Course Offerings
Core Curriculum grading policy July 09
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BIOST 2000: Teaching Practicum
Credit(s): 3.0; Term(s): Spring; Offered: Annually
This course will provide doctoral students with an opportunity to obtain teaching experience. This course is intended for doctoral students during their dissertation stage. Teaching experience will enhance the professional growth of students. Students will further develop oral and written communication skills and an art for explaining material, which is an integral part of a biostatistician's career.
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BIOST 2011: Principles of Statistical Reasoning
Credit(s): 3.0; Term(s): Fall, Summer; Offered: Annually
This is the Biostatistics
core course for the Graduate School of Public Health. Students obtain
an understanding of the concepts of statistical reasoning as applied
to the study of public health problems. This includes learning basic
terminology and its meaning, the calculations of various statistical
measures and indices, quantification of health relationships and
the interpretation of inferential statistical techniques. (admission
by permission of instructor for Summer Session); Prerequisite:
college algebra or a higher-level math course with a grade of C
or better
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BIOST 2015: Elements in Statistical Learning
Credit(s): 3.0; Term(s): Spring; Offered: Bi-annually
The purpose of the course is to present the theory and practice of statistical learning algorithms, placing "statistical learning" or "data mining" techniques in the proper context with regard to their origins in simple classical methods like linear regression, to clarify the strengths and weaknesses from theoretical and practical sides. "Supervised learning" techniques studied include using regularization and Bayesian methods kernel methods, basis function methods, neural networks, support vector machines, additive trees, boosting, bootstrap-based methods. Unsupervised learning techniques studied include cluster analysis self-organizing maps, independent component analysis and projection pursuit. Prerequisites: BIOST 2041, BIOST 2042, BIOST 2043 and BIOST 2044; or permission of instructor
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BIOST 2016: Introduction to Sampling
Credit(s): 2.0; Term(s): Spring; Offered: Annually
Presents practical
sampling methods and their theoretical background. Covers simple random,
stratified, systematic, and simple stage cluster sampling techniques;
also, ratio, regression, and difference estimation. Emphasizes sampling
human populations in large communities. Prerequisite:
BIOST 2011 or BIOST 2041; or permission of instructor
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BIOST 2018: Statistical Foundations for Bioinformatics
Data Mining
Credit(s): 3.0; Term(s): Spring; Offered: Bi-annually
Course introduces
data analysis methods widely used or rapidly gaining use in bionformatics.
Methods deal with prediction, classification, optimization, and
clustering and include classification trees, flexible varieties
of discriminant analysis including support vector machines. EM algorithm
and Monte Carlo Markov chain, bootstrap andbagging, boosting &
self-organizing maps. Methods are in context of principles and models
of statistical science, with emphasis on Bayesian methods. Examples
will be taken from microarrays, analysis of genetic networks, proteomics,
computational pharmacology, and research text mining. Prerequisite:
three credits of statistics or biostatistics; solid understanding
of basic principles of statistics; working knowledge of calculus;
and permission of the instructor
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BIOST 2021: Special Studies in Biostatistics
Credit(s): 1.0-15.0; Term(s): Fall, Spring, Summer; Offered: Annually
Advanced work with
approval or guidance of faculty member
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BIOST 2025: Biostatistics Seminar
Credit(s): 1.0; Term(s): Fall, Spring; Offered: Annually
Introduces current
health problems in biostatistics methods and theory. Includes seminars
from faculty at other academic institutions.
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BIOST 2040: Elements of Stochastic Processes
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
Covers generating
functions and convolutions of random variables, the Poisson and compound
Poisson distributions, ranching processes, random walk, and the gambler's
ruin problems, plus Markov chains, and simple birth and death processes.
Prerequisites: MATH 0240, BIOST 2034; or permission
of instructor
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BIOST 2041: Introduction to Statistical Methods 1
Credit(s): 3.0; Term(s): Fall, Summer; Offered: Annually
This course is an
introductory applied biostatistical course for students needing
a more comprehensive approach than provided in the Core Course (BIOS
2011). Topics covered include probability, confidence intervals,
estimation and hypothesis testing. Statistical procedures covered
include t-test, contingency tables, analysis of variance, linear
regression and basic nonparametric procedures. Prerequisite:
college algebra
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BIOST 2042: Introduction to Statistical Methods 2
Credit(s): 3.0; Term(s): Spring; Offered: Annually
This course constitutes
the second part of the basic sequence of applied statistical methods
(components BIOS 2041). The course covers nonparametric methods,
multiple linear regression, odds ratios, relative risk, logistic
regression, methods in survival analysis (Kaplan-Meier, lifetable
analyses, Cox proportional hazards models), multiple comparisons
procedures, the general linear contrast, multi-way ANOVA (general
fixed effects model, factorial design, qualitative and quantitative
interactions, randomized blocks, random effects models, repeated
measures) and analysis of covariance. Prerequisite:
BIOST 2041; or permission of instructor
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BIOST 2043: Introduction to Statistical Theory 1
Credit(s): 3.0; Term(s): Fall; Offered: Annually
Basic introduction
to statistical theory. Topics covered include joint, marginal and
conditional probabilities; moment generating and characteristic
functions; transformation of variables; convergence of random variables;
law of large numbers; and the central limit theorem. Prerequisite:
MATCH 0240; or permission of instructor.
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BIOST 2044: Introduction to Statistical Theory 2
Credit(s): 3.0; Term(s): Spring; Offered: Annually
Continuation of
the introduction to statistical theory introduced in BIOS 2043.
Topics covered include sufficiency, completeness, Rao-Cramer's inequality,
fundamentals of hypothesis testing, Neyman-Pearson Lemma, and likelihood
ratio tests. Prerequisite: BIOST 2043
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BIOST 2045: Analysis of Case-Control Studies
Credit(s): 2.0; Term(s): Spring; Offered: Annually
Teaches methods to
study health problems in community population groups. Covers measures
of disease occurrence and association for various study designs; classical
analysis of grouped and matched case-control studies. Both conditional
and unconditional logistic regressions are covered. Methods are given
for analyzing a variable number of controls for each case, assessing
the effect of multiple expansive levels, and assessing model fit.
Prerequisites: BIOST 2041, 2042; or BIOST 2041, 2042
concurrently; or permission of instructor
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BIOST 2046: Analysis of Cohort Studies
Credit(s): 3.0; Term(s): Fall; Offered: Annually
This introductory applied course in statistical modeling focuses on maximum likelihood and related regression methods for the analysis of cohort data. Topics include generalized linear models, generalized estimating equations, and generalized linear mixed models. The course emphasizes logistic and Poisson regression, and discrete survival models with time-dependent covariates. Students analyze several cohort data sets, assess the adequacy of their models, and interpret their results. Prerequisite:
BIOST 2042; and BIOST 2049
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BIOST 2049: Applied Regression Analysis
Credit(s): 3.0; Term(s): Spring; Offered: Annually
Covers the basics
of classical and modern regression techniques. Topics covered include
multiple regression, indicator variables, multicolinearity, selection
of a best model, influence diagnostics, and nonlinear regression.
Prerequisite: BIOST 2042; or permission of instructor
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BIOST 2051: Statistical Estimation Theory
Credit(s): 3.0; Term(s): Fall; Offered: Annually
This course covers
selected topics in classical estimation and builds on some of the
estimation topics covered in Biostatistics 2044. Topics covered
include comparisons of different methods of estimation, properties
of maximum likelihood estimations, brief overview of measure theory,
and the decision theoretic framework work for estimation. Although
this course is primarily theoretical practical issues are discussed
such as convergence problems when obtaining ,maximum likelihood
estimations, impact of missing data, and the role of some of the
recent computationally intensive methods. Prerequisite:
BIOST 2044; or permission of instructor
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BIOST 2052: Multivariate Analysis
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
Topics covered
include the multivariate normal distribution, estimation of the
mean vector and covariance matrix, distributions and uses of simple,
partial and multiple conclation correlation coefficients, the generalized T2
statistic, the distribution of the sample generalized variance,
multivariate analysis of variance and the multivariate Behrens-Fisher problem. Multivariate methods are
applied to repeated measures analysis, factor analysis, and discriminant
analysis. The beginning of the course emphasizes theory. Later applications
and computational methods are emphasized. Several lectures are devoted to the review and presentation of current and classical literature involving methods in multivariate analysis. Prerequisite:
BIOST 2044; or permission of instructor
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BIOST 2053: Nonparametric Methods in Statistics
Credit(s): 3.0
Order statistics
and quantiles: the U statistic and Hoeffding's theorem; ranks and
mid-ranks; Kendall's and Spearman's rank correlation coefficients;
the sign test; Kolmogorov-Smirnov and Cramer-Von Mises tests of
goodness of fit; rank (order) test; Mann-Whitney (Wilcoxon) rank
test; the several-sample problem; the Mood Brown median test; Mood's
median test; the Kruska-Wallis H test; Friedman's test; efficiency
of nonparametric tests; Pitman efficiency of tests. Prerequisite:
BIOST 2044; or permission of instructor
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BIOST 2054: Survival Analysis
Credit(s): 3.0; Term(s): Spring; Offered: Annually
Covers the basic
theoretical aspects of various models to analyze "time to event"
data. Introduces basic concepts such as the survival function, hazard
function, left and right hand censoring, and common parametric models
for analyzing survival data. Also includes the proportional hazards
model with fixed and time dependent covariates, the stratified PH
model, regression diagnostics for survival models, additive hazards
regression models and multivariate survival models. Prerequisite:
BIOST 2044; or permission of instructor
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BIOST 2055: Statistical Methods & Data Mining in Micro-array Analysis
Credit(s): 3.0; Term(s): Spring; Offered: Annually
In this course, we will discuss statistical methods and data mining techniques used in modern genomic experimental data. Special emphasis will be on microarray expression profiles though other related topics including protein-protein interaction and mass spectrometry data will also be touched. Some of the methods are typical traditional methods but many others are rapidly evolving which may not be taught in any standard statistical course. We will discuss statistical issues in data processing in various microarray platform. Gene screening, visualization, clustering and classification of microarray data will be emphasized. Methods of detecting genetic regulatory network will also be touched. R and Bioconductor will be mainly used as the software tool in class while many freely available packages will be introduced in hands-on labs. Prerequisite: One year of elementary statistical course (BIOST 2041 and BIOST 2042 or equivalent).
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BIOST 2056: Introduction to Diagnostic Test Evaluation and ROC Analysis
Credit(s): 3.0; Term(s): Spring; Offered: Annually
The course offers an introduction to the concepts and approaches common for the statistical assessments of diagnostic systems, technologies or practices. The course covers different measures of diagnostic accuracy, certain aspects of the design of accuracy studies, statistical estimation and hypothesis testing, sample size calculations and some of more advanced topics. The emphasis will be made on the applications in the diagnostic medicine. General prerequisites include knowledge of basic statistical concepts and approaches related to estimation and hypothesis testing (e.g. Biost 2041, 2042, 2043, 2044); some knowledge of the regression modeling and SAS statistical package is desirable.
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BIOST 2061: Likelihood Theory & Applications
Credit(s): 2.0; Term(s): Spring; Offered: Annually
The purpose of
this course is to introduce the student to modern likelihood theory
and its applications. The course will cover maximum likelihood theory,
profile likelihood theory, pseudo likelihood theory and generalized
estimating equations. The course is taught at the doctoral level
and much of the theory is illustrated through applications. Prerequisites:
BIOST 2043 and BIOST 2044
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BIOST 2062: Clinical Trials: Methods and Practice
Credit(s): 3.0; Term(s): Spring; Offered: Annually
Topics include: experimental designs for safety
and efficacy trials, quantitative methods for design, interim monitoring,
and analysis of randomized comparative clinical trials including
crossover, factorial and equivalence designs. Ethical, organizational,
and practical considerations of design and conduct of single and
multicenter studies are integrated in lectures and case studies.
The course also covers international guidelines on statistical considerations
for drug development, guidelines adopted for publication of trials
in major medical journals, and recommended approaches for meta-analyses.
Prerequisites: The equivalent of a one-term course
in introductory biostatistics is recommended. Permission of instructor.
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BIOST 2063: Bayesian and Empirical Bayes Statistical
Methods
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
Teaches how to use
Bayesian and empirical Bayes statistical methods in data analysis.
Gives examples and includes discussion of common data-analysis issues.
Compares and contrasts Bayesian, empirical Bayesian, and classical
methods. Topics covered include Savage axioms, conjugate priors,
the likelihood principle, noninformative priors, Empirical Bayes
and hierarchal Bayes approaches. Prerequisites: BIOST
2042, BIOST 2044
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BIOST 2064: Bayesian and Empirical Bayes Computational Methods
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
This course provides
the students with an understanding of both the theory and practice
with regard to the EM algorithm, Markov-chain, sampling techniques,
importance sampling, and the solution of decision trees. Students
gain hands-on experience programming with S-Plus. The course is designed
to complement BIOS 2063. Prerequisite: BIOST 2063
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BIOST 2065: Analysis of Incomplete Data
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
This course will introduce the missing-data problems and
implication in statistical inference. Naive methods, standard
likelihood-based methods, theory and application of multiple imputation,
data augmentation, Gibbs sampler, and some robust statistical methods will
be discussed. Need to program for the homework assignments or final project. Prerequisite: Calculus, linear algebra, and elementary
probability; BIOST 2043, BIOST 2044 and BIOST 2051; knowledge in categorical
data anlaysis or generalize linear models is recommended.
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BIOST 2066: Applied Survival Analysis
Credit(s): 3.0; Term(s): Fall; Offered: Annually
This course covers fundamental concepts and methods important for analysis of datasets where the outcome is the time to an event of interest, such as death, disease occurrence or disease progression. Topics include: basic methods for summarizing and presenting time-to-event in tabular form and graphically as life tables, non-parametric statistical techniques for testing hypotheses comparing life tables for two or more groups, approaches to fitting the semi-parametric Cox proportional hazard model and other commonly used parametric models that incorporate study covariables, methods for assessing goodness-of-fit of the models, and sample size considerations. In addition to didactic lectures, there are group projects that involve analysis of datasets and presentation of report on analyses. Prerequisite: BIOST 2042 and; BIOST 2049.
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BIOST 2081: Mathematical Methods for Statistics
Credit(s): 3.0; Term(s): Fall; Offered: Annually
This course is designed
to bridge the gap between students with an undergraduate mathematics
background and the mathematics required for the mathematical statistics
courses. It is recommended for students who meet only the minimum
requirement of one year of calculus at the time of entry into the
program. It covers selected topics in advanced calculus and linear
algebra. Prerequisite: 1 year of college calculus
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BIOST 2083: Linear Models
Credit(s): 3.0; Term(s): Fall; Offered: Annually
Teaches linear model
techniques for analyzing balanced and unbalanced data. Basic topics
covered include properties of quadratic forms, noncentral chi-square
and F distributions, best linear unbiased estimations, and likelihood
ratio test. Also covers generalized inverses, models not of full
rank, orthogonal contrasts with unbalanced data, regression on dummy
variables, analysis of covariance; and analysis of variance components.
Prerequisites: BIOST 2044, BIOST 2081; or permission
of instructor
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BIOST 2086: Applied Mixed Models Analysis
Credit(s): 3.0; Term(s): Fall, Spring; Offered: Annually
Mixed model analysis
provides a new approach to modeling which allows one to relax the
usual independence assumptiosn and take nito account comlicated
data structures. This course will consider all types of mixed models
into a general framework and consider the practical implications
of their use. Topics will include; normal mixed models, generalized
mixed models, and mixed models for categorical data, repeated measures
data analysis and cross-over trials with mixed models. Software
for fitting mixed models will be discussed. Prerequisites:
BIOST 2083; or permission of instructor
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BIOST 2087: Biostatistics Consulting Practicum
Credit(s): 1.0; Term(s): Fall, Spring; Offered: Annually
For second-year
master's and doctoral students. Provides exposure and experience
in consulting on the biostatistical aspects of research problems
in biomedical or allied fields. Students have discussions with investigators,
leading to the design or analysis of a current research problem.
Includes weekly group discussions with instructor. Prerequisite:
admission by permission of instructor
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Special
Topics 0-8: 2070(2), 2071(2), 2072 (2), 2075(3), 2076(3), BIOST
2088(1), 2089(1), 2090(3), 2091(1)
Credit(s): 1.0-3.0
Introduces the
student to specialized topics in biostatistics in areas of current
interest to the field. Two to four special topics courses
are given each year. These courses are given to broaden
the exposure of the students to the large variety of existing
methods and applications in biostatistics. Courses may be
one, two or three credits and may be given by faculty with secondary
appointments and visiting faculty as well as faculty with primary
appointments in the Department of Biostatistics. Special
topics given in recent years include: meta analysis, multiple
comparisons procedure in clinical trials, methods and applications
with ROC curves, special topics in mixed models, statistical methods
in AIDS research and smoothing techniques using splines. Prerequisite:
variable, depending on specific topic; permission of instructor
may be required for admission
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BIOST 2092: Introduction to Computing
Credit(s): 1.0; Term(s): Fall; Offered: Annually
Provides an overview of the University of Pittsburgh computing and electronic resources; An introduction to MINITAB, an interactive statistical software package for storing, displaying, summarizing and analyzing data. Both the command line and Windows menu approaches of the program will be presented; Techniques for computerized bibliographic database searching and the use of electronic library resources for public health.
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BIOST 2093: Data Management and Analysis
Credit(s): 1.0; Term(s): Fall; Offered: Annually
This course is intended to cover the utility of SAS as a data management, data manipulation, and data analysis tool. The focus of this course will not be statistical analysis, but rather how to use SAS as a programming tool. Emphasis will be placed on program code writing techniques. Illustrated examples from elementary descriptive statistical analyses will be presented.
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BIOST 2096: Numerical Methods in Biostatistics
Credit(s): 3.0; Term(s): Fall; Offered: Bi-annually
The purpose of
this course is to familiarize students with a broader range of numerical
methods which are useful in biostatistical research. Selected computational
techniques used in statistical research are covered. Some background
will be provided to facilitate understanding of a few numerical
algorithms widely used in statistics. The following topics are covered:
recurrence relations, power series and asymptotic expansions, generating
pseudo-random deviates, basic simulation methodology, solutions
of nonlinear equations, Newton's method, vector and matrix norms,
linear regression and matrix inversion, independent Monte Carlo and Markov Chain Monte Carlo methods. Prerequisites:
BIOST 2043 and BIOST 2044 and BIOST 2049; or permission of instructor
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BIOST 3010: Research and Dissertation for the Doctoral Degree
Credit(s): 1.0-15.0; Term(s): Fall, Spring Summer; Offered: Annually
Variable number
of credits assigned for work on student research dissertation.
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BIOST 3023: Geographic Information Systems
& Spatial Data Analysis
Credit(s): 3.0; Term(s): Fall; Offered: Annually
This course covers
the use of GIS and spatial data analysis techniques in empirical
public health research. Basic descriptive and analytical functions
of GIS are introduced along with spatial and geographic concepts.
The interrelationship between GIS and spatial data analysis will
be demonstrated through the use of specialized GIS and spatial data
analysis software with a particular emphasis on the study of spatial
patterns and spatial autocorrelation in public health research.
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FTDR 3999: Full-time Dissertation Study
Credit(s): 0.0; Term(s): Fall, Spring, Summer; Offered: Annually
For doctoral candidates
who have finished all credit requirements and minimum dissertation
requirements. Full-time work on dissertation. No credit. |
