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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:
- Graduate School of Education.
- Department of Economics.
- Department of Government.
- Department of Psychology.
- Department of Sociology.
- Department of Statistics.
- Kennedy School of Government.
- School of Public Health/Biostatistics.
Within each department-specific table, there is a link that will return you to the head of this page.
Harvard Graduate School of Education(Return to top of page) |
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Introductory-Level Courses |
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Answering
Questions with Quantitative Data |
Introductory
to the concepts, principles and vocabulary of quantitative methods.
Prerequisite: none (restricted to entering doctoral students
in APSP). |
Willett |
|
Introduction
to Educational Research |
Introduction
to the rationale and procedures of educational research. Prerequisite:
none, for master's and first-year doctoral students. |
Tivnan |
|
Principles
of Educational Assessment |
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. |
Koretz |
|
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. |
Tivnan |
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Intermediate-Level Courses |
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Intermediate
Statistics |
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. |
Chase |
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Advanced-Level Courses |
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Applied
Data Analysis |
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. |
Willett |
|
Methods
of Educational Measurement |
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. |
Koretz |
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Applied
Longitudinal Data Analysis |
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. |
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Answering
Complex Questions with Multivariate Methods |
Methods
of covariance structure analysis, including path analysis, structural
equation modeling, confirmatory factor analysis, and latent growth
modeling, using LISREL. Prequisite: S052. |
Willett |
|
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 |
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Faculty of Arts & Sciences: Department of Economics(Return to top of page) |
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ECON
1126 |
Quantitative
Methods in 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(Return to top of page) |
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GOV
1000 |
Quantitative
Methods for Political Science I |
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(Return to top of page) |
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PSY
1901 |
Methods
of Behavioral Research |
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(Return to top of page) |
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SOC
203a |
Methods
of Quantitative Sociological Research I |
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(Return to top of page) |
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STAT
100 |
Introduction
to Quantitative Methods |
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.
|
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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. | Zaslavsky |
John F. Kennedy School of Government(Return to top of page) |
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API
201 |
Quantitative
Analysis and Empirical Methods |
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. |
Hogan |
API
210 |
Advanced
Quantitative Methods II: Econometric Methods |
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. | Cleary |
Harvard School of Public Health(Return to top of page) |
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BIO 111 |
Introduction
to Programming in SAS |
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 Splus SpatialStats 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. | Rotnitzky
Robins |
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Contact me: John_Willett@Harvard.Edu Page last updated: May 31, 2005 |
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