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: Practical projects in consultation and statistical analysis of data in research studies with health investigators. Course requirements include an approved practical work experience related to Biostatistics in consultation with a faculty advisor. May be elected more than once. Enrollment limited to Biostatistics majors with at least two full terms of prior registration.
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: Biostatistics 601 and Biostatistics 651
Description: This course is designed for individuals with a strong quantitative background who are interested in the statistical design and analysis aspects of clinical trials and the interface between statistics and policy in this area
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.
Prerequisites: Biostat 602 or STAT 511, and Biostat 650 or Perm. Instr
Description: First half covers theory and applications of rank and randomization tests: sampling and randomization models, randomization t-test, Wilcoxon rank sum and signed rank tests, Kruskal-Wallis test, asymptotic result under randomization, relative efficiency; second half covers theory and applications of nonparametric regression: smoothing methods, including kernel estimators, local linear regression, smoothing splines, and regression splines, methods for choosing the smoothing parameter, including unbiased risk estimation and cross-validation, introduction to additive models.
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.
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.
Description: It is an exciting time for research in population genetics. Technological advances are making it increasingly possible to obtain large numbers of genotypes from individuals in a population, and theoretical and algorithmic advances are improving the prospects for obtaining detailed inferences about populations and their evolutionary history. To make use of these dramatic advances in the field, it is important to understand the processes that act on populations and affect the properties of the genotypes that will eventually be drawn from these populations. In this course, by learning the mathematical models used in population genetics, students will learn how various population-genetic phenomena influence the properties of genetic variation. Students will also gain an understanding of the statistical methods used for analysis of population-genetic data.
The course is split into two major sections. The first section covers classical population genetics, including subjects first introduced by RA Fisher and S Wright. We cover Hardy-Weinberg equilibrium, natural selection in infinite and finite populations, stochastic effects in finite populations (drift), recombination and linkage disequilibrium, and admixture and population subdivision. Moreover, we cover the most commonly used models of mutation, such as the infinite sites model and the infinite alleles model. The goal of this section is to give students a broad understanding of the statistical principles underlying population genetics and to provide a connection between these classical results and modern challenges in statistical genetics.
In the second section of the course we cover coalescent theory. We introduce the basic coalescent model for constant Wright-Fisher populations. We then introduce commonly used extensions of this model to scenarios with recombination, population expansion and population subdivision. We introduce methods of parameter inference based on these models, including both simple method-of-moments estimates as well as more sophisticated Monte-Carlo based estimation methods. The goal of this section is to give students the ability to design realistic simulation algorithms and perform population genetic inference.
Classes on population structure and population admixture (~4) will be taught by Noah Rosenberg.
In the biweekly homeworks, we expect the students to be able to apply and extend the presented theory. Early in the course, each student will select a topic for a project; the student is expected to work on this project throughout the semester and to give at the end of the semester a written project report and a 20-minute presentation on the results of his analysis. Typical projects are
" Simulate a model of rare variants under mutation-selection balance and estimate power for rare variants testing methods.
" Calculate the contribution of low frequency variants to heritability in structured populations
" Perform a principal components analysis on genetic data
" Explore recent resequencing data for signs of natural selection.
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.
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.