Prerequisites: Statistics 401 or permission of instructor
Description: This course will make use of case studies to discuss problems and applications of biostatistics. Topics will include cohort and case control studies, survival analysis with applications in clinical trials, evaluation of diagnostic tests, and statistical genetics. The course will conclude with a survey of areas of current biostatistical research.
This course is cross-listed with Statistics 449 in the Literature, Science and the Arts department.
BIOSTAT502 Application of Regression Analysis to Public Health Studies
Description: Longitudinal data sets occur often in a Public Health setting. This course will introduce students to methods for analyzing both clustered and longitudinal data using the statistical software packages SAS and Stata.
Models for both continuous and discrete (e.g., binary, count) outcomes will be discussed and illustrated. The course will have one session of lecture and one session of lab per week.
The course will be driven primarily by using both software packages to analyze real data sets.
Prerequisites: BIOSTAT521; BIOSTAT501 w/ instructors permission.
Description: A second course in applied biostatistical methods and data analysis. Concepts of data analysis and experimental design for health-related studies. Emphasis on categorical data analysis, multiple regression, analysis of variance and covariance.
Description: Fundamental theory that is the basis of inferential statistical procedures. Point and interval estimation, sufficient statistics, hypothesis testing, maximum likelihood estimates, confidence intervals, criteria for estimators, methods of constructing test and estimation procedures.
Prerequisites: Graduate Standing and STAT400, BIOSTAT522, or BIOSTAT521 or permission of instructor
Description: The course will cover statistical methods used to analyze data in experimental molecular biology. The course will primarily cover topics relating to gene expression data analysis, but other types of data such as genome sequence and epigenomics data that is sometimes analyzed in concert with expression data will also be covered.
Description: Introduction to maximum likelihood estimation; exponential family; proportion, count and rate data; generalized linear models; link function; logistic and Poisson regression; estimation; inference; deviance; diagnosis. The course will include application to real data.
Description: Master's level seminar designed to provide an extensive review of a number of substantive and methods and skill areas in biostatistics. Readings, discussion, and assignments are organized around issues of mutual interest to faculty and students. Reviews and reports on topics required in the areas selected. May be elected more than once.
Description: The first half of the course concentrates on classical population genetics. We introduce topics such as Hardy-Weinberg equilibrium, models of selection for populations of infinite size and population subdivision.
The second half of the course focuses on coalescent theory, covering migration, changes in population size and recombination. We provide guidelines how these models can be used in to infer population genetic parameters. Finally, some recent results and methods from the population genetic literature are discussed.
Description: Regression models for the analysis of categorical data: logistic, probit and complementary log-log models for binomial random variables; log-linear models for cross-classifications of counts; regression models for Poisson rates; and multinomial response models for both nominal and ordinal responses. Model specification and interpretation are emphasized, and model criticism, model selection, and statistical inference are cast within the framework of likelihood based inference.
Description: This course will introduce the theory and methods of spatial and spatio-temporal statistics. It will present spatial and spatio-temporal statistical models and will discuss methods for inference on spatial processes within a geostatistical and a hierarchical Bayesian framework.
Prerequisites: Registration for last term of studies to complete MS or MPH
Description: Identifying and solving design and data analysis problems using a wide range of biostatistical methods. Written and oral reports on intermediate and final results of case studies required.
Prerequisites: Graduate level Biostatistics students only
Description: Presentations and discussions of current consulting and research problems. Enrollment limited to biostatistics majors. Students must attend 2/3 of all seminars offered during the semester to receive credit. Maximum credit is 0.5 per semester. No more than 1 credit total allowed. May only be taken a maximum of 2 semesters.
Prerequisites: Biostat 601, Biostat 602, and MATH 451 or equivalent
Description: This sequence covers advanced topics in probability theory, theory of point estimation, theory of hypothesis testing, and related large sample theory. This sequence replaces STAT 610/611 as biostatistics Ph.D. requirements.
Course Goals: The goal of the sequence is to provide broad and deep theoretical training to Biostatistics Ph.D. students. Such training is essential for success in their thesis research and their future career.
Competencies: The following competencies under Appendix 2.6.c in ``University of Michigan School of Public Health Self-Study -- Appendices" for Biostatistics PhD students are met:
2. Statistical techniques
a. Advanced Mathematical Statistics
b. Generalized Linear and Mixed Models
c. Advanced Biostatistical Inference
d. Stochastic Processes
j. Bioinformatics and analysis of high-throughput biological data
k. Survival analysis
m. Bayesian inference techniques
n. Nonparametric statistical methods
3. Mathematical foundation
The graduate must acquire mathematical proficiency to be able to pursue theoretical development of
statistical methods to address the needs of Biostatistical Inference.
BIOSTAT815 Advanced Topics in Computational Statistics
Prerequisites: BIOSTAT601, BIOSTAT602 and BIOSTAT615 or equiv and proficiency in C++
Description: Modern numerical analysis for statisticians. Combination of theory and practical computational examples illustrating the current trends in numerical analysis relevant to probability and statistics. Topics choose from numerical linear algebra, optimization theory, quadrature methods, splines, and Markov chains. Emphasis on newer techniques such as quasi-random methods of integration, the EM algorithm and its variants, and hidden Markov chains. Applications as time permits to areas such as genetic and medical imaging.
Description: Advanced training in biostatistical methods primarily for doctoral students. Format will include lectures, readings, presentations and discussions in an area of special interest to students and faculty, such as stopping rules and interim analysis in clinical trials, conditional and unconditional inference and ancillarity, or nonparametric regression.
Prerequisites: Biostat 601, Biostat 602, Biostat 666 or Perm. Instr.
Description: Advanced topics in quantitative genetics with emphasis on models for gene mapping, pedigree analysis, reconstruction of evolutionary trees, and molecular genetics experiments, computational mathematics, and statistical techniques such as Chen-Stein Poisson approximations, hidden Markov chains, and the EM algorithm introduced as needed.
Description: Lectures and readings from the literature on advanced topics in survival analysis. Covers regression for censored data, general event-history data and models, competing risks. Statistical, mathematical, and probabilistic tools used in survival analysis are extended for these general problems.
Prerequisites: Biostat 602 and 651, and at least one of Biostat 690, Biostat 851, Biostat 890, or Biostat 895 or Perm Inst.
Description: Statistical analysis of data sets with missing values. Pros and cons of standard methods such as complete-case analysis, imputation. Likelihood-based inference for common statistical problems, including regression, repeated-measures analysis, and contingency table analysis. Stochastic censoring models for nonrandom nonresponse. Computational tools include the EM algorithm, the Gibbs' sampler, and multiple imputation.