Programs by Campus

Indianapolis

Biostatistics

Courses

Curriculum
Courses
Faculty

500 Level

STAT 51200 Applied Regression (3 cr.) P: STAT 51100 or equivalent. Inference in simple and multiple linear regression, residual analysis, transformations, polynomial regression, model building with real data, nonlinear regression. One-way and two-way analysis of variance. Use of existing statistical computing package.

STAT 51300 Statistical Quality Control (3 cr.) P: STAT 51100 or equivalent. Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, statistics of combinations, and some nonparametric methods. Use of existing statistical computing packages.

STAT 51400 Design of Experiments (3 cr.) P: STAT51200 or equivalent. Fundamentals, completely randomized design, randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot and optimum design. Use of existing statistical computing packages.

STAT 51900 Introduction to Probability (3 cr.) P: MATH26100 or equivalent. Algebra of sets, sample spaces, combinatorial problems, conditional probability, independence, random variables, distribution functions, characteristic functions, special discrete and continuous distributions, distributions of function of random variables, limit theorems.

STAT 52000 Time Series and Applications (3 cr.) P: STAT 51900 or equivalent . A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationary, auto-covariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering; transfer function models; estimation of spectrum; multivariate time series; Kalman filtering, Burg’s algorithm.

STAT 52100 Statistical Computing (3 cr.) P: STAT51200 or equivalent. This course demonstrates how computing can be used to understand the performance of core statistical methods and introduces modern statistical methods that require computing in their application. Covers relevant programming fundamentals in at least two programming environments (e.g. SAS and R/Splus).

STAT 52200 Sampling and Survey Techniques (3 cr.) P: STAT 51200 or STAT 51100 or equivalent. Survey designs, simple random, stratified, cluster and systematic sampling; systems of sampling; methods of estimation, ratio and regression estimates, costs; non-response analysis; spatial sampling.

STAT 52300 Categorical Data Analysis Models (3 cr.) P: STAT 52800 or equivalent, or consent of instructor. Generating binary and categorical response data, two way classification tables, measures of association and agreement, goodness-of-fit tests, testing independence, large sample properties. General linear models, logistic regression, probit and extreme value models. Log-linear models in two and higher dimensions; maximum likelihood estimation, testing Goodness-of-fit, partitioning Chi- Square, models for ordinal data. Model-building, selection and diagnostics. Other related topics as time permits. Computer applications using SAS.

STAT 52400 Applied Multivariate Analysis (3 cr.) P: STAT 52800 or equivalent, or consent of instructor. Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminate analysis and misclassification errors, canonical correlation, principal components, factor analysis.

STAT 52500 Generalized Linear Model (3 cr.) P: STAT52800 or equivalent or consent of instructor. Generalized linear models, likelihood methods for data analysis, diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical log-linear models for contingency tables.

STAT 52800 Mathematical Statistics I (3 cr.) P: STAT51900 or equivalent. Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell Theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-PearsonLemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, sequential probability ratio test.

STAT 52900 Bayesian Statistics and Applied Decision Theory (3 cr.) P: STAT 52800 or equivalent. Bayesian and decision theoretic formulation of problems;

construction of utility functions and quantification of prior information; choice of prior; methods of Bayesian decision and inference,; Bayesian computations; MCMC methods; empirical Bayes; hierarchical models, Bayes factors; combination of evidence; game theory and minimax rules, Bayesian design and sequential analysis.

STAT 53200 Elements of Stochastic Processes (3 cr.) P: STAT 51900 or equivalent. A basic course in stochastic models including discrete and continuous time processes, Markov chains and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes and Poisson processes. Applications to economics, epidemic models, birth and death processes, point processes, and reliability problems.

STAT 53300 Nonparametric Statistics (3 cr.) P: STAT51900 or equivalent. Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one and two sample Kolmogorov-Smirnov tests, nonparametric regression.

STAT 53600 Introduction to Survival Analysis (3 cr.) P: STAT 51700 or equivalent. Deals with the modern statistical methods for analyzing time-to-event data. Background theory is provided, but the emphasis is on the applications and the interpretations of results. Provides coverage of survivorship functions and censoring patterns; parametric models and likelihood methods, special lifetime distributions; nonparametric inference, life-tables, estimation of cumulative hazard functions, the Kaplan-Meier estimator; one and two-sample nonparametric tests for censored data; semiparametric proportional hazards regression (Cox Regression), parameters’ estimation, stratification, model fitting strategies and model interpretations. Heavy use of statistical software such as Splus and SAS.

PBHL –B 561: Introduction to Biostatistics I (3 cr.) P: consent of instructor. This course introduces the basic principles and methods of data analysis in public health biostatistics. Emphasis is placed on public health examples as they relate to concepts such as sampling, study design, descriptive statistics, probability, statistical distributions, estimation, hypothesis testing, chi-square tests, t- tests, analysis of variance, linear regression and correlation.  SAS software is required for some of the homework questions.

PBHL –B 562: Biostatistics-Public Health II (3cr.) P: PBHL –B 561 or equivalent. This course introduces the advanced principles and methods of data analysis in public health biostatistics.  Emphasis is placed on public health examples as they relate to concepts such as:  Multiple regression, analysis of variance and covariance, logistic regression, nonparametric statistics, survival analysis, epidemiology statistics, and repeated measures analysis.  

PBHL –B 571 Biostatistics Method I-Linear Regression Model (4 cr.) P: PBHL –B 561 or equivalent. It course covers fundamental methods in Experiment Design, ANOVA, Analysis of Covariance, Simple and Multiple Linear Regressions with applications in biomedical study and public health. The focus of this course is to prepare students with solid skill in data analysis and interpretation of analytic results for numerical outcomes.  Extensive use of Statistical software SAS is anticipated.

PBHL –B 572: Biostatistics Method II-Categorical Data Analysis (4 cr.) P: PBHL –B 571 or equivalent. This course covers applied statistical methods for the analysis of categorical data with special emphasis on data collected from epidemiologic studies and general biomedical studies in various designs such as prospective cohort and retrospective case-control designs. The focus of this course is to prepare students with solid skill in data analysis and interpretation of analytic results for binary, multilevel and count data. Extensive use of Statistical software SAS is anticipated.

PBHL –B 573: Biostatistics Method III-Applied Survival Data Analysis (4 cr.) P: PBHL –B 571, 572 or equivalent This course covers basic components in modern survival data analysis with emphasis on its application in biomedical research and public health. It includes the topics of types of censoring and truncation, life tables and survival function estimation, nonparametric log-rank test, parametric accelerated failure time model, semiparametric Cox proportional hazards model and extended Cox regression for time-dependent variables, competing risks and correlated survival data.  The focus of this course is to prepare students with solid skill in data analysis and interpretation of analytic results for time-to-event data. Extensive use of statistical software SAS is anticipated.

PBHL –B 574 Biostatistics Method IV-Applied Longitudinal Data Analysis (3 cr.) P: STAT 51200, 52500 or PBHL –B 571, 572 or permission of instructor. Covers modern methods for the analysis of repeated measures, correlated outcomes and longitudinal data. Topics: repeated measures ANOVA, random effects and growth curve models, generalized estimating equations (GEE) and generalized linear mixed models (GLMMs). Extensive use of statistical software, e.g. SAS, R.

PBHL –B 581 Biostatistics Computing (3 cr.) P: consent of instructor. The objective of this course is to prepare students with the necessary SAS skills for general data preparation, description, visualization, and some advanced skills. This course may be viewed as computing preparation for Biostatistics methods courses. Data steps and the following procedures will be covered: IMPORT, SORT, PRINT, FORMAT, TABULATE, REPORT, MEANS, UNIVARIATE, FREQ, CORR, SQL, GPLOT, SGPLOT, SGPANEL. SAS macro, ODS and IML will also be briefly introduced.

PBHL –B 582 Introduction to Clinical Trials (3 cr.) P: STAT 51200, exposure to survival analysis; or consent of instructor. Prepares biostatisticians for support of clinical trial projects. Topics: fundamental aspects of the appropriate design and conduct of medical experiments involving human subjects including ethics, design, sample size calculation, randomization, monitoring, data collection analysis and reporting of the results.

PBHL –B 583 Applied Multivariate Statistical Methods for Public Health (3 cr.) P: PBHL –B 551, 652 or equivalent.  This is an introductory applied multivariate statistics course designed specifically for graduate students with a PhD major in epidemiology (or advanced masters epidemiology students). The course can also be taken by other non-statistician majors, for example, PhD students in other medical sciences and health care professionals. Students are expected to have taken two previous courses in statistics (introductory and intermediate) covering up through t-test, ANOVA, ANCOVA, linear regression, and logistic regression. The overall objective of this course is to use public health examples while introducing classic multivariate statistical techniques. The course will focus on applications using the SAS software. Very little attention will be given to matrix algebra. Instead, greater importance will be placed on conceptual understanding and interpretations. Basic bivariate statistics, data screening (e.g., missing data, outliers, assumptions, multi-collinearity), and regression will be reviewed. The following classic multivariate techniques will be covered: canonical correlation, MANOVA, MANCOVA, discriminant analysis, principal components analysis, exploratory factor analysis, confirmatory factor analysis, and structural equation modeling (SEM). Two special topics will be introduced but not tested over: (1) mixed linear models for repeated measures analysis and multi-level modeling of clustered data; and (2) analysis of sample survey data, obtained from complex sampling designs, using the SAS SURVEY procedures with sampling weights.

PBHL –B 584 Biostatistical Practicum (1-3 cr.) P: STAT52100; PBHL –B 582, 574; or consent of instructor. Real-world projects in biostatistics involving participation in consulting sessions, directed reading in the literature, research ethics, design of experiments, collection of data and applications of biostatistical methods. Detailed written and oral reports required. May be repeated up to 6 credits.

PBHL –B 585 Analysis and Interpretation of Observational Studies (3 cr.) P. PBHL-B 561, 562 or equivalent. This course examines fundamental aspects of analyzing data generated by observational epidemiology studies. The focus is on developing a solid understanding of contemporary analytical techniques to increase the validity of the study and control for possible confounding factors and biases.

PBHL -B 587 Nonlinear Mixed Models (3 cr.) P: STAT52800, 51200 or equivalent. . This course will develop the student’s ability to understand the pharmacokinetic/pharmacodynamic model, fit the nonlinear mixed model through the required software package, conduct the diagnosis of model fitting, perform the hypothesis tests, and provide the interpretation of the data.

600 Level

PBHL -B 612 Modern Statistical Learning Methods (3 cr.) P: STAT 52500 or equivalent.. This course covers the topics pertaining to the modern methods of high-dimensional data analysis.

STAT 61900 Probability Theory (3 cr.) P: STAT 51900, 52800 or equivalent. Theory Measure theory based course in probability. Topics include Lebesgue measure, measurable functions and integration. Radon-Nikodym Theorem, product measures and Fubini’s Theorem, measures on infinite product spaces, basic concepts of probability theory, conditional probability and expectation, regular conditional probability, strong law of large numbers, martingale theory, martingale convergence theorems, uniform integrability, optional sampling theorems, Kolmogorov’s Three series Theorem, weak convergence of distribution functions, method of characteristic functions, the fundamental weak compactness theorems, convergence to a normal distribution, Lindeberg’s Theorem, infinitely divisible distributions and their subclasses.

STAT 62800 Advanced Statistical Inference (3 cr.) P: STAT 51900, 52800, C: STAT 61900 or equivalent.. Real analysis for inference, statistics and subfields, conditional expectations and probability distributions, UMP tests with applications to normal distributions and confidence sets, invariance, asymptotic theory of estimation and likelihood based inference, U-statistics, Edgeworth expansions, saddle point method.

PBHL -B 621 Advanced Statistical Computing (3 cr.) P: STAT 52100 or experience with R/Splus programming. This course covers selected computational techniques useful in advanced statistical applications and statistical research, such as methods for solving linear equations, numerical optimization, numerical integration, Bayesian methods, bootstrap methods, and stochastic search algorithms.

PBHL -B 627 Statistics in Pharmaceutical Research (3 cr.) P: STAT 51200; PBHL –B 582, PBHL –B 574 or equivalent. An overview of the drug development process, including the various phases of development from pre-clinical to post-marketing. Topics: statistical issues in design, study monitoring, analysis and reporting. Additional topics may include regulatory and statistical aspects of population pharmacokinetics and real world applications.

PBHL –B 626 Advanced Likelihood Theory (3 cr.) P: STAT51900, STAT52800 or equivalent.  This course covers fundamental theory in likelihood-based inferences and their applications in statistical models for various types of data encountered in biomedical research. It prepares students with extensive skills in applying law of large number and central limit theorems to a large range of likelihood related problems and missing data problems.

PBHL -B 634 Stochastic Modeling in Biomedical and Health Sciences (3 cr.) P: STAT 52800 or equivalent. The aim of this course is to develop those aspects of stochastic processes that are relevant for modeling important problems in health sciences. Among the topics to be covered are: Poisson processes, birth and death processes, Markov chains and processes, semi-Markov processes, modeling by stochastic diffusions. 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.

BIOS-S 636 Advanced Survival Analysis (3 cr.) P: STAT 53600, 62800, or PBHL –B 626 or equivalent.  Addresses the counting process approach to the analysis of censored failure time data. Standard statistical methods in survival analysis will be examined, such as the Nelson-Aalen estimator of the cumulative hazard function, the Kaplan-Meier estimator of the survivor function, the weighted log-rank statistics, the Cox proportional hazards regression model, and the accelerated failure time model.

PBHL –B 646 Advanced Generalized Linear Model (3 cr.) P: STAT52500 or equivalent. This course focuses on the key concepts and theoretical underpinnings of generalized linear models (GLM). It describes the basic modeling structure, theoretical properties of parameter estimates, and model fitting approaches in the context of GLM. It also covers some of the more recent extensions of GLM. 

PBHL -B 656 Advanced Longitudinal Data Analysis (3 cr.) P: PBHL –B 574 or equivalent. The theory of classical and modern approaches to the analysis of clustered data, repeated measures, and longitudinal data: random effects and growth curve models, generalized estimating equations, statistical analysis of multivariate categorical outcomes, estimation with missing data. Discussion of computational issues: EM algorithm, quasi-likelihood methods, Bayesian methods for both traditional and new methodologies.

PBHL -B 688 Theory of Statistical Genetics (3 cr.) P: Graduate level statistics courses (such as PBHL -B582, B574) and Q730, Methods in Human Genetics. This course is designed to provide solid training in statistical theory used in genetic analyses.

PBHL -B 698 Topics in Biostatistical Methods (1-3 cr.) P: Consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

STAT 69500 Seminar in Mathematical Statistics (1-3 cr.) P: Consent of advisor. Individual study that meets 3 times per week for 50 minutes per meeting for 16 weeks.

PBHL -B 800 Research-Ph.D. Thesis (1---15 cr.) P: Must have been admitted to candidacy. See advisor for more information. Research required by the graduate students for the sole purpose of writing a Ph.D. Dissertation.

Academic Bulletins

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