Description: Fundamental statistical concepts related to the practice of public health: descriptive statistics; probability; sampling; statistical distributions; estimation; hypothesis testing; chi-square tests; simple and multiple linear regression; one-way ANOVA. Use of computer in statistical analysis.
Description: Fundamental statistical concepts related to the practice of public health: descriptive statistics; probability; sampling; statistical distributions; estimation; hypothesis testing; chi-square tests; simple and multiple linear regression; one-way ANOVA. . Taught at a more advanced mathematical level than Biostat 503. Use of the computer in statistical analysis.
Prerequisites: EPID501 or EPID601 or EPID600; AND BIOSTAT522
Description: Statistical methods commonly used in environmental epidemiology. Emphasis on choosing appropriate statistical methods and subsequent interpretation. Topics include probability, measures of association and risk, sample size calculations, SMR and PMR analysis, logistic regression and survival analysis.
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 probability and distribution theory needed for statistical inference. Probability, discrete and continuous distributions, expectation, generating functions, limit theorems, transformations, sampling theory.
Prerequisites: One course in introductory statistics; Co-requisite Biostat 601 or equivalent or Perm. Instr
Description: This course provides incoming master's students in biostatistics with basic experience in SAS programming for data set creation and manipulation, an introduction to SAS macros, and SAS matrix manipulation.
Description: This short course introduces basic computational environments and tools to graduate students with limited prior experience. It will provide an introduction to UNIX systems, software compilation / installation, cluster job management as well as data formats, management, and visualization. A brief introduction to scripting programming languages will also be presented.
Course Goals: Students enrolled in the class will develop skills to accelerate their research in computational research environments. Topics will include an intensive introduction to (a) UNIX systems and software management, (b) data processing and simple programming, (c) data formats and visualization, and (d) software version and cluster control. This training will provide a computational foundation that will allow students to focus on the theoretical and biological aspects of their research.
Competencies: After completing this class, students are expected to be able to attain the following competencies:
• Navigate and organize UNIX files and folders
• Compile and install software in UNIX environments
• Understand basic programming data structures and processes
• Create simple scripts to manage and analyze data
• Utilize and apply popular file formats to modern large-scale data sets
• Apply proper visualization tools and strategies to view data
• Utilize software versioning technologies for documenting and organizing software
• Utilize high-throughput computing clusters for parallel data processing
This course is cross-listed with Biostat 606 = HG 606 = Bioinfo 606.
Description: A survey of key algorithms for statistical computing and its applications in Biostatistics. The course will cover fundamental computational techniques for dynamic programming, sorting, and searching, as well statistical methods for random number generation, numerical integration, function optimization, Markov-Chain Monte Carlo, and the E-M algorithm. Enables students to understand numerical results produced by a computer and to implement their own statistical methods.
BIOSTAT645 Time Series Analysis with Biomedical Applications
3 Credit Hour(s)
Not offered 2017-2018
Prerequisites: Biostat 602, Biostat 650 or Perm. Instr
Description: Introduction to statistical time series analysis with an emphasis on frequency domain (spectral) methods and their applications to biomedical problems. Topics include autocorrelation, stationarity, autoregressive and moving average processes, power spectra, periodgrams, spectral estimation, linear filters, complex demodulation, autoregressive integrated moving average (ARIMA) models, cross-correlation, cross-spectra, coherence, time and frequency domain linear regression. The methods will be illustrated in applications to various areas of public health and medical research such as environmental health, electrophysiology, and endocrinology.
Description: Graphical methods, simple and multiple linear regression; simple, partial and multiple correlation; estimation; hypothesis testing, model building and diagnosis; introduction to nonparametric regression; introduction to smoothing methods (e.g., lowess) The course will include applications to real data.
Description: Planning of experiments, use of contrasts in analysis of complete and incomplete block designs. A unified approach to analysis of designs through use of eigen-values and eigenvectors of the association matrix. A-D-E optimality criteria factorial exponents; efficiency of a design, confounding, fractional replication, response-surface designs, rotability criterion, mixture designs, analysis of two-way designs, analysis when blocks are random, applications in biological and biomedical problems.
Prerequisites: BIOSTAT650 and concurrent enrollment in BIOSTAT651
Description: This course provides an overview of statistical models and methodologies for analyzing repeated measures/longitudinal data. The course covers general linear models and linear mixed models for analyzing correlated continuous data, as well as marginal (i.e. GEE), conditional (i.e. generalized linear mixed model) and transition models for analyzing correlated discrete 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: Introduction to current statistical methods used in human genetics. Topics will include sampling designs in human genetics, gene frequency estimation, the coalescent method for simulation of DNA sequences, linkage analysis, tests of association, detection of errors in genetic data, and the multi-factorial model. The course will include a simple overview of genetic data and terminology and will proceed with a review of numerical techniques frequently employed in human genetics.
Description: Concepts and methods for analyzing survival time data obtained from following individuals until occurrence of an event or their loss to follow-up. Survival time models, clinical life tables, survival distributions, mathematical and graphical methods for evaluating goodness of fit, comparison of treatment groups, regression models, proportional hazards models, censoring mechanisms.
Prerequisites: Biostat 602, Biostat 650 and Biostat 651
Description: Introduction to Bayesian Inference. Bayesian large sample inference, relationship with maximum likelihood. Choice of model, including prior distribution. Bayesian approaches to regression generalized linear models, categorical data, and hierarchical models. Empirical Bayes methods. Comparison with frequentist methods. Bayesian computational methods. Assessment of sensitivity to model assumptions. Emphasis on biomedical applications.
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: EPID600, BIOSTAT522 and BIOSTAT523 for epid students; BIOSTAT650, BIOSTAT651 for biostat students
Description: The goal of this pilot course is to create an interdisciplinary educational experience for Ph.D. students in Epidemiology (also available as an optional elective for Masters students in Biostatistics) through a uniquely designed course that contains lectures on advanced biostatistical methods, but places them in the context of epidemiological applications.
Course Goals: Students enrolled in the class will learn about cutting edge statistical methods in these four contemporary topics that arise frequently in the present scientific context. These four topics are: (a) Modern techniques for model building and variable selection; (b) Methods for analyzing longitudinal data; (c) Spatial regression methods; (d) Methods for studies of interaction/effect modification. The course will equip the new generation epidemiologists with state-of-the-art statistical methods in these domains, and teach them the craft of translating a practical problem into mathematical equations. However, the entire theoretical learning process will be placed in the context of sophisticated modeling of data from large complex studies with a focused problem to solve. Data for the projects will come from two studies that Professors Park and Mendes de Leon are involved with: the Normative Aging Study (NAS) and the Chicago Health and Aging Project (CHAP).
Competencies: After completing this class, students are expected to be able to attain the following competencies:
•Describe preferred methodological alternatives to commonly used statistical methods when assumptions are not met.
•Distinguish among the different measurement scales and the implications for selection of statistical methods to be used based on these distinctions.
•Apply descriptive techniques commonly used to summarize public health data.
•Apply common statistical methods for inference.
•Apply descriptive and inferential methodologies according to the type of study design for answering a particular research question.
•Interpret results of statistical analyses found in public health studies.
•Develop knowledge to communicate and collaborate effectively with scientists in a variety of health-related disciplines to which biostatistics are applied (e.g. public health, medicine, genetics, biology; psychology; economics; management and policy).
•Become well-versed in the application of core statistical techniques (biostatistical inference, linear regression, generalized linear models, nonparametric statistical methods, linear mixed models) and 4-5 selected statistical specialization techniques.
•Select appropriate techniques and apply them to the processing of data from health studies.
•Interpret the results of statistical analysis and convert them into a language understandable to the broad statistical community.
•Develop written and oral presentation skills and other scientific reporting skills, based on statistical analyses for public health, medical and basic scientists and educated lay audiences
•Employ state-of-the-art statistical and other quantitative methods in the analysis of epidemiologic data.
•Demonstrate a thorough understanding of causal inference, sources of bias, and methods to improve the validity of epidemiologic studies.
•Understand the principles and methods of data-collection and data-processing procedures in the design and conduct of epidemiologic research, with sound knowledge of measurement validity and reliability, data quality control, data management, documentation, and security
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 is the first course of the sequence that 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: The purpose of this class is to describe biostatistical research that is occuring in collaboration with cancer researchers, and to provide exposure to the field of cancer research. Activities inlcude seminars on statistical methods in cancer; presentations of cancer research; presentations of articles from statistical literature; discussion of cancer clinical tiral protocals and grant proposals; and visits to research laboratories. Students formally in the training program are expected to enroll in this course every semester. The course is open to students not participating in the training grant. It is open to both PhD and Masters students.
Description: This course will cover a series of topics that encompass Responsible Conduct of Research and Scholarship (RCRS) as defined by the National Institutes of Health (NIH), as well as focus upon the written and oral communication skills necessary for effective collaboration with public health investigators.
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: BIOSTAT617, BIOSTAT650, BIOSTAT651, or instructor permission
Description: This course examines a range of statistical regression analysis techniques for modeling survey data, and presents methods to compensate for design features for complex sample survey data. Course topics include likelihood estimation and testing; application of likelihood methods to linear and generalized linear models, including logistic, probit, generalized (multinomial) logit, Poisson, and negative binomial models; time-to-event (survival analysis) models; regression models for longitudinal data; and propensity score and Bayesian regression modeling.
Prerequisites: Math 417, Biostat 602, Biostat 651 and one of Biostat 690, Biostat 851, or Biostat 890
Description: Mixed model analysis of variance; multivariate profile analysis; linear mixed effects models with unbalanced designs, time-varying covariates, and structured covariance matrices; maximum likelihood (ML), restricted maximum likelihood (REML), and Bayes estimation and inference; nonlinear mixed effects models.
Prerequisites: Biostat 651 and Biostat 695 or Perm. Instr.
Description: Probability models for two-way tables; multi-factor, multi-response framework; product multinomial distribution theory; Taylor series estimates of variance, weighted least squares and Wald statistics; constraint equations; models for characterizing interactions; step-wise variable selection; factorial designs with multinomial responses; repeated measurement experiments; log-linear models; paired-choice and bioassay experiments; life-table models.