Correlated data arise in many situations, particularly when observations are made over time and space or on individuals who share certain underlying characteristics. This course covers techniques for exploring and describing correlated data, along with statistical methods for estimating population parameters (mostly means) from these data. The focus will be primarily on generalized linear models (both with and without random effects) for normally and non-normally distributed data. Wherever possible, techniques will be illustrated using real-world examples. Computing will be done using R and SAS. prereq: Regression at the level of PubH 6451 or PubH 7405 or Stat 5302. Familiarity with basic matrix notation and operations (multiplication, inverse, transpose). Working knowledge of SAS or R (PubH 6420).

Introduction to Bayesian methods. Comparison with traditional frequentist methods. Emphasizes data analysis via modern computing methods: Gibbs sampler, WinBUGS software package. prereq: [[7401 or STAT 5101 or equiv], [public health MPH or biostatistics or statistics] grad student] or instr consent

Introduction to statistical problems arising in molecular biology. Problems in physical mapping (radiation hybrid mapping, DDP), genetic mapping (pedigree analysis, lod scores, TDT), biopolymer sequence analysis (alignment, motif recognition), and micro array analysis. prereq: [6450, [6451 or equiv]] or instr consent; background in molecular biology recommended

Statistical methodologies in analysis of survival data. Kaplan-Meier estimator, Cox's proportional hazards multiple regression model, time-dependent covariates, analysis of residuals, multiple failure outcomes. Typical biomedical applications, including clinical trials and person-years data. prereq: 7405, [STAT 5101 or STAT 8101]

Diagnostic medicine, including methods for ROC curve. Bioassays. Early-phase clinical trials, methods including dose escalation, toxicity, and monitoring. Quality of life. prereq: [[6450, 6451] or equiv], [grad student in biostatistics or statistics or clinical research], familiarity with SAS

Various statistical techniques for extracting useful information (i.e., learning) from data. Linear discriminant analysis, tree-structured classifiers, feed-forward neural networks, support vector machines, other nonparametric methods, classifier ensembles, unsupervised learning. prereq: [[[6450, 6452] or equiv], programming backgroud in [FORTRAN or C/C++ or JAVA or Splus/R]] or instr consent; 2nd yr MS recommended

Although most of statistical inference focuses on associational relationships among variables, in many biomedical and health sciences contexts the focus is on establishing the causal effect of an intervention or treatment. Drawing causal conclusions can be challenging, particularly in the context of observational data, as treatment assignment may be confounded. The first part of this course focuses on methods to establish the causal effect of a point exposure, i.e., situations in which treatment is given at a single point in time. Methods to estimate causal treatment effects will include outcome regression, propensity score methods (i.e., inverse weighting, matching), and doubly robust approaches. The second half of the course focuses on estimating the effect of a series of treatment decisions during the course of a chronic disease such as cancer, substance abuse, mental health disorders, etc. Methods to estimate these time-varying treatments include marginal structural models estimated by inverse probability weighting, structural nested models estimated by G-estimation, and the (parametric) G-computation algorithm. We will then turn our attention to estimating the optimal treatment sequence for a given subject, i.e., how to determine “the right treatment, for the right patient, at the right time,” using dynamic marginal structural models and methods derived from reinforcement learning (e.g., Q-learning, A-learning) and classification problems (outcome weighted learning, C-learning). PubH 8485 is appropriate for Ph.D students in Biostatistics and Statistics. The homework and projects will focus more on the theoretical aspects of the methods to prepare students for methodological research in this area. PubH 7485 is appropriate for Masters students in Biostatistics and PhD students in other fields who wish to learn causal methods to apply them to topics in the health sciences. This course uses the statistical software of R, a freely available statistical software package, to implement many of the methods we discuss. However, most of the methods discussed in this course can be implemented in any statistical software (e.g., SAS, Stata, SPSS, etc.) and students will be free to use any software for homework assignments. prereq: Background in regression (e.g. linear, logistic, models) at the level of PubH 7405-7406, PubH 6450-6451, PubH 7402, or equiv. Background in statistical theory (Stat 5101-5102 or PubH 7401) is helpful.

Hypotheses/endpoints, choice of intervention/control, ethical considerations, blinding/randomization, data collection/monitoring, sample size, analysis, writing. Protocol development, group discussions. prereq: 6414 or 6450 or one semester graduate-level introductory biostatistics or statistics or instr consent

Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews. prereq: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instr consent

Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews. prereq: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instr consent

Statistical methodologies in analysis of survival data. Kaplan-Meier estimator, Cox's proportional hazards multiple regression model, time-dependent covariates, analysis of residuals, multiple failure outcomes. Typical biomedical applications, including clinical trials and person-years data. prereq: 7405, [STAT 5101 or STAT 8101]

Theory/application of Bayesian methods. Bayesian methods compared with traditional, frequentist methods. prereq: [[7460 or experience with FORTRAN or with [C, S+]], Stat 5101, Stat 5102, Stat 8311, grad student in [biostatistics or statistics]] or instr consent

Methods of inference for outcome variables measured repeatedly in time or space. Linear/nonlinear models with either normal or non-normal error structures. Random effects. Transitional/marginal models with biomedical applications. prereq: [Stat 5102, Stat 8311, experience with [SAS or S+], advanced [biostats or stat] student] or instr consent

Statistical methods for counting processes. Martingale theory (transforms, predictable processes, Doob decomposition, convergence, submartingales). Applications to nonparametric intensity estimation. Additive/relative risk models. Inference for event history data, recurrent events, multivariate survival, diagnostics. prereq: [7450, 8432, Stat 5102, advanced [biostatistics or statistics] major] or instr consent

Spatial data, spatial statistical models, and spatial inference on unknown parameters or unobserved spatial data. Nature of spatial data. Special analysis tools that help to analyze such data. Theory/applications. prereq: [[STAT 5101, STAT 5102] or [STAT 8101, STAT 8102]], some experience with S-plus; STAT 8311 recommended

Statistical techniques for extracting useful information from data. Linear discriminant analysis, tree-structured classifiers, feed-forward neural networks, support vector machines, other nonparametric methods, classifier ensembles (such as bagging/boosting), unsupervised learning. prereq: [[[6450, 6451, 6452] or STAT 5303 or equiv], [biostatistics or statistics PhD student]] or instr consent

Statistical methods for design/analysis of sequential experiments. Wald theorems, stopping times, martingales, Brownian motion, dymamic programming. Compares Bayesian/fequentist approaches. Applications to interim monitoring of clinical trials, medical surveillance. prereq: Stat 8101-8102 or equivalent, [students should be comfortable with the multivariate normal distribution or instr consent]

Although most of statistical inference focuses on associational relationships among variables, in many biomedical and health sciences contexts the focus is on establishing the causal effect of an intervention or treatment. Drawing causal conclusions can be challenging, particularly in the context of observational data, as treatment assignment may be confounded. The first part of this course focuses on methods to establish the causal effect of a point exposure, i.e., situations in which treatment is given at a single point in time. Methods to estimate causal treatment effects will include outcome regression, propensity score methods (i.e., inverse weighting, matching), and doubly robust approaches. The second half of the course focuses on estimating the effect of a series of treatment decisions during the course of a chronic disease such as cancer, substance abuse, mental health disorders, etc. Methods to estimate these time-varying treatments include marginal structural models estimated by inverse probability weighting, structural nested models estimated by G-estimation, and the (parametric) G-computation algorithm. We will then turn our attention to estimating the optimal treatment sequence for a given subject, i.e., how to determine "the right treatment, for the right patient, at the right time," using dynamic marginal structural models and methods derived from reinforcement learning (e.g., Q-learning, A-learning) and classification problems (outcome weighted learning, C-learning). PubH 8485 is appropriate for PhD students in Biostatistics and Statistics. The homework and projects will focus more on the theoretical aspects of the methods to prepare students for methodological research in this area. PubH 7485 is appropriate for Masters students in Biostatistics and PhD students in other fields who wish to learn causal methods to apply them to topics in the health sciences. This course uses the statistical software of R, a freely available statistical software package, to implement many of the methods we discuss. However, most of the methods discussed in this course can be implemented in any statistical software (e.g., SAS, Stata, SPSS, etc.) and students will be free to use any software for homework assignments.

Part of two-course sequence intended for PhD students in School of Public Health who need rigorous approach to probability/statistics/statistical inference with applications to research in public health. prereq: Background in calculus; intended for PhD students in public hlth and other hlth sci who need rigorous approach to probability/statistics and statistical inference with applications to research in public hlth

Second of two-course sequence. Rigorous approach to probability/statistics, statistical inference. Applications to research in public health. prereq: 7401; intended for PhD students in health sciences

T-tests, confidence intervals, power, type I/II errors. Exploratory data analysis. Simple linear regression, regression in matrix notation, multiple regression, diagnostics. Ordinary least squares, violations, generalized least squares, nonlinear least squares regression. Introduction to General linear Model. SAS and S-Plus used. prereq: [[Stat 5101 or concurrent registration is required (or allowed) in Stat 5101], biostatistics major] or instr consent

This course introduces students to a variety of concepts, tools, and techniques that are relevant to the rigorous design and analysis of complex biomedical studies. Topics include ANOVA, sample-size calculations, multiple testing, missing data, prediction, diagnostic testing, smoothing, variable selection, the bootstrap, and nonparametric tests. R software will be used. Biostatistics students are strongly encouraged to typeset their work using LaTeX or in R markdown. prereq: [7405, [STAT 5102 or concurrent registration is required (or allowed) in STAT 5102], biostatistics major] or instr consent

Correlated data arise in many situations, particularly when observations are made over time and space or on individuals who share certain underlying characteristics. This course covers techniques for exploring and describing correlated data, along with statistical methods for estimating population parameters (mostly means) from these data. The focus will be primarily on generalized linear models (both with and without random effects) for normally and non-normally distributed data. Wherever possible, techniques will be illustrated using real-world examples. Computing will be done using R and SAS. prereq: Regression at the level of PubH 6451 or PubH 7405 or Stat 5302. Familiarity with basic matrix notation and operations (multiplication, inverse, transpose). Working knowledge of SAS or R (PubH 6420).

Introduction to Bayesian methods. Comparison with traditional frequentist methods. Emphasizes data analysis via modern computing methods: Gibbs sampler, WinBUGS software package. prereq: [[7401 or STAT 5101 or equiv], [public health MPH or biostatistics or statistics] grad student] or instr consent

Introduction to statistical problems arising in molecular biology. Problems in physical mapping (radiation hybrid mapping, DDP), genetic mapping (pedigree analysis, lod scores, TDT), biopolymer sequence analysis (alignment, motif recognition), and micro array analysis. prereq: [6450, [6451 or equiv]] or instr consent; background in molecular biology recommended

Statistical methodologies in analysis of survival data. Kaplan-Meier estimator, Cox's proportional hazards multiple regression model, time-dependent covariates, analysis of residuals, multiple failure outcomes. Typical biomedical applications, including clinical trials and person-years data. prereq: 7405, [STAT 5101 or STAT 8101]

Diagnostic medicine, including methods for ROC curve. Bioassays. Early-phase clinical trials, methods including dose escalation, toxicity, and monitoring. Quality of life. prereq: [[6450, 6451] or equiv], [grad student in biostatistics or statistics or clinical research], familiarity with SAS

Various statistical techniques for extracting useful information (i.e., learning) from data. Linear discriminant analysis, tree-structured classifiers, feed-forward neural networks, support vector machines, other nonparametric methods, classifier ensembles, unsupervised learning. prereq: [[[6450, 6452] or equiv], programming backgroud in [FORTRAN or C/C++ or JAVA or Splus/R]] or instr consent; 2nd yr MS recommended

Although most of statistical inference focuses on associational relationships among variables, in many biomedical and health sciences contexts the focus is on establishing the causal effect of an intervention or treatment. Drawing causal conclusions can be challenging, particularly in the context of observational data, as treatment assignment may be confounded. The first part of this course focuses on methods to establish the causal effect of a point exposure, i.e., situations in which treatment is given at a single point in time. Methods to estimate causal treatment effects will include outcome regression, propensity score methods (i.e., inverse weighting, matching), and doubly robust approaches. The second half of the course focuses on estimating the effect of a series of treatment decisions during the course of a chronic disease such as cancer, substance abuse, mental health disorders, etc. Methods to estimate these time-varying treatments include marginal structural models estimated by inverse probability weighting, structural nested models estimated by G-estimation, and the (parametric) G-computation algorithm. We will then turn our attention to estimating the optimal treatment sequence for a given subject, i.e., how to determine “the right treatment, for the right patient, at the right time,” using dynamic marginal structural models and methods derived from reinforcement learning (e.g., Q-learning, A-learning) and classification problems (outcome weighted learning, C-learning). PubH 8485 is appropriate for Ph.D students in Biostatistics and Statistics. The homework and projects will focus more on the theoretical aspects of the methods to prepare students for methodological research in this area. PubH 7485 is appropriate for Masters students in Biostatistics and PhD students in other fields who wish to learn causal methods to apply them to topics in the health sciences. This course uses the statistical software of R, a freely available statistical software package, to implement many of the methods we discuss. However, most of the methods discussed in this course can be implemented in any statistical software (e.g., SAS, Stata, SPSS, etc.) and students will be free to use any software for homework assignments. prereq: Background in regression (e.g. linear, logistic, models) at the level of PubH 7405-7406, PubH 6450-6451, PubH 7402, or equiv. Background in statistical theory (Stat 5101-5102 or PubH 7401) is helpful.

Hypotheses/endpoints, choice of intervention/control, ethical considerations, blinding/randomization, data collection/monitoring, sample size, analysis, writing. Protocol development, group discussions. prereq: 6414 or 6450 or one semester graduate-level introductory biostatistics or statistics or instr consent

Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews. prereq: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instr consent