04200 Biostatistics I. 3 credits.
This is an introductory course in biostatistical methods for non-biostatistics majors. Topics include elementary probability, sampling, point and interval estimation and hypothesis testing.
04201 Biostatistics II. 3 credits.
A continuation of Biostatistics I. Topics include statistical methods for categorical data, regression and correlation, and analysis of variance.
04202 Principles of Biostatistics. 1 credit.
This course provides an introduction to statistical concepts used in medical research at a non-mathematical level. Topics include introduction to study designs, descriptive statistics, probability, estimation, test of hypothesis, regression and correlation.
04214 Design and Analysis of Clinical Trials. 3 credits.
The clinical trial protocol, sources of bias in clinical trials, blinding, randomization, sample size calculation; phase I, phase II, phase III and hybrid trials; interim analysis, stochastic curtailment, Bayes designs, and administrative issues in study design.
04220 Research Seminar. 1 credit.
Students present plans for an analysis of research projects and research data. Projects and examples from classical and current literature are discussed by students and faculty.
04221 Theory of Statistical Consulting. 2 credits.
Theory of consulting, statistical techniques most often used in consulting, practical experience in the real consulting setting and writing statistical reports.
04222 Statistical Consulting. 1-3 credits.
This course is designed for students to gain experience in statistical consulting by working with the biostatistics faculty members on various consulting projects.
04224 Biostatistical Computing. 3 credits.
This course will cover the details of manipulating and transforming data required for statistical analysis, such as reshaping the data from a per case to a per event within a case and vice-versa. It will also cover the techniques necessary to write functions and macros in both SAS and S-Plus for developing new/modified data analysis methods. Students are expected to be facile in the use of computers before they take this course. Admission is only by consent of instructor.
04231 Statistical Models and Methods I. 3 credits.
Models and analyses for count data and contingency tables, basic nonparametric methods including sign, rank-sum and signed-rank tests, simple linear regression model and inference, checking model assumptions, correlation analysis, one-way and two-way analysis of variance. Emphasis is on models, their application to data and interpretation.
04232 Statistical Models and Methods II. 3 credits.
Factorial, nested, split-plot and repeated measures designs, multiple regression and variable selection, multiple comparisons, logistic regression, discriminant analysis, principal components and factor analysis, rates and proportions, introduction to survival analysis.
04233 Statistical Models and Methods III. 3 credits.
Model diagnostics in regression analysis, influence and leverage, outliers, collinearity, remedies including transformations and ridge regression; Models for discrete data, two-way and multi-way tables, loglinear models, analysis of loglinear models, Mantel-Haenszel test, models for ordinal variables, multinomial response and matched pairs, analysis of repeated response data.
MTHSTAT 761 * Mathematical Statistics I. 3 credits. (UWM registration)
Fundamentals of probability, independence, distribution and density functions, random variables, moments and moment-generating functions, discrete and continuous distributions, exponential families, location and scale families, marginal and conditional distributions, transformation and change of variables, multivariate distributions, random samples, convergence concepts, sampling from normal distributions, order statistics.
MTHSTAT 762 * Mathematical Statistics II. 3 credits. (UWM registration)
Point estimation, interval estimation, hypothesis testing, minimal sufficiency and completeness, ancillary statistics, likelihood and invariance principle, asymptotic properties of estimators and likelihood ratio tests, LMP tests, union-intersection tests, pivotal quantities, coverage probability, large-sample estimation and testing.
MTHSTAT 564A * Time Series Analysis. 3 credits. (UWM registration)
An introduction to univariate and bivariate time series with emphasis on stationary ARIMA processes, Box-Jenkins model building and forecasting, spectral representation of stationary time series, model testing and diagnostic evaluation, piecewise nonlinear models, and bivariate ARMA processes.
04265 Nonparametric Statistics. 3 credits.
Nonparametric statistical methods for estimation and testing as an alternative to the commonly used normal-theory models. Topics include order statistics, goodness of fit tests, tests based on ranks, association analysis, power and efficiency of nonparametric tests.
04275 Applied Survival Analysis. 3 credits.
Basic parameters in survival studies; Censoring and truncation, Competing risks; Univariate estimation including the Kaplan-Meier and Nelson-Aalen estimator; tests comparing two or more populations, the log rank test; Semi-parametric regression, the Cox model; Aalen’s Additive hazards regression model; regression diagnostics.
MATHSTAT 571* Introduction to Probability Models. 3 credits.
Markov chains in discrete and continuous time, Poisson processes, random walks, branching processes, birth and death processes, queuing systems, applications to survival and other biomedical models.
04285 Introduction to Bayesian Analysis. 3 credits.
This course introduces basic concepts and computational tools for Bayesian statistical methods. Topics covered include one and two sample inference, regression models and comparison of several populations with normal, dichotomous and count data.
04295 Reading and Research. 1-9 credits.
Readings in recent literature and supervised research project.
04313 Advanced Statistical Computing. 3 credits.
Numerical algorithms useful in biostatistics including likelihood maximization using the Newton-Raphson method, numerical integration using quadrature and Monte Carlo methods, interpolation using splines, random variate generation methods, the data augmentation algorithm, Markov chain Monte Carlo and the Metropolis-Hastings algorithm.
04363 Advanced Statistics I. 3 credits.
Exponential family of distributions: likelihood, score, information, mle; asymptotic related to likelihood, Wald, Score, and Likelihood Ratio statistics, delta method; types of likelihoods, e.g. marginal, conditional and profile likelihood; generalized estimating equations and quasi-likelihood; multiple comparisons.
04364 Advanced Statistics II. 3 credits.
A mathematically rigorous survey of selected topics in the theory of statistical inference such as sequential analysis, robust procedures, resampling plans—jackknife and bootstrap, decision theory, minimax analysis and variance components.
04365 Linear Models I. 3 credits.
Review of matrix algebra and vector spaces, multivariate normal distribution and quadratic forms, least squares estimation, testing nested models, weighted least squares, one-way ANOVA, testing contrasts, multiple comparison, partial and multiple correlation coefficients, polynomial regression, lack-of-fit tests.
04371 Probability Theory. 3 credits.
Mathematically rigorous definitions of probability space, random variable, random vector, stochastic process, absolute continuity and the Radon-Nikodym derivative, integration and expectation, independence, Borel-Cantelli lemma, zero-one laws, conditional expectation, martingales and submartingales, the martingale convergence theorem, sums of independent random variables, infinitely divisible laws and stable laws, the Central Limit Theorem.
04384 Statistical Genetics. 3 credits.
Fundamental elements of mathematical and population genetics, and statistical theory of the methods of human genetic analysis. Topics include Hardy-Weinberg equilibrium, models for polygenic and multifactorial inheritance, variance components estimation familial aggregation, linkage and association analysis, disequilibrium mapping and ascertainment problems.
04385 Advanced Bayesian Analysis. 3 credits.
A combination of Bayesian principles, tools and methods; emphasis is on models, computations and analysis. Likelihood function, prior, posterior and predictive distributions, Bayes factors, HPD regions, conjugate and non-informative priors in the exponential family, Markov chain Monte Carlo methods for the generalized linear model, hierarchical models, restricted parameter spaces and censored data, examples of Bayesian analyses of complex biomedical models.
04386 Theory of Survival Analysis. 3 credits.
Analysis of survival data using counting process techniques. Topics include the mathematical theory of counting process, censoring and truncation, estimation of the survival and cumulative hazard functions, extensions of k sample nonparametric tests to censored and truncated data, proportional hazards and additive hazards regression models.
04391 Special Topics in Statistics. 1-3 credits.
This course is designed to cover special topics in biostatistics that are not covered in regular courses. The topics will depend on the research interests of the instructor and the students.
04399 Doctoral Dissertation. 9 credits.