Graduate School of Biomedical Sciences

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Biostatistics

Degrees Offered
Doctor of Philosophy
Master of Science (limited availability)


Dual-Degree Program
Students with outstanding academic records who have been accepted into the MD program may apply for admission to a combined degree program leading to the MS and MD or to the PhD and MD degrees. Completion of the dual-degree program usually requires a minimum of seven years.


Program Admissions Requirements
In addition to the general Graduate School admission requirements, this program has additional specific requirements.

Any graduate of an accredited college or university with an undergraduate degree in mathematics or closely related fields with strong preparation in mathematics is eligible for admission. Applicants are expected to have completed and performed well in courses in advanced calculus, linear/matrix algebra and scientific programming. Those who haven’t done so may be considered for admission to the program upon approval of the biostatistics admission committee, and if admitted, these requirements must be completed during the first year of study. In addition, the applicant must have strong interest in pursuing statistical research in biomedical sciences.


Fields of Research

  • Nonlinear time series analysis, Markov chain Monte Carlo, statistical methods for epidemiology and biology. (Dr. Ahn)
  • Survival analysis competing risks theory, nonparametric statistics. (Dr. Brazauskas)
  • Bayesian statistics, linear and generalized linear models, nonparametric inference and Monte Carlo methods. (Dr. Laud)
  • Multiple comparisons, dose-response studies, clinical trials, multiple endpoints, fMRI analysis. (Dr. Logan)
  • Categorical and correlated data analysis, statistical models in epidemiology. (Dr. Szabo)
  • Estimation with additional information, missing data, censored and partially grouped data, survey data. (Dr. Tarima)
  • Statistical genetics, linkage and association mapping, haplotype analysis. (Dr. Wang)
  • Survival analysis, inference from stochastic processes and non-linear models. (Dr. Zhang)


*  Indicates University of Wisconsin Milwaukee (UWM) course number. All UWM courses require an off-campus course registration procedure.


Overall Course Requirements
A requirement of this program is to fulfill two credits in Bioethics by completing Course (10222) Ethics and Integrity in Science and Course (10444) Research Ethics Discussion Series.  For course descriptions of 10222 and 10444 see listing within the Bioethics Program.




Required courses for the PhD degree include:

10222 Ethics and Integrity in Science. 1 credit.
10444 Research Ethics Discussion Series. 1 credit.
04224 Biostatistical Computing. 3 credits.
04221 Theory of Statistical Consulting. 2 credits.
04222 Statistical Consulting. 1-3 credits.
04214 Design and Analysis of Clinical Trials. 3 credits.
04275 Applied Survival Analysis. 3 credits.
04285 Introduction to Bayesian Analysis. 3 credits.
04231 Statistical Models and Methods I. 3 credits.
04232 Statistical Models and Methods II. 3 credits.
04233 Statistical Models and Methods III. 3 credits.
MTHSTAT 761 * Mathematical Statistics I. 3 credits.
MTHSTAT 762 * Mathematical Statistics II. 3 credits.
MTHSTAT 564A * Time Series Analysis. 3 credits.
MTHSTAT 571* Introduction to Probability Models. 3 credits.
04313 Advanced Statistical Computing. 3 credits.
04363 Advanced Statistics. 3 credits.
04365 Linear Models I. 3 credits.
04384 Statistical Genetics. 3 credits.
04385 Advanced Bayesian Analysis. 3 credits.
04386 Theory of Survival Analysis. 3 credits.

04399 Doctoral Dissertation. 9 credits.

A minimum of six credit hours of electives in a biology-related field is a requirement for a candidate seeking the PhD degree in Biostatistics.


Required courses for the MS degree include:

04214 Design and Analysis of Clinical Trials. 3 credits.
04224 Biostatistical Computing. 3 credits.
04231 Statistical Models and Methods I. 3 credits.
04232 Statistical Models and Methods II. 3 credits.
04233 Statistical Models and Methods III. 3 credits.
MTHSTAT 761 * Mathematical Statistics I. 3 credits.
MTHSTAT 762 * Mathematical Statistics II. 3 credits.
04275 Applied Survival Analysis. 3 credits.
04285 Introduction to Bayesian Analysis. 3 credits.
04221 Theory of Statistical Consulting. 2 credits.


Also for the MS Degree any two of the following courses:

MTHSTAT 564A * Time Series Analysis. 3 credits.
MTHSTAT 571 * Introduction to Probability Models. 3 credits.
04313 Advance Statistical Computing. 3 credits.
04363 Advance Statistics I. 3 credits.
04365 Linear Models I. 3 credits.
04384 Statistical Genetics. 3 credits.
04385 Advanced Bayesian Analysis. 3 credits.
04386 Theory of Survival Analysis. 3 credits.


Oral Exam
Students seeking a MS degree will select an examination committee consisting of an advisor and two additional graduate faculty members. The composition of the committee must be approved by the Director of Graduate Studies and the Division Director. This committee will administer an oral exam over the material covered by the student in his or her course of study. The length and content of the exam will be determined by the committee. At the end of the examination, the committee will vote on the student’s performance on the examination. A majority vote is needed for passage. Students who fail this oral exam can take it a second time.

Writing Requirement
Students seeking a MS degree are required to prepare written reports on two consulting/collaborative research projects. These reports should include a description of the biological problem, a discussion of the statistical methods used in the analysis and a presentation of results. The reports must be written for presentation to the clinical investigator and not be focused wholly on statistical techniques. A guide to writing consulting reports can be found in The Statistical Consultant in Action by D.J. Hand and B.S. Everitt, Cambridge University Press, 1987.

 



Courses

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.

Contact Information

Graduate School of
Biomedical Sciences
8701 Watertown Plank Rd.
Milwaukee, WI 53226

Phone: 414-955-8218
Fax: 414-955-6555
gradschool@mcw.edu

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MCW Biostatistics News

International Conference on Survival Analysis in Memory of J.P. Klein

April 29 - The Division of Biostatistics will host an International Conference on Survival Analysis in Memory of John P. Klein, on Thursday, June 26, and Friday, June 27, in the Kerrigan Auditorium.

Biotechnology and Bioengineering Center launches Visiting Faculty Program

Feb. 11 - The Biotechnology and Bioengineering Center has launched a Visiting Faculty Program that will bring exceptional researchers to the Medical College of Wisconsin for long-term visits. These visiting scholars will present seminars and establish collaborations with MCW faculty during their appointments.

Dr. Prakash Laud appointed Acting Director of the Division of Biostatistics

Sept. 16 - Dr. Purushottam “Prakash” Laud, PhD, has accepted my offer to serve as the Acting Director of the Division of Biostatistics in the MCW Institute for Health and Society.

Congratulations to the Class of 2012

The 99th annual commencement took place on May 18 at the Milwaukee Theatre, at which the Medical College of Wisconsin and its Graduate School of Biomedical Sciences awarded 202 MD, 38 PhD, 27 MS, 4 MA, and 18 Master of Public Health degrees, as well as bestowed numerous honors.

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Page Updated 03/27/2014