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Quantitative Policy Analysis in Education
Introductory-Level Courses
| S010Y |
Answering Questions with Quantitative Data |
Introduction to the concepts, principles and vocabulary of quantitative
methods. Prerequisite: none, restricted to entering doctoral
students. |
| S005 |
Introduction to Educational Research |
Introduction to the rationale and procedures of educational research. |
| S011 |
Understanding Today's Educational Testing |
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, to provide
a context for understanding assessment results; second, to provide
a basic understanding of essential concepts in measurement, such as
reliability, validity, and bias; and third, to apply these principles
to a variety of current issues in education policy. |
| S012 |
Empirical Methods: Introduction to Statistics for Research |
Introduction to basic principles of elementary statistics, for students
continuing with course work in statistical methods. |
Intermediate-Level Courses
| S030 |
Intermediate Statistics: Applied Regression and Data Analysis |
Intermediate course covering general linear model-regression, correlation,
analysis of variance and covariance to address educational, and social
questions. Using real data as a catalyst, students will learn how
to formulate research questions; select appropriate statistical techniques;
conduct necessary calculations; examine assumptions; interpret results;
identify rival explanations; and summarize findings in a convincing
argument. Computer-based statistical analyses are an integral part
of the course. Prerequisite: S010Y or S012. |
Advanced-Level Courses
| S052 |
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, introductions to multilevel modeling and discrete-time
survival analysis, nonlinear regression analysis, binomial and multinomial
logistic regression analysis, ordinal logit analysis, principal components
analysis, cluster analysis, and exploratory factor analysis. Applied
course offering conceptual explanations of statistical techniques
along with practice in real data. Prerequisite: S030. |
| S061 |
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. Prerequisite: S052. |
| S077 |
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. |
| S090 |
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. |
| S290 |
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, and correction for selection bias. Prerequisite: S052 and
familiarity with basic concepts of microeconomics. |
|
Doctoral Research Practicum: Using Quantitative Methods to Make
Causal Inferences about the Consequences of Educational Initiatives
and Policies |
Research practicum on methods of causal inference in quantitative
research. Course serves as a forum for exploring creative methodologies
for addressing important educational policy questions and for providing
students constructive feedback on their ongoing research. Prerequisite:
S290. |
Faculty of Arts & Sciences: Department
of Economics
| ECON 1123 |
Introduction to Econometrics |
Introduction to multiple regression techniques with focus on
economic applications. Discusses extensions to discrete response,
panel data, and time series models, and issues such as omitted variables,
missing data, sample selection, randomized and quasi-experiments,
and instrumental variables. Prerequisite: Statistics 100. |
| 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. Prerequisite: Statistics 100 or 110, Mathematics
20. |
| 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. Prerequisite: Statistics
100, Mathematics 21a, 21b, and 112. |
| 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. Prerequisite:
Economics 2110 or equivalent. |
| 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. Prerequisite:
Economics 2120 or equivalent. |
| 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. Prerequisite: Economics 2120
or equivalent. |
| ECON 2141 |
Advanced Topics in Microeconometrics |
Topics include censoring, sample selection, attrition, stratified
sampling, estimation of average treatment effects, and duration
analysis. |
| 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. |
| ECON 2144 |
Advanced Applied Econometrics |
Introduction to the theory and application of recently developed
econometric techniques used in advanced applied work. Simulation
techniques, estimation subject to inequality restrictions, as well
as semiparametric and nonparametric tools will be studied in a variety
of empirical contexts. |
Faculty of Arts & Sciences: Department
of Government
| GOV 1000 |
Quantitative Methods for Political Science I |
Introduction to key ideas that underlie statistical and quantitative
reasoning, including probability spaces, random variables, distributions,
descriptive and summary statistics, sampling, hypothesis testing,
and estimation. |
| GOV 1001 |
Introduction to Quantitative Methods in Political Science
|
Designed for students 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?" |
| GOV 1005 |
The Practice of Research in Political Science |
Introduction to methods of research as practiced across a broad
range of the social sciences. Enables students to be critical in
evaluations of claims about politics, society, and the economy.
Topics include: constructing and testing hypotheses, designing research
projects, and bringing data to bear on political questions. |
| GOV 1010 |
Survey Research Methods |
Introduction to history, theories, and methods of survey research.
Course focuses on design, development, execution, interpretation
and analysis of political surveys and polls. Topics include survey
mode (mail, telephone, in-person, web), measurement and questionnaire
design, survey sampling, and survey error. |
| GOV 1015 |
Strategic Models of Political Economy |
Introduction to modeling techniques and the practice of applying
such techniques to the study of political science and economics.
Though theoretically motivated, the course will also discuss the
role of empirical evaluation in model building and testing. |
| GOV 2000 |
Introduction to Quantitative Methods II |
Introduction to modern statistical methods including least squares,
robust estimation, propensity score matching, maximum likelihood
and Bayesian inference. Emphasizes theoretical principles and making
inferences from actual data using the minimum of assumptions. Prerequisite:
Government 1000. |
| GOV 2001 |
Advanced Quantitative Research Methodology |
Introduction to 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, and causal
inference. Prerequisite: Government 1000 or equivalent. |
| GOV 2002 |
Topics in Quantitative Methods |
Focuses on the robust estimation of generalized linear models
but also covers some time series cross-section methods. Prerequisite:
Government 1000 or equivalent. |
| 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. Prerequisite: Government
1000 and Government 2000 or equivalents. |
Faculty of Arts & Sciences: Department
of Psychology
| PSY 1900 |
Introduction to Statistics for the Behavioral Sciences |
Introduction to statistics used in psychology and other behavioral
sciences. Topics include measures of central tendency and variability;
probability and distributions, correlations and regression, hypothesis
testing, t-tests, analysis of variance, and chi-square tests. |
| 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. Prerequisite:
Psychology 1900, Statistics 100, 101, 102, 104, or equivalent. |
| 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. Prerequisite: Psychology
1900, Statistics 100, 101, 102, 104, or equivalent. |
| 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. Prerequisite:
Psychology 1951. |
| PSY 2100 |
Research Methodology |
Covers all major steps in conducting an empirical research project,
with emphasis on studies that involve human participants. Topics
include formulating problems; design strategies; developing and
validating concepts; designing and assessing measures and manipulations;
issues in data collection, analysis, and interpretation; and publishing
findings. |
| 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.
|
Faculty of Arts & Sciences: Department
of Sociology
| SOC 202 |
Intermediate Quantitative Research Methods |
Research designs and measurement techniques used in quantitative
sociological research. Regression methods for continuous and binary
response variables, including categorical predictors, nonlinearity,
interactions, diagnostics, criticism. Prerequisite: Familiarity
with basic statistics. |
| SOC 203a |
Advanced Quantitative Research Methods |
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. Prerequisite:
Sociology 202 or basic course in regression analysis. |
| SOC 203b |
Analysis of Longitudinal Data |
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. Prerequisite: Sociology 203a. |
| SOC 276 |
The new Causal Analysis: Seminar |
Considers new methods of causal analysis based on the so-called
counterfactual or potential outcomes model. Focuses on sociological
applications with an emphasis on situations where the new methods
give new insights and/or results. |
Faculty of Arts & Sciences: Department
of Statistics
| STAT 100 |
Introduction to Quantitative Methods |
Introduction to 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.
|
| 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.
|
| 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. |
| 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.
Prerequisite: Mathematics 21a or equivalent, concurrent Mathematics
21b recommended. |
| 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 categorical data analysis. Prerequisite: Statistics
110, Mathematics 21a and 21b or equivalent. |
| STAT 131 |
Time Series Analysis and Forecasting |
Introduction to time series models and associated methods of data
analysis and inference. Auto regressive (AR), moving average (MA),
ARMA, and ARIMA processes, stationary and non-stationary processes,
seasonal processes, auto-correlation and partial auto-correlation
functions, identification of models, estimation of parameters, diagnostic
checking of fitted models, forecasting, time domain regression approach
including Box-Jenkins method, and spectral analysis. Prerequisite:
Statistics 111 and 139 or equivalent. |
| STAT 139 |
Statistical Sleuthing Through Linear Models |
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. Prerequisite: Statistics 100 or equivalent,
Mathematics 21a and 21b or equivalent. |
| 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. Prerequisite: Statistics 100 and
139 or equivalent. |
| 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. Prerequisite:
Statistics 139 or equivalent. |
| 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. Prerequisite: Statistics
111 or 139 or equivalent. |
| STAT 210 |
Probability Theory and Mathematical Statistics |
Random variables, their distributions and densities. Families
of distributions. Expectation. Independence, product spaces, and
joint distributions. Types of convergence. Limit theorems (weak
and strong laws, central limit problem). Conditional probability
and expectation, multivariate Normal distribution, particular examples
of conjugate, marginal, and conditional distributions. Inequalities,
approximations, and stochastic simulation. Sampling distributions,
likelihood function, sufficiency, and information. Prerequisite:
Courses in probability and statistics at least at the level of Statistics
110, 111. |
| STAT 211 |
Probability Theory and Mathematical Statistics II |
Introduction to statistical inference. Frequency, Bayesian, and
decision-theoretic approaches. Likelihood, sufficiency, and exponential
families. Testing hypotheses and estimation. Maximum likelihood
estimation, likelihood ratio tests, Bayes Factor, models for frequency
data, large and moderate sample approximations, including the delta
method.
Prerequisite: Advanced calculus, Statistics 210,
or equivalent. |
| STAT 214 |
Causal Inference in Statistics and the Social and Biomedical
Sciences |
Approaches to causal inference. Covers randomized experiments
with and without noncompliance, observational studies with and without
ignorable treatment assignment, instrumental variables and sensitivity
analysis. |
| STAT 220 |
Bayesian Data Analysis |
Begins with basic Bayesian models, whose answers often appear
similar to classical answers, followed by more complicated hierarchical
and mixture models with nonstandard solutions. Includes methods
for monitoring adequacy of models and examining sensitivity of conclusions
to change in models. Throughout, emphasis on drawing inferences
via computer simulation rather than mathematical analysis.
Prerequisite: Statistics 110 and 111. |
| STAT 221 |
Statistical Computing Methods |
Computing methods commonly used in statistics. Topics include
generation of random numbers, Monte Carlo methods, optimization
methods, numerical integration, and advanced Bayesian computational
tools such as the Gibbs sampler, Metropolis Hastings, the method
of auxiliary variables, marginal and conditional data augmentation,
slice sampling, exact sampling, and reversible jump MCMC. Prerequisite:
Linear algebra, Statistics 111, and knowledge of a computer programming
language. Statistics 220 is recommended. |
| STAT 230 |
Multivariate Statistical Analysis |
Probability theory and inference for multivariate distributions,
especially the normal and offpring distributions and those arising
via multi-level modeling. Includes advanced matrix theory, principal
components, and other topics in the theory.
Prerequisite:
Statistics 210 and 211 or equivalent. |
John F. Kennedy School of Government
| API 201 |
Quantitative Analysis and Empirical Methods |
Introduction to concepts and techniques for the quantitative
analysis of policy issues. Combination of introductory probability
and statistics with selected topics in decision analysis, and illustration
of 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.
|
| API 202 |
Empirical Methods II |
Equips students with an understanding of the most common tools
of empirical analysis in policy applications using hands-on analysis
of data sets. Topics include: multiple regression; dummy variables;
binary dependent variables; program evaluation; selection effects;
the advantages and disadvantages of experimental, quasi-experimental,
and observational data; and instrumental variable techniques. Prerequisite:
API-201or equivalent. |
| API 205 |
Empirical Methods and Statistics for Managers |
Overview of ways to gather, analyze, and interpret data to improve
management. Emphasizes statistics and basic program evaluation.
Topics include standard statistical methods, such as probability
distributions; distributions of sample proportions and sample means;
confidence intervals; hypothesis testing, regression, and correlation
analysis; and chi-square analysis for data in tables. Issues of
research design are also considered, including random and stratified
sampling and randomization versus observational studies. Classes
will emphasize choosing an effective design to gather data; analyzing
imperfect or messy data; and interpreting findings from several
studies to make a decision. |
| API 206 |
Policy Evaluation for Managers |
Introduction to approaches used to evaluate the implementation
and impacts of public policies. Topics include reasons for
and uses of program evaluations; implementation analysis; evaluation
designs; issues in data collection; estimation of program
impacts; the integration of qualitative and quantitative findings;
and using the results of program evaluations. Prerequisite:
API-205 or equivalent. |
| 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. Prerequisite:
familiarity with basic concepts of statistical inference and regression
analysis. |
| 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. Prerequisite: multivariate calculus and linear
algebra. |
| 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. Prerequisite:
API-209. |
| 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. Prerequisite: API-202A or equivalent. |
| 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. |
Harvard School of Public Health
| 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.
|
| 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. |
| BIO
200 |
Principles of Biostatistics |
Introduction to basic concepts of biostatistics and their applications
and interpretation. Topics include descriptive statistics, graphics,
diagnostic tests, probability distributions, inference, tests of
significance, association, linear and logistic regression, life
tables, and survival analysis. |
| 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 BIO-200, for students
desiring more emphasis on theoretical developments. Background in
algebra and calculus strongly recommended. |
| BIO 202 |
Principles of Biostatistics I |
First part of introduction to 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. |
| 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. Prerequisite: BIO-202. |
| BIO 205
|
Statistical Methods for Health and Social Policy |
Introduction 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.
|
| BIO 206 |
Introductory Statistics for Medical Research |
Introduction to 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. |
| 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. Prerequisite:
BIO-206. |
| 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 BIO-207 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. Prerequisite: BIO-206. |
| 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. Prerequisite:
BIO-206. |
| 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. Prerequisite: BIO-200,
or BIO-201, or BIO-202 and BIO-203, or BIO-205, or BIO-206 and one
of BIO-207, BIO-208, or BIO-209. |
| 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. Prerequisite:
BIO-200, or BIO-201, or BIO-202 and BIO-203, or BIO-205, or BIO-206
and one of BIO-207, BIO-208, or BIO-209. |
| 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. |
| 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. Prerequisite:
BIO-200, or BIO-201, or BIO-202 and BIO-203, or BIO-205, or BIO-206
and one of BIO-207, BIO-208, or BIO-209. |
| 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. Prerequisite:
BIO-200, or BIO-201, or BIO-202 and BIO-203, or BIO-205, or BIO-206
and one of BIO-207, BIO-208, or BIO-209. |
| 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. Prerequisite: background inalgebra and
calculus, one intermediate biostatistics course, such as BIO-210
or BIO-211. |
| 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. Prerequisite: BIO-210 and BIO-213,
or BIO-230. |
| 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. Prerequisite:
BIO-210, BIO-211, BIO-213. |
| 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). Prerequisite: BIO-211, BIO-213,
or BIO-232. |
| 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. Prerequisite: BIO-222. |
| 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. Prerequisite: BIO-230. |
| BIO
232 |
Methods I |
Introductory course in the analysis of Gaussian and categorical
data. The general linear regression model, ANOVA, robust alternatives
based on permutations, model building, resampling methods (bootstrap
and jackknife), contingency tables, exact methods, logistic regression.
|
| BIO
233 |
Methods II |
Intermediate course in the analysis of Gaussian, categorical,
and survival data. The generalized linear model, Poisson regression,
random effects and mixed models, comparing survival distributions,
proportional hazards regression, splines and smoothing, the generalized
additive model. Prerequisite: BIO-232. |
| 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.
|
| 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. Prerequisite: BIO-230
and BIO-232. |
| 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.
Prerequisite: BIO-231. |
| 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. Prerequisite: BIO-231
and BIO-233. |
| 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.
Prerequisite: BIO-231 and BIO-235. |
| 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. Prerequisite: BIO-235. |
| 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. Prerequisite: BIO-235. |
| 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. Prerequisite: BIO-231 and BIO-232. |
| BIO
250 |
Probability Theory and Applications II |
Basic set theory, measure theory, Riemann-Stieltjes and Lebesgue
integration, conditional probability, conditional expectation (projection),
martingales, Radon-Nikodym derivative, product measure and Fubini's
Theorem, limit theorems on sequences of random variables, stochastic
processes, weak convergence. Prerequisite: BIO-230 and BIO-232. |
| BIO
251 |
Statistical Inference II |
Considers several advanced topics in statistical inference. Topics
include 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. Prerequisite: BIO-231. |
| 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. |
| BIO
275 |
Operational Mathematics |
The aim of this course is to strengthen students' background in
analysis and operational use of mathematics. The course will emphasize
the application of several fundamental results, and not the proofs
of these results. Students will work several problems which illustrate
fundamental mathematical operations. Topics include concepts of
convergence (e.g., power series, Taylor's series), functions (limits,
continuity, step functions, L'Hopital's rule, differentiability),
integration (Riemann, Stieltjes, Lebesque), operations convergence
theorem, complex variables (e.g., Laplace transforms, Fourier transforms,
inversion formulas). |
| BIO
276 |
Sequential Analysis |
This course will cover the basic theory underlying the design
and interim monitoring of group sequential clinical trials and will
illustrate the theory with examples of real clinical trials. Topics
include: distribution theory for stochastic processes with independent
increments; the recursive integration algorithm; stopping boundaries
and error spending functions; maximum information trials; conditional
power and stochastic curtailment; repeated confidence intervals;
inference following group sequential testing; sample size re-estimation;
more general adaptive
designs. Prerequisite: BIO-230. |
| BIO 282 |
Theory of Parametric, Semi-Parametric, and Non-Parametric
Inference |
This course presents a unified theory of inference in parametric,
semiparametric, and non-parametric models based on the construction
of higher order influence functions. Applications to the very high
dimensional data sets encountered in complex longitudinal studies
and in genomics will be highlighted. Prerequisite: BIO-288.
|
| 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. |
| 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. Prerequisite: BIO-231, BIO-244, and
BIO-250. |
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