Courses in Quantitative
Methods at
HGSE and Harvard
There are a great
many courses in quantitative methods
available at the Harvard Graduate School of Education and
Harvard University, at different levels of technicality and practicality.
They are listed
below, by academic department, each with a course number, a brief description
of the content,
and the name of the professor(s) responsible for the course:
Introductory
to the concepts, principles and vocabulary of quantitative methods.
Prerequisite: none (restricted to entering doctoral students
in APSP).
Introduction
to the fundamental principles of educational measurement designed
for students who will need to evaluate test-based information in
their later work. The course has three main goals. First, it will
provide a context for understanding assessment results students
will encounter outside the course. Second, the course will provide
a basic understanding of essential concepts in measurement, such
as reliability, validity, and bias. Third, the course will apply
these principles to a variety of current issues in education policy.
Empirical
Methods: Introduction to Statistics for Research
Introduces
basic principles of elementary statistics, for students who want
to continue course work in statistical methods. Prerequisite:
none, for master's and first-year doctoral students.
Students
will learn how to use correlation analysis, regression analysis,
analysis of variance and covariance to address educational, psychological,
and social questions. Using real data as a catalyst, we will discuss
how to (1) formulate research questions; (2) select appropriate
statistical techniques; (3) conduct necessary calculations; (4)
examine assumptions; (5) interpret results; (6) identify rival explanations;
and (7) summarize findings in a convincing argument. Computer-based
statistical analyses are an integral part of the course. Prequisite:
A-010Y or H-012.
Extends
data-analytic skills beyond basic regression analysis and ANOVA.
Topics include: extensive use of transformations, influence statistics,
building taxonomies of regression models, general linear hypothesis
testing, intro to multilevel modeling, nonlinear regression analysis,
binomial and multinomial logistic regression analysis, ordinal logit
analysis, principal components analysis, cluster analysis, exploratory
factor analysis, intro to discrete-time survival analysis, etc.
Applied course offering conceptual explanations of statistical techniques
along with practice in real data. Prerequisite: S030.
Survey
course on educational measurement for students with prior statistical
training who will become critical consumers of test-based information
or who will apply the methods in their own research. Topics include:
traditional psychometric methods (classical test theory), generalizability
theory and item response theory (IRT). Course addresses current
policy issues in education and requires the application of psychometric
methods to real data. Prequisite: S052.
Course
covers the practical application of two analytic strategies for
analyzing longitudinal data: discrete-time survival analysis and
individual growth modeling. Class lectures will be devoted to introducing
basic concepts underlying the models, describing computer programs
for conducting analyses, and interpreting the results. Prequisite:
S052.
Quantitative
Methods for Improving Causal Inference in Educational Research
Seminar
in techniques of research design and data analysis for strengthening
causal inferences in quantitative research, including: randomized
experiments, instrumental variables estimation, regression discontinuity
designs, correction for selection bias, etc. Prerequisite: S052.
Murnane
& Willett
Faculty
of Arts & Sciences: Department of Economics
Statistical
decision theory and related experimental evidence; game theory and
related experimental evidence; maximum likelihood; logit, normal,
probit, and ordered probit regression models; panel data models with
random effects; omitted variable bias and random assignment; incidental
parameters and conditional likelihood; demand and supply.
Chamberlain
ECON
2110
Introductory
Probability and Statistics for Economists
Introduction
to probability and statistics. Emphasis on general methods applicable
to both econometrics and economic theory. Topics include probability
spaces, random variables, limit laws, estimation, hypothesis testing,
and Bayesian methods.
Moreira
ECON
2120
Introduction
to Applied Econometrics
Introduction
to applied econometrics, including linear regression, instrumental
variables, panel data techniques, generalized method of moments, and
maximum likelihood. Includes discussion of papers in applied econometrics
and computer exercises.
Jorgenson
ECON
2130
Applied
Econometrics
Advanced
methods in applied econometrics, including nonlinear regression, discrete
and limited dependent variables, models of selection, and stationary
and non-stationary time series. Includes detailed discussion of empirical
applications.
Jorgenson
ECON
2140
Econometric
Methods
Statistical
decision theory with applications to portfolio choice, panel data
topics, selection bias, demand and supply, qualitative choice, and
quantile regression.
Chamberlain
ECON
2141
Analysis
of Cross Section and Panel Data
Topics
include censoring, sample selection, attrition, stratified sampling,
estimation of average treatment effects, and duration analysis.
Moreira
ECON
2142
Time
Series Analysis
Survey
of modern time series econometrics. Topics include univariate models,
vector auto-regressions, linear and nonlinear filtering, frequency
domain methods, unit roots, structural breaks, empirical process theory
asymptotics, forecasting, and applications to macroeconomics and finance.
Stock
ECON
2110
Introductory
Probability and Statistics for Economists
Introduction
to probability and statistics. Emphasis on general methods applicable
to both econometrics and economic theory. Topics include probability
spaces, random variables, limit laws, estimation, hypothesis testing,
and Bayesian methods.
Moreira
ECON
2120
Introduction
to Applied Econometrics
Introduction
to applied econometric methods, including linear regression, instrumental
variables, panel data techniques, generalized method of moments, and
maximum likelihood. Includes discussion of applied econometrics papers
and use of standard econometric computer packages.
Jorgenson
ECON
2130
Applied
Econometrics
Advanced
methods in applied econometrics, including nonlinear regression, discrete
and limited dependent variables, models of selection, and stationary
and non-stationary time series. Includes detailed discussion of empirical
applications.
Jorgenson
ECON
2140
Econometric
Methods
Statistical
decision theory with applications to portfolio choice, panel data
topics, selection bias, demand and supply, qualitative choice, and
quantile regression.
Chamberlain
ECON
2141
Analysis
of Cross Section and Panel Data
Topics
include censoring, sample selection, attrition, stratified sampling,
estimation of average treatment effects, and duration analysis.
Moreira
ECON
2142
Time
Series Analysis
Survey
course. Topics include univariate models, vector auto-regressions,
linear and nonlinear filtering, frequency domain methods, unit roots,
structural breaks, empirical process theory asymptotics, forecasting,
and applications to macroeconomics and finance.
Stock
Faculty
of Arts & Sciences: Department of Government
Introduces key ideas that underlie statistical and quantitative reasoning,
including probability spaces, random variables, distributions, descriptive
and summary statistics, sampling, hypothesis testing, and estimation.
Sekhon
GOV
1001
Introduction
to Quantitative Methods in Political Science
Designed
for undergraduates who wish to use quantitative research methods in
their own work. Topics include research design, causal inference,
descriptive and summary statistics, probability, sampling, and statistical
inference including estimation and tests of hypotheses. Course emphasizes
multiple regression, with applications that focus on substantive research
questions such as "How do citizens evaluate elected officials?"
or "Is it really the economy, stupid?"
Sekhon
GOV
2001
Advanced
Quantitative Research Methodology
Introduces
theories of inference underlying most statistical methods and how
new approaches are developed. Examples include discrete choice, event
counts, durations, missing data, ecological inference, time-series
cross sectional analysis, compositional data, causal inference, and
others.
King
GOV
2002
Topics
in Quantitative Methods
Focuses
on the robust estimation of generalized linear models but also covers
some time series cross-section methods.
Sekhon
GOV
2003
Hierarchical
Bayesian Modeling
Provides
a solid understanding of Bayesian inference and Markov chain Monte
Carlo methods. Topics covered include: Bayesian treatment of the linear
model, Markov chain Monte Carlo methods, assessing model adequacy,
and hierarchical models.
Quinn
Faculty
of Arts & Sciences: Department of Psychology
Theoretical and practical introduction to planning, conducting, reporting,
and evaluating research in the social and behavioral sciences. Topics
include experimental design, reliability and validity, experimental
artifacts, and analysis of published research.
Snidman
PSY
1951
Intermediate
Quantitative Methods
Emphasizes
analysis of variance designs and contrasts for applied behavioral
research. Additional topics include reliability, validity, correlation,
effect size, and meta-analysis.
Baer
PSY
1952
Multivariate
Analysis in Psychology
Emphasizes
multiple regression analysis and factor analysis. Additional topics
include multivariate analysis of variance, analysis of covariance,
discriminant analysis, and logistic regression.
Baer
PSY
2100
Research
Methodology
Covers
all major steps in conducting an empirical research project, with
emphasis on studies that involve human participants. Topics include
finding and formulating research problems; research design strategies;
developing and validating concepts; designing and assessing empirical
measures and manipulations; issues in data collection, analysis, and
interpretation; and writing and publishing research reports.
Hackman
PSY
3800
Psychometric
Theory
Basic
psychometric theory and methods essential for reliable and valid measurement.
Reliability, validity, and generalizability reviewed. Detailed survey
of techniques used to create and evaluate a scale.
McNally
Faculty
of Arts & Sciences: Department of Sociology
Matrix approach to regression analysis with an emphasis on the assumptions
behind OLS. Instrumental variables, generalized least squares,
probit and logit models, survival analysis, hierarchical linear models,
and systems of equations are studied.
Winship
SOC
203b
Methods
of Quantitative Sociological Research II
Treats
longitudinal design and methods for the statistical analysis of longitudinal
data with an emphasis on the analysis of change in discrete variables,
or event history analysis. Includes an introduction to time series
analysis. Both statistical theory and practical applications covered.
Marsden
Faculty
of Arts & Sciences: Department of Statistics
Introduces key ideas underlying statistical and quantitative reasoning,
including fundamentals of probability. Topics may include elements
of sample surveys, experimental design and observational studies,
descriptive and summary statistics for both measured and counted variables,
and statistical inference including estimation and tests of hypotheses
as applied to one- and two-sample problems, regression with one or
more predictors, correlation, and analysis of variance. Emphasizes
simple and multiple regression and applications in non-experimental
fields including, but not limited to, economics.
Harrington
Taback
STAT
101
Introduction
to Quantitative Methods
Same
topics as STAT100. Emphasizes the analysis of variance, applied
in experimental fields such as psychology and other behavioral sciences.
Vaida
STAT
104
Introduction
to Quantitative Methods
Same
topics as STAT100 and STAT101 combined, at a slightly
higher level. Applications will be drawn from fields such as economics,
behavioral and health sciences, policy analysis, and law.
Irwin
STAT
110
Introduction
to Probability
Comprehensive
introduction to probability. Basics: sample space, conditional probability,
Bayes Theorem. Univariate distributions: mass functions and density,
expectation and variance, binomial, Poisson, normal, and gamma distributions.
Multivariate distributions: joint and conditional distribution, independence,
transformation, multivariate normal and related distributions. Limit
laws: probability inequalities, law of large numbers, central limit
theorem. Markov chains: transition probability, stationary distribution
and convergence.
Wong
STAT
111
Introduction
to Theoretical Statistics
Basic
concepts of statistical inference from frequentist and Bayesian perspectives.
Topics include maximum likelihood methods, confidence and Bayesian
interval estimation, hypothesis testing, least squares methods, and
analysis of variance.
Kou
STAT
139
Statistical
Sleuthing Through Linear Models
Formerly
"Regression Analysis", now a serious introduction to statistical
inference when linear models and related methods are used. Topics
include the pros and cons of t-tools and their alternatives, multiple-group
comparisons, linear regressions, model checking and refinement. The
emphasis is on statistical thinking and tools for real-life problems,
including current events whenever relevant.
Meng
STAT
140
Design
of Experiments
Statistical
designs for the estimation of the effects of treatments in randomized
experiments. Topics include brief review of some basic structural
inference procedures, analysis of variance, randomized block and Latin
square designs, balanced incomplete block designs, factorial designs,
nested factorial designs, confounding in blocks, and fractional replications.
STAT
149
Generalized
Linear Models
An
introduction to methods for analyzing categorical data. Emphasis will
be on understanding models and applying them to datasets. Topics include
visualizing categorical data, analysis of contingency tables, odds
ratios, log-linear models, generalized linear models, logistic regression,
Poisson regression and model diagnostics. Examples drawn from many
fields, including biology, medicine and the social sciences.
DiRienzo
STAT
160
Survey
Methods
Methods
for design and analysis of sample surveys. The toolkit of sample design
features, their use in optimal sample design strategies, and sampling
weights) and variance estimation methods (including resampling methods).
Brief overview of nonstatistical aspects of survey methodology such
as questionnaire design and validation. Additional topics include
variance estimation for complex surveys and estimators, nonresponse,
missing data, hierarchical models for survey data, and small-area
estimation.
Introduces students to concepts and techniques for the quantitative
analysis of policy issues. Combines material typically found in an
introductory course on probability and statistics with selected topics
in decision analysis, and illustrates the ways in which theory can
be applied to policy questions. A secondary goal of the course is
to familiarize students with the use of spreadsheet programs for analyzing
quantitative data. Topics include: descriptive statistics, basic probability,
conditional probability, Bayes' Theorem, expected utility theory,
risk aversion, decision-making under uncertainty, insurance markets
(including moral hazard and adverse selection), probability distributions,
statistical inference, hypothesis testing.
Avery
DeLeire Piehl Jacob
API
202
Empirical
Methods II
Continuation
of API201. Equips students with an understanding of the most
common tools of empirical analysis in policy applications using hands-on
analysis of data sets. The first part of the course covers regression
analysis, including multiple regression, dummy variables, and binary
dependent variables. The second part of the course covers program
evaluation, including selection effects; the advantages and disadvantages
of experimental, quasi-experimental, and observational data; and instrumental
variable techniques. The final part of the course is an integrative
empirical exercise.
Wise
Cooper DeLeire Abadie
API
208
Program
Evaluation: Estimating Program Effectiveness with Empirical Analysis
This
methodological course develops skills in quantitative program evaluation.
Students will study a variety of evaluation designs (from random assignment
to quasi-experimental evaluation methods) and analyze data from actual
evaluations. The course evaluates the strengths and weaknesses of
alternative evaluation methods.
Abadie
API
209
Advanced
Quantitative Methods I: Constrained Optimization and Mathematical
Statistics
Introduction
to tools of quantitative reasoning and analytic approaches used to
address policy problems. The course introduces modeling, optimization
theory, probability theory, statistical estimation, hypothesis testing,
and experimental design. Students learn the theoretical foundations,
basic derivations, and complete illustrative applications.
Continuation
of Advanced Quantitative Methods I, this course focuses on
developing the theoretical basis and practical application of the
most common tools of empirical analysis. Foundations of analysis will
be coupled with hands-on examples and assignments involving analysis
of data sets. The first part of the course covers the linear model
in detail. The second part treats extensions to the linear model,
as well as model specification and testing.
Jensen
API
212
Advanced
Empirical Analysis for Public Choice
Applies
probability models and statistical techniques to questions of public
concern. Topics include: analysis of individual "discrete"
choices, like college attendance, employment status, high school dropout.
Social experimentation and the analysis of experimental data versus
observations collected by more traditional surveys are considered.
Empirical studies are used to demonstrate methods of analysis.
Wise
API
213
Research
Methods: Primary Data Collection
Course
familiarizes students with different primary data collection and analysis
strategies and equips them to develop and conduct surveys. Course
covers strategies for collecting and analyzing survey data, including
briefly addressing qualitative data collection techniques, such as
focus groups and in-depth interviewing. Topics covered include study
design, survey development, sample design, and data collection protocols.
Also briefly covers analytic techniques specific to such data, such
as psychometric analytic techniques.
Provides an overview in the use of SAS to prepare data for
statistical analysis. The focus is on database management and programming
problems.
Fenton
Pagano
BIO
113
Introduction
to Data Management and Programming in SAS
Provides
intensive instruction in the use of SAS to prepare data for
statistical analysis. The focus is on database management and programming
problems.
Allred
Pagano
BIO
200
Principles
of Biostatistics
Lectures
and laboratory exercises acquaint the student with the basic concepts
of biostatistics and their applications and interpretation. The computer
is used throughout the course. Topics include descriptive statistics,
graphics, diagnostic tests, probability distributions, inference,
tests of significance, association, linear and logistic regression,
life tables, and survival analysis.
Pagano
BIO
201
Introduction
to Statistical Methods
Covers
basic statistical techniques important for analyzing data arising
from epidemiology, environmental health, biomedical and other public
health-related research. Major topics include descriptive statistics,
elements of probability, introduction to estimation and hypothesis
testing, nonparametric methods, techniques for categorical data, regression
analysis, analysis of variance, and elements of study design. Designed
as an alternate to BIO200, for students desiring more emphasis
on theoretical developments. Background in algebra and calculus strongly
recommended.
Gauvreau
BIO
202
Principles
of Biostatistics I
First
part of introductory biostatistics on the basic concepts and methods
of biostatistics, their applications, and their interpretation. The
material covered includes: data presentation, numerical summary measures,
rates and standardization, and life tables. Probability is introduced
to quantify uncertainty, especially as it pertains to diagnostic and
screening methods. Also covered are sampling distributions, confidence
intervals and hypothesis testing. The computer is used throughout
, with the software package STATA.
Testa
BIO
203
Principles
of Biostatistics II
Second
part of introductory biostatistics; it continues to explore inference
in greater depth. Lectures and laboratory exercises emphasize applied
data analysis, building upon the fundamentals in BIO202.
Topics covered include the comparison of two means, analysis of variance,
non-parametric methods, inference on proportions, contingency tables,
multiple 2 X 2 tables, correlation, simple regression, multiple regression
and logistic regression, analysis of survival data, and sampling theory.
The computer is used throughout the course, with STATA.
Park
Lagakos
BIO
205
Statistical
Methods for Health and Social Policy
Introduces
students to probability and statistics, illustrating their application
in the areas of health policy and management and the behavioral sciences.
Understanding of basic statistical concepts will be emphasized through
problem solving and examples. Topics include: descriptive statistics,
diagnostic testing, probability distributions, sampling methods, hypothesis
testing, confidence intervals, sample size determination, parametric
and non-parametric methods, categorical data and simple linear and
logistic regression.
Lagakos
Lindsey
BIO
206
Introductory
Statistics for Medical Research
Introduces
basic biostatistical techniques with an emphasis on applications to
clinical research. Topics include probability and statistics, hypothesis
testing, confidence intervals, non-parametrics, and power calculations.
Orav
BIO
207
Statistics
for Medical Research II
Presents
additional biostatistical techniques that commonly appear in the analysis
of clinical databases and trials. Topics include contingency table
analyses, log-rank tests, paired and matched analyses, analysis of
variance and multiple comparisons procedures.
Reed
Orav
BIO
208
Statistics
for Medical Research, Advanced
Presents
additional biostatistical techniques that commonly appear in the analysis
of clinical databases and trials. This course will move at a faster
pace than the alternative BIO207 while covering all of the
same topics (contingency tables, log-rank tests, paired and matched
analyses, analysis of variance and multiple comparisons procedures).
In addition, linear and logistic regression will be introduced.
Orav
BIO
209
Statistics
for Medical Research, Translational
Presents
additional biostatistical techniques that are most relevant to researchers
involved with designed experiments. Topics include contingency tables,
paired analyses, simple analysis of variance, multiple comparisons
procedures, two-way analysis of variance, and simple repeated measures
analysis of variance.
Wang
BIO
210
Analysis
of Rates and Proportions
Emphasizes
concepts and methods for analysis of data which are categorical, rate-of-occurrence
(e.g., incidence rate), and time-to-event (survival duration). Stresses
applications in epidemiology, clinical trials, and other public health
research. Topics include measures of association, 2x2 tables, stratification,
matched pairs, logistic regression, model building, analysis of rates,
and survival data analysis using proportional hazards models.
Glynn
BIO
211
Regression
and Analysis of Variance in Experimental Research
Covers
analysis of variance and regression, including details of data-analytic
techniques and implications for study design. Also included are probability
models and computing. Students learn to formulate a scientific question
in terms of a statistical model, leading to objective and quantitative
answers.
Shih
BIO
212
Survey
Research Methods In Community Health
Covers
research design, sample selection, questionnaire construction, interviewing
techniques, the reduction and interpretation of data, and related
facets of population survey investigations. Focuses primarily on the
application of survey methods to problems of health program planning
and evaluation. Treatment of methodology is sufficiently broad to
be suitable for students who are concerned with epidemiological, nutritional,
or other types of survey research.
Mangione
Lagakos
BIO
213
Applied
Regression for Clinical Research
This
course will introduce students involved with clinical research to
the practical application of multiple regression analysis. Linear
regression, logistic regression and proportional hazards survival
models will be covered, as well as general concepts in model selection,
goodness-of-fit, and testing procedures. Each lecture will be accompanied
by data analysis using SAS. The course will introduce, but
will not develop the underlying likelihood theory.
Orav
BIO
214
Principles
of Clinical Trials
Designed
for individuals interested in the scientific, policy, and management
aspects of clinical trials. Topics include types of clinical research,
study design, treatment allocation, randomization and stratification,
quality control, sample size requirements, patient consent, and interpretation
of results. Students design a clinical investigation in their own
field of interest, write a proposal for it, and critique recently
published medical literature.
Ware
Antman
Stanley Gelber
BIO
222
Basics
of Statistical Inference
This
course will provide an introduction to the probability theory and
mathematical statistics that underlie commonly used techniques in
public health research. Topics to be covered include probability distributions
(normal, binomial, Poisson), means, variances and expected values,
finite sampling distributions, parameter estimation (method of moments,
maximum likelihood), confidence intervals, hypothesis testing (likelihood
ratio, Wald and score tests). All theoretical material will be motivated
with problems from epidemiology, biostatistics, environmental health
and other public health areas. This course is aimed towards second
year doctoral students in fields other than Biostatistics. Background
in algebra and calculus required.
Catalano
BIO
223
Applied
Survival Analysis and Discrete Data Analysis
This
course will cover topics in both discrete data analysis and applied
survival analysis. The course will begin with a review of sampling
plans and contingency table for discrete data. Further topics in discrete
data analysis will include logistic regression, exact inference, and
conditional logistic regression. This short survey of discrete data
topics will provide a natural transition to analysis of survival data.
Survival topics include: hazard, survivor, and cumulative hazard functions,
Kaplan-Meier and actuarial estimation of the survival distribution,
comparison of survival using log rank and other tests, regression
models including the Cox proportional hazards model and accelerated
failure time model, adjustment for time-varying covariates, and use
of parametric distributions (exponential, Weibull) in survival analysis.
Class material will include presentation of statistical methods for
estimation and testing, along with current software (SAS,
Stata, Splus) for implementing analyses of discrete
data and survival data.
Gentleman
BIO
224
Survival
Methods in Clinical Research
This
course will cover the common approaches to the display and analysis
of survival data, including Kaplan-Meier curves, log rank tests, and
Cox proportional hazards regression. Computing, using SAS,
will be an integral component of the course.
Davis
Jiang
BIO
226
Applied
Longitudinal Analysis
This
course covers modern methods for the analysis of repeated measures,
correlated outcomes and longitudinal data, including the unbalanced
and incomplete data sets characteristic of biomedical research. Topics
include an introduction to the analysis of correlated data, repeated
measures ANOVA, random effects and growth curve models, and
generalized linear models for correlated data, including generalized
estimating equations (GEE).
Coull
BIO
230
Probability
Theory and Applications I
A first
course in probability. Topics include axiomatic foundations, frequency
and personal concepts of probability, combinatorics, discrete and
continuous sample spaces, independence and conditional probability,
random variables, expectation operator, moments, generating functions
and characteristic functions, standard distributions, transformations,
sampling distributions related to the normal distribution, convergence
concepts, weak and strong laws of large numbers, the central limit
theorem, and elements of stochastic processes. Background in multivariable
calculus required.
Bonetti
BIO
231
Statistical
Inference I
A fundamental
course in statistical inference. Discusses general principles of data
reduction: exponential families, sufficiency, ancilliarity and completeness.
Describes general methods of point and interval parameter estimation
and the small and large sample properties of estimators: method of
moments, maximum likelihood, unbiased estimation, Rao-Blackwell and
Lehmann-Scheffe theorems, information inequality, asymptotic relative
efficiency of estimators. Describes general methods of hypothesis
testing and optimality properties of tests: Neyman-Pearson theory,
likelihood ratio tests, score and Wald tests, uniformly and locally
most powerful tests, asymptotic relative efficiency of tests.
DeGruttola
BIO
232
Methods
I
Introductory
methods course aimed at first year Biostatistics students. The course
deals mainly with the linear regression family of models including
simple linear regression, analysis of variance and one- and two-sample
t-tests. Robust alternatives such as the Wilcoxon signed rank test
will be treated. Exploratory data analysis, model formulation and
fitting, diagnosis, interpretation and graphical display of results
will be emphasized. Some of the underlying theory will also be given.
Several public health problems and data sets will be used to illustrate
the methods. The use of software packages S-PLUS, Stata
and SAS will be described. Background in calculus, linear
algebra and introductory statistics is required.
Neuberg
BIO
233
Methods
II
This
course focuses on the analysis of categorical data and count data,
and provides an introduction to methods for analysis of survival data.
Topics include a review of sampling plans, analysis of contingency
tables, large sample and exact methods for constructing confidence
intervals and hypothesis tests, measures of association, logistic
regression, and log-linear analysis. Survival topics will include
estimation of survival distributions, comparison of groups, and regression
models such as the Cox proportional hazards model and the accelerated
failure time models.
Wypij
BIO
234
Research
Synthesis & Meta-Analysis in Public Health
Concerned
with the use of existing data to inform clinical decision making and
health care policy, the course focuses on research synthesis (meta-analysis).
The principles of meta-analytic statistical methods are reviewed and
the application of these to data sets is explored. Application of
methods includes considerations for clinical trials and observational
studies. The use of meta-analysis to explore data and identify sources
of variation among studies is emphasized, as is the use of meta-analysis
to identify future research questions.
Stoto
BIO
235
Regression
and Analysis of Variance
Advanced
course in data analysis for linear models - regression and analysis
of variance. Estimation methods (maximum likelihood and least squares)
and issues of inference (confidence intervals, hypothesis testing,
analysis of residuals) are presented from a theoretical and data analysis
perspective. Background in matrix algebra and linear regression required.
Rotnitzky
BIO
240
Sample
Surveys
Methods
for design and analysis of sample surveys. A brief introduction to
questionnaire design and evaluation will be followed by a discussion
of sample design techniques. Estimation methods, including calculation
and use of sampling weights, and variance estimation methods.
Zaslavsky
Lagakos
BIO
243
Nonparametric
Methods
Presents
the theory and application of nonparametric methods. Topics include
permutation tests, permutation limit theorems, 2-sample rank tests
and their asymptotic efficiency, k-sample rank tests, 1-sample tests
of location, paired comparisons, rank tests for symmetry and independence,
and analogues of linear modeling based on ranks.
Hughes
BIO
244
Analysis
of Failure Time Data
Discusses
the theoretical basis of concepts and methodologies associated with
survival data and censoring, nonparametric tests, and competing risk
models. Much of the theory is developed using counting processes and
martingale methods.
Wei
BIO
245
Analysis
of Multivariate and Longitudinal Data
Presents
classical and modern approaches to the analysis of multivariate observations,
repeated measures, and longitudinal data. Topics include the multivariate
normal distribution, Hotelling's T2, MANOVA, the multivariate linear
model, random effects and growth curve models, generalized estimating
equations, statistical analysis of multivariate categorical outcomes,
and estimation with missing data. Discusses computational issues for
both traditional and new methodologies.
Williams
BIO
247
Design
of Scientific Investigations
Discusses
those aspects of statistical theory and practice relevant to the design
of scientific investigations in the health sciences. Topics include
sample size considerations, basic principles of experimental design
(randomization, replication, and balance), block designs, factorial
experiments, response surface modeling, clinical trials, adaptive
designs, cohort studies, early detection trials, and double sampling
techniques.
Hughes
BIO
248
Advanced
Statistical Computing
Course
in computing algorithms useful in statistical research and advanced
statistical applications. Topics include computer arithmetic, matrix
algebra, numerical optimization methods with application to maximum
likelihood estimation and GEEs, spline smoothing and penalized
likelihood, numerical integration, random number generation and simulation
methods, Gibbs sampling, bootstrap methods, missing data problems
and EM, imputation, data augmentation algorithms, and Fourier
transforms. Students should be proficient with C or Fortran programming.
Gray
BIO
249
Bayesian
Methods in Biostatistics
This
course examines basic aspects of the Bayesian paradigm including Bayes
theorem, decision theory, general principles (likelihood, exchangeability,
de Finetti's theorem), prior distributions (conjugate, non-conjugate,
reference), single-parameter models (binomial, poisson, normal), multi-parameter
models (normal, multinomial, linear regression, general linear model,
hierarchical regression), inference (exact, normal approximations,
non-normal approximations, non-normal iterative approximations), computation
(Monte Carlo, convergence diagnostics), model diagnostics (Bayes factors,
predictive ordinates), design, and empirical Bayes methods.
Normand
BIO
250
Probability
Theory and Applications II
Sequel
to BIO230, covering a variety of advanced topics in probability
theory. Topics include a brief overview of measure theory integration,
convergence on sequences of random variables and stochastic processes,
limit theorems, projections, and conditional expectation.
Li
BIO
251
Statistical
Inference II
Sequel
to BIO231. Presents advanced topics in statistical inference,
including limit theorems, multivariate delta method, properties of
maximum likelihood estimators, saddlepoint approximations, asymptotic
relative efficiency, robust and rank-based procedures, resampling
methods, and nonparametric curve estimation.
Cai
BIO
262
Statistical
Problems in Drug Development
This
course will introduce the student to the "real life" applications
of statistical methodology required for pharmaceutical drug development.
Weekly seminars will cover statistical techniques used in the various
phases of drug development, including assessment of pharmacologic
activity; preclinical animal models and toxicology studies; clinical
trials (Phase I dose ranging through Phase III comparative efficacy
trials); and post-surveillance, pharmacoepidemiologic and pharmacoeconomic
studies. Statistical techniques and examples include applications
of optimum screening designs, use of non-parametric estimators, problems
of multiplicity, tests for monotonicity, parametric and nonparametric
regression, ordered categorical data analysis, survival methods, issues
of power and sample size, bioequivalence studies, longitudinal data
analysis, univariate and multivariate general linear models, multiple
endpoint problems and quality-of-life measurement models. Exposure
to linear models and non-parametric statistics recommended.
Testa
BIO
263
Computational
Methods for Categorical Data Analysis
This
course deals with exact nonparametric methods of inference. These
methods use fast numerical algorithms to permute the observed data
in all possible ways, and thereby derive exact distributions for the
test statistics of interest without making any distributional or large-sample
assumptions. Exact nonparametric methods are particularly important
for small, sparse or unbalanced data where the usual asymptotic theory
breaks down. This course will cover exact inference for one, two and
K-sample problems, ordered and unordered RxC contingency tables, 2x2
and 2xC contingency tables with or without stratification, and logistic
regression. A unified view, encompassing both continuous and categorical
data, will be presented based on the permutation principle. Modern
algorithmic advances that make exact permutational inference computationally
feasible will be treated in depth. The methods will be illustrated
by several biomedical data sets. This course will use StatXact
and LogXact statistical packages.
Mehta
BIO
268
Seminar
on Statistical Methods in Human Genetics
This
course provides a self-contained introduction to statistical genetics.
Emphasis is placed on modern methods for gene mapping. Topics include
Hardy-Weinberg disequilibrium, estimation of allele frequencies, linkage
analysis, association analysis and haplotypes. Genetic concepts will
be introduced as necessary.
Laird
BIO
270
Statistical
Science Outreach
Seminar
for broadening the background of students in probability and statistics.
Students will give short presentations from expository articles and
papers. This course is suitable for students in any year of the Biostatistics
program.
Gelman
DeGruttola
BIO
271
Statistical
Computing Environments
Acquaints
students with modern computing environments needed for careers in
biostatistics. Course contains lectures and computer labs, with guest
lecturers. Topics include: programming environments in statistics,
algorithmic and symbolic mathematics, source language programming
and its tools, editors, typesetters, Internet tools, UNIX
and other tools that have potential for research in and practice of
statistics.
Wang
BIO
274
Applied
Stochastic Processes and Models in Public Health
Course
develops stochastic processes for modeling important problems in public
health. Among the topics to be covered are: Poisson processes, birth
and death processes, Markov chains and processes, semi-Markov processes.
Applications will be made to models of prevalence and incidence of
disease, therapeutic clinical trials, clinical trials for prevention
of disease, length biased sampling, models for early detection of
disease, cell kinetics and family history problems.
Zelen
BIO
276
Sequential
Analysis
This
course covers the basic theory underlying the design and interim monitoring
of group sequential clinical trials and illustrates the theory with
examples taken from real clinical trials. Topics include: 1) Distribution
theory for sequentially computed test statistics derived from normal
binomial and time-to-event data; 2) General distribution theory based
on the theorem of Scharfstein, Tsiatis and Robbins (JASA,
1997); 3) The recursive integration algorithm for computing boundary
crossing probabilities for processes of independent increments; 4)
Stopping boundaries -- Haybittle-Peto p-value boundaries, Wang-Tsiatis
power boundaries, efficacy boundaries derived from alpha spending
functions, futility boundaries derived from beta spending functions;
5) Design of superiority trials with normal, binomial and time-to-event
endpoints; 6) Design of non-inferiority trials with normal, binomial
and time to event endpoints; 7) Design of maximum information trials;
8) Interim monitoring -- recomputing stopping boundaries from error
spending functions, optimal placing of last look, conditional power,
repeated confidence intervals, p-values, point estimates and confidence
intervals adjusted for multiple looks; 9) Adaptive designs.
Mehta
Betensky
BIO
279
Smoothing
in Biostatistical Modeling
Smoothing
is means by which non-linear structure can be incorporated into a
statistical model without the need for parametric modeling. This course
will describe some of the main smoothing techniques and illustrate
their use in biostatistical modeling. Computational and some theoretical
issues will also be discussed. The package S-PLUS will be
used.
BIO
284
Spatial
Statistics for Health Research
This
course will introduce students to a broad range of topics in spatial
statistics, including but not limited to types of spatial data, kriging,
parametric and non-parametric methods, tests for spatial randomness.
The course will draw on many real examples. Students will become proficient
in the use of SplusSpatialStats and ARCView.
Ryan
BIO
288
Semiparametric
Methods for Analysis of Missing and Censored Data
Discusses
estimation techniques for low dimensional parameters of semiparametric
models (i.e. models with infinite dimensional nuisance parameters)
for complex longitudinal data subject to informative censoring or
missingness. The course will start with the discussion of the fundamental
notions and results of semiparametric theory: pathwise derivatives,
tangent space, semiparametric variance and information bounds, and
influence functions. It will then provide a general estimating function
methodology for locally semiparametric efficient estimation and doubly
robust estimation under data that are coarsened at random. This general
methodology will then be applied to derive locally efficient doubly
robust estimators of 1) regression parameters in multivariate generalized
linear models subject to missing at random data, 2) the survival function
of an endpoint subject to dependent right censoring, 3) the quality
of life adjusted survival time subject to dependent right censoring
4) the survival function of multivariate failure time data subject
to univariate (dependent) censoring, 5) Cox regression parameters
based on dependent right censored data and 6) smooth parameters of
the distribution of a time to an endpoint outcome based on current
status data and interval censored data.