The package S-PLUS will be used for computing.

BIO 284d. Spatial Statistics for Health Research
Dr. L. Ryan, Dr. M. Wand
2.5 credits
To be given 2001-2002; offered alternate years.
Lectures, seminars. Two 2-hour sessions each week.

This course will introduce students to a broad range of topics in spatial statistics, including but not limited to types of spatial data, kriging, parametric and non-parametric methods, tests for spatial randomness. The course will draw on many real examples. Students will become proficient in the use of Splus SpatialStats and ARCView.
Course Activities: Homework assignments, project and class presentation.
Course Note: Minimum enrollment of 10 students; instructor's signature required.

BIO 300 a,b,c,d,s. Independent Study
Department Members
Time and credit to be arranged.

An opportunity for independent study is offered for interested and qualified students or small groups of students. Arrangements must be made with individual faculty members and are limited by the amount of faculty time available. These programs are open to all students who wish to go beyond the content of the regular courses.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required.

BIO 301 a,b,c,d,s. Tutorial
Department Members
Time and credit to be arranged.

An opportunity for independent study is offered for interested and qualified students or small groups of students. Arrangements must be made with individual faculty members and are limited by the amount of faculty time available. These programs are open to all students who wish to go beyond the content of the regular courses.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required.

BIO 310a,b,c,d,s. Statistical Methods
Department Members
Time and credit to be arranged.

Guided study in specific areas of statistical methodology and applications.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 311a,b,c,d,s. Teaching
Department Members
Time and credit to be arranged.

Work with members of the department in laboratory instruction and the development of teaching materials.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 312a,b,c,d,s. Consultation
Department Members
Time and credit to be arranged.

Work with members of the department on current statistical consultation activities.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 313a,b,c,d,s. Computing
Department Members
Time and credit to be arranged.

Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 314a,b,c,d,s. Study Design
Department Members
Time and credit to be arranged.

Guidance in developing statistical design of a study in which the student has a particular interest.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 315a,b,c,d,s. Data Analysis
Department Members
Time and credit to be arranged.

Guidance in the statistical analysis of a body of data in which the student is interested.
Course Note: Completed independent study contract is required at the time of registration; maximum of 5 credits per independent study topic; pass/fail only; signature of instructor required; students may register for a maximum of 5 credits in the summer term.

BIO 350a,b,c,d,s. Research
Department Members
Time and credit to be arranged.

For doctoral candidates who have passed their school-wide Oral Qualifying Examination and who are undertaking advanced work along the lines of fundamental or applied research in the department.
Course Note: Pass/Fail only; maximum of 20 credits; signature of instructor required.

BIO 400 a,b,c,d,s Non-Resident Research
Department Members
Time and credit to be arranged.

For doctoral candidates who have passed their school-wide Oral Qualifying Examination and who are undertaking advanced work along the lines offundamental or applied research in the department.
Course Note: Pass/Fail only; maximum of 20 credits; signature of instructor required.

EEB 271c. Advanced Regression Techniques for Environmental Epidemiology (Departments of Environmental Health, Epidemiology and Biostatistics)
Dr. J. Schwartz, Dr. W. Huang
2.5 credits
Lectures and seminars. Two 2-hour sessions each week.

The course will cover nonlinear exposure-response relationships and repeated measure designs, including non-parametric and semi-parametric smoothing techniques, generalized additive models, robust regression and time series models. In addition to the theoretical material, students will apply these techniques using S-plus and SAS to actual datasets including modeling the effects of environmental exposures on health outcomes. These techniques also are widely applicable to problems in infectious disease, psychiatric, nutritional, occupational, and cancer epidemiology.
Course Activities: Lectures and structured workshops in the instructional computer facility.
Course Note: EPI 200a, EPI 200s, EPI 201a or EPI 208st, and BIO 233cd or BIO 211cd required; EPI 202b and EPI 204d are strongly recommended; minimum enrollment of 3 students required and limited to 15 students; signature of instructor required; lab or section time to be announced at first meeting.

HPB 280b. Decision Analysis for Health and Medical Practices (Department of Health Policy and Management and the Department of Biostatistics)
Dr. S. Goldie
2.5 credits
Lectures. Two 2-hour sessions each week.

This course is designed to introduce the student to the methods and growing range of applications of decision analysis, cost-effectiveness analysis, and benefit-cost analysis in health care technology assessment, medical decision making, and health resource allocation. The objectives of the course are: (1) to provide a technical understanding of the methods used, (2) to give the student an appreciation of the practical problems in applying these methods to the evaluation of medical procedures and public health policies, and (3) to give the student an appreciation of the uses and limitations of these methods in decision making at the levels of national policy, health care organizations including hospitals and health maintenance organizations, and individual patient care.
Course Note: Introductory course in probability and statistics required; BIO 200ab, BIO 201ab, or BIH 203b may be taken concurrently; introductory economics is recommended but not required.

HPB 281c. Methods for Decision Analysis in Public Health and Medicine (Department of Health Policy and Management and the Department of Biostatistics)
Dr. K. Kuntz
2.5 credits
Lectures, seminars. Two 2-hour sessions each week.

An intermediate-level course on methods and health applications of decision analysis and other modeling techniques. Topics include Markov models, life expectancy modeling, deterministic and probabilistic sensitivity analysis, simulation models, ROC analysis and diagnostic technology assessment, quality of life valuation, multi-attribute utility, and behavioral decision theory.
Course Note: HPB 280b, HPM 286s, or equivalent introductory course on decision analysis required; signature of instructor required; familiarity with matrix algebra and elementary calculus may be helpful but not required.

HPB 282d. Cost-Effectiveness and Cost-Benefit Analysis in Public Health and Medicine (Department of Health Policy and Management and the Department of Biostatistics)
Dr. J. Hammitt
2.5 credits
Lectures, seminars. Two 2-hour sessions each week.

Topics include: methods and applications of cost-effectiveness and cost-benefit analysis for health program evaluation, medical technology assessment, and environmental risk analysis; theoretical foundations; "shadow" pricing; economic valuation of life saving; choice of discount rates; cost accounting applied to economic evaluation in institutional settings; methods for assessing costs of environmental controls; economic evaluation of biomedical research; health status indices; ethical issues; and modern critiques.
Course Note: HPB 280b, HPM 286s, HPM 205ab and HPM 206ab, or signature of instructor required.

ID 265c. Practice of Quantitative Methods (MPH Program)
Dr. M. Testa, Dr. R. Monson
2.5 credits
Lectures, seminars, case studies. Two 2-hour sessions each week.

Explores practical and conceptual issues in the design, conduct, analysis and evaluation of human studies through the discussion of current research and methodologies. Students design studies to address important health problems. Class discussion and group projects are emphasized.
Course Note: Acceptance into the MPH concentration in Quantitative Methods or signature of instructor required.

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