## Biostatistics PhD Course Descriptions

Courses in Numerical Order

**500 Level Courses**

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**STAT 51200 Applied Regression (3 cr.) **P: STAT 51100. 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. 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: STAT 51200. Fundamentals, completely randomized design, randomized complete blocks. Latin squares, multi-classification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot and optimum design. Use of existing statistical computing packages.

**PBHL–B 515 Biostatistical Practicum (1–3 cr.) **P: STAT 52100; PBHL B527, B546; 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.

**STAT 51900 Introduction to Probability (3 cr.) **P: MATH 26100. 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. 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: STAT 51200. 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. 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 Models (3 cr.) **P: STAT 52800 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.

**PBHL–B 527 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.** **

**STAT 52800 Mathematical Statistics I (3 cr.) **P: STAT 51900. 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-Pearson Lemma, 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.

**BIOS–S 530 Statistics Methods in Bioinformatics and Computational Biology (3 cr.) **P: STAT 51200, 51900; or consent of instructor. Covers statistical methods used in many areas of bioinformatics research, including sequence alignment, genome sequencing and gene finding, gene expression microarray analysis, transcriptional regulation and sequence motif finding, comparative genomics, and proteomics. (Pending final approval by the University Graduate School.)

**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: STAT 51900 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. 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; semi-parametric proportional hazards regression (Cox Regression), parameters’ estimation, stratification, model fitting strategies and model interpretations. Heavy use of statistical software such as R and SAS.

**PBHL–B 546 Applied Longitudinal Data Analysis (3 cr.) **P: STAT 51200, 52500; 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 587 Nonlinear Mixed Models (3 cr.) **P: Undergraduate statistics course and familiarity with statistical inference. This course will develop the student’s ability to understand the pharmacokinetic/pharmaco-dynamic 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 Courses**

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

**STAT 61900 Probability Theory (3 cr.) **P: STAT 51900, 52800. Theory Measure theory based course in probability. Topics include Lebesgue measure, measurable functions and integration. Radon-Nikodyn 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.

**PBHL–B 621 Advanced Statistical Computing (3 cr.) **P: STAT 52100, 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 B527, B546. 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.

**STAT 62800 Advanced Statistical Inference (3 cr.) **P: STAT 51900, 52800, C: STAT 61900. 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.

**BIOS–S 634 Stochastic Modeling in Biomedical and Health Sciences (3 cr.) **P: STAT 52800. 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.

**PBHL–B 636 Advanced Survival Analysis (3 cr.) **P: STAT 53600, 62800. 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 logrank statistics, the Cox proportional hazards regression model, and the accelerated failure time model.

**PBHL–B 646 Advanced Generalized Linear Models (3 cr.) **P: PBHL B546. 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.

**BIOS-S 688 Theory of Statistical Genetics (3 cr.) **P: Graduate level statistics courses (such as PBHL B527, B546, and STAT 53600) 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.

**BIOS-S 699 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.