Department of Biostatistics
Courses Offered
Course List

Course Description

P6100 Introduction to vital statistics
1 point.
Mass data of the health fields; the content of vital statistics; methods of collecting, tabulating, and graphing population data; A discussion of vital indices and the distinction between crude, specific and adjusted rates. Direct standardization. Life Table Analysis.

P6103 Introduction to biostatistics
3 points.
This course covers the language of biostatistics and the standard techniques of data collection and analysis. It is designed as a first semester course and includes topics discussed in Public Health P6100. The inferential topics include the Normal distribution, measures of central tendency and despersion, hypothesis testing, confidence intervals, regression and correlation.

P6104 Introduction to biostatistical methods
4 points.
An enriched core course for students majoring in biostatistics and others who expect to take additional courses in biostatistics such as Public Health P8100, P8111, P8120, or P8129. It covers in greater depth all of the topics in P6103, and is the best preparation for students anticipating a quantitative orientation in their degree programs. Topics covered include standard distributions, measures of central tendency and dispersion, hypothesis testing, point estimation, confidence intervals, and an introduction to correlation and regression.

P6105 Introductory probability with statistical applications
3 points.
Corequisite: Public Health P6104. Intended for M.P.H. students concentrating in biostatistics and for other students likely to take advanced courses in biostatistics. Develops probability models for discrete and continuous variables, and illustrates their applications to inferences about contingency tables, to nonparametric problems, and to estimation using maximum likelihood.

P6110 Statistical and computer methods in health data
3 points.
Uses of the computer in cleaning, summarizing, and cross-classifying data. Expansion of the material covered in Public Health P6103 - regression, correlation and contingency table analysis, and the analysis of variance - with data analysis carried out using standard statistical packages.

P8100 Applied regression analysis
3 points.
Prerequisite: Public Health P6104. The study of linear statistical models. Regression and correlation with one independent variable. Partial and multiple correlation. Multiple and polynomial regression. Single factor analysis of variance. Simple logistic regression.

P8104 Probability
3 points.
Prerequisite: Public Health P6104. Suggested preparation: Working knowledge of calculus. Fundamentals, random variables, and distribution functions in one or more dimensions; moments, conditional probabilities, and densities; Laplace transforms and characteristic functions. Infinite sequences of random variables, weak and strong large numbers; central limit theorem.

P8108 Survival analysis
3 points.
Prerequisite: Public Health P6105 or the equivalent. Clinical trials concerning chronic disease, comparison of survivorship functions, parametric models for patterns of mortality and other kinds of failures, and competing risks.

P8109 Statistical inference
3 points.
Prerequisite: Public Health P8104. Suggested preparation: P6104, P8104 and working knowledge of calculus, population parameters, sufficient statistics. Basic distribution theory. Point and interval estimation. Method of maximum likelihood. Method of least squares regression. Introduction to the theory of hypothesis testing. Likelihood ratio tests. Nonparametric procedures. Statistical design theory.

P8110 Topics in biometry
3 points.
Prerequistites: Public Health P6104, P8100. An introduction to the application of statistical methods in survival analysis, generalized linear models, and design of experiments. Topics to be covered include estimation and comparison of survival curves, regression models for survival data, log-linear models, logit models, analysis of repeated measurements, and the analysis of data from blocked and split-plot experiments. Examples will be drawn from the health sciences.

P8111 Linear regression models
3 points.
Prerequisite: Public Health P6105 and some computer background. The theoretical background underlying regression techniques. Simple regression. Bivariate normal distribution and correlation. Multiple and polynomial regression.

P8113 Wavelets: Concepts and applications in biostatistics
3 points.
Permission of instructor required.  Provides students with both a solid background in the foundations of wavelets and a detailed overview of a variety of statistical applications.  Upon completion, students can evaluate whether wavelets will be useful in new problems, and if so, work out basic methods of applying wavelets to such situations. 

P8116 Design of medical experiments
3 points.
Prerequisite: Public Health P8111 or the equivalent. Principles in the design and analysis of controlled experiments: Sample size and power, reliability of measurement, the parallel-groups design, factorial designs, blocking, stratification, analysis of covariance, the crossover study, latin squares.

P8117 Nonparametric statistics
3 points.
Prerequisite: Public Health P6104 or the equivalent. Presentation of statistical techniques valid for data from distributions requiring minimal assumptions. Topics include rank tests, permutation tests, contingency tables, rank correlation methods, analysis of variance and regression methods for ranked data, and methods of nonparametric survival analysis.

P8121 Generalized linear models
3 points.
Prerequisites: Public Health P8111 and Statistics W4107. An examination of a generalization of the classical regression model. Topics include log-linear models for count data, probit and logit models, analysis of data with discrete ordered responses, and analysis of continuous data where the variability increases with the mean. Survival analysis and model checking are discussed as time allows.

P8129 Theory of multivariate analysis
4 points.
Prerequisite: Public Health P8111 or the equivalent. Thorough review of matrix algebra; inverses; orthonormalization; affine transformations; eigenvectors and eigenvalues. The multivariate normal distribution. Multivariate sampling distributions. The multivariate general linear model. Hotelling's T².

P8133 Sequential experimentation
3 points.
Prerequisites: Public Health P6105 and P8111 or their equivalents. An introduction to sequential analysis as it applies to statistical problems in clinical trials, hypothesis testing, selection, and estimation. Emphasis is placed on a study of procedures, operating characteristics, and problems of implementaion, rather than mathematical theory. Students obtain an overview of currently available sequential designs and the advantages and disadvantages they offer in comparison with classical designs.

P8139 Theoretical genetic modeling
3 points.
Prerequisite: probability, genetics (at least one course each). Permission of instructor is also required. 
The theoretical foundations underlying models and techniques used in mathematical genetics and genetic epidemiology. Topics include (but are not limited to): use and interpretation of likelihood methods; formulation of mathematical models; segregation analysis; ascertainment bias; linkage analysis; genetic heterogeneity; and complex genetic models.

P8140 The randomized clinical trial
2 points.
Prerequisite: Public Health P6104 or the equivalent. Fundamental methods and concepts of the randomized clinical trial: protocol development, randomization, blindedness, patient recruitment, informed consent, compliance, sample size determination, crossovers, collaborative trials. Each student prepares and submits the protocol for a real or hypothetical clinical trial.

P8141 Genetic analysis laboratory
3 points.
Prerequisite: Public Health P6104, P8175, and the instructor's permission.  Provides students with a hands-on feel for the problems and vagaries of genetic linkage data.  Students use computer simulation to human linkage data under a variety of conditions - varying such parameters as the mode of inheritance, penetrance, gene frequency, and heterogeneity - and then analyze those data using both correct and incorrect assumptions about the true origin of the data.  In so doing, students gain an understanding of the variation in the results that occurs due to random factors and also acquire insights into the reliability of results.  Topics include basics of linkage analysis, mode of inheritance assumptions, heterogeneity, complex models, ascertainment, multipoint analysis.

P8149 Statistical aspects of human population genetics
3 points.
Prerequisites: probability, genetics (at least one course each). Permission of instructor is also required.  Fundamental principles of population genetics, with emphasis on human populations.  Genetics drift, natural selection, nonrandom mating, quantitative genetics, linkage analysis, and application of current technology (e.g., SNPs).  Students master basic principles of population genetics and are able to model these principles mathematically/statistically.

P8150 Topics in applied statistics
3 points.
Prerequisites: Public Health P8111 and Statistics G4107. This course will present some recently developed ideas in applied statistics including the EM algorithm; the jackknife, bootstrap, other resampling methods; model selection; and regression diagnostics.

P8151 Methods of statistical adjustment
3 points.
Prerequisite: Public Health P6104. A survey intended to introduce students to the wide variety of techniques available for the statistical adjustment of data, with an emphasis on broad coverage rather than depth. Techniques for testing and estimation with covariate adjustment including stratification, matching, direct and indirect standardization of rates, analysis of covariance linear and logistic regression models, conditional likelihood methods, piecewise exponential, and Cox regression models in survival analysis.

P8157 Analysis of repeated measurements
3 points.
Prerequisite: Public Health P8111. Topics include features of repeated measurements studies: balance in time, time-varing covariates, and correlation structure. Examination of the models for continuous repeated measures based on normal theory: random effects models, mixed models, multivariate analysis of variance, growth curve models, and autoregressive models. Nonparametric approaches and models for repeated binary data. Applications of generalized linear models to repeated data. Empirical Bayes approaches are discussed as time allows.

P8175 Principles of genetics for biostatisticians 
3 points.
Prerequisite: Public Health P6104.  A one-semester course on the fundamentals of genetics necessary to understand statistical methods used in genetics.  Methods are based on biological principles shared by many aspects of statistical research in genetics.  Students must be familiar with these concepts before taking more advanced courses.  Tailored to biostatistics students: focuses on biological phenomena necessary for understanding statistical genetics and demonstrates how principles of genetics are translated from biological phenomena to applied mathematical methodologies.

P9105 Topics in the analysis of longitudinal studies
3 points.
Prerequisite: Public Health P8108 or the equivalent. Seminar for advanced students planning to pursue doctoral work in this area. Reading of recent articles of theoretical and practical importance for the planning and analysis of long-term longitudinal studies. Lectures, discussions, presentations by students.

P9107 Statistical modeling for data analysis I
4 points.
Prerequisites: Public Health P8109 or equivalent; familiarity with matrix algebra.

P9108 Statistical modeling for data analysis II
4 points.
Prerequisite: Public Health P9107 or instructor's permission.
This two-semester sequence will be a core course in modern methods of applied statistics for doctoral candidates in Statistics and Biostatistics. It will complement and parallel the existing core requirements in probability and methematical statistics. The course will be an intensive survey of statistical data analysis within an interactive comuting environment. Assignments requiring computer analysis of scientific data will be due approximately every week. Topics from the subjects of regression, ANOVA, ANOCOVA, design of experiments, random effects, variance components, contingency tables, logistic regression, survival curves, time series, and multivariate analysis will be included. These toics will be covered in less depth and with less mathematical formalism than in other courses in Statistics and Biostatistics that devote and entire semester to some of the above subjects. However, the lectures will assume a doctoral level of sophistication during presentation of the theoretical bases of each method, and of the connections and relationships among methods. The mechanics of computer usage will not be discussed in lectures but will be covered in a weekly recitation section.

P9109 Theory of statistical inference I
4.5 points.
Prerequisite: Statistics G6105 (Real analysis and probability theory), or the equivalent. Suggested preparation: This is a doctoral level course. A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, uniformity, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymptotic properties. Likelihood ration tests, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis.

P9110 Theory of statistical inference II
4.5 points.
Prerequisite: Public Health P9109; this is a continuation of that course. A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, uniformity, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymtotic properties. Likelihood ratio test, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis.

P9111 Asymptotic statisics
3 points.
Prerequisite: Public Health P9110; A comprehensive introduction to the field of asymptotic statistics. The first half is a review of most of the standard topics of limit theory, such as the delta method and central limit theorems, while avoiding many technicalities. The second half presents advanced topics such as semiparametric models, counting processes, empirical likelihood, the bootstrap, and empirical processes.

P9145 Advanced statistical methods in AIDS research
3 points.
Prerequisite: Public Health P8108 or the equivalent. Seminars for advanced students planning to pursue doctoral work in this area. Reading of recent articles with theoretical results for the analysis of HIV/AIDS studies.

P9154 Discrete statistical analysis
3 points.
Prerequisites: P8104 and P8109. Discrete univariate and multivariate distributions; sampling models for discrete data; maximum likelihood and best asymptotically normal estimation; asymptotic behavior of goodness of fit statistics; homogeneity of association and symmetry in multiway contingency tables; log-linear models; polytomous logistic regression.

P6190, P8190, P9190 Tutorials in biostatistics
1 to 6 points.
For appropriately qualified students wishing to enrich their programs by undertaking literature reviews, speical studies, or small group instruction in topics not covered in formal courses.