The Essentials of Curvature and Optimal Design in Biostatistics

Applied Nonlinear Statistical Methods

Dr. Timothy E. O’Brien, Ph.D.

Loyola University of Chicago

ABSTRACT

Researchers often recognize that nonlinear regression models are more applicable for modelling their physical and medical processes than are linear ones for several important reasons. Nonlinear models usually fit their data well and often in a more parsimonious manner (typically with far fewer model parameters). Also, nonlinear models and the corresponding model parameters are usually more scientifically meaningful. But selecting an efficient experimental design; choosing, fitting and interpreting an appropriate nonlinear model; and deriving and interpreting confidence intervals for key model parameters can present practitioners with fundamental and important challenges.

This course first reviews the essentials of linear regression, and subsequently introduces and illustrates generalized linear models (such as logistic regression), Gaussian nonlinear models, and generalized nonlinear models, focusing on applications. Illustrations are given from the domains of bioassay, relative potency and drug or similar compound synergy useful in biomedical and environmental sciences. Caveats are discussed regarding convergence, diagnostics, and the inadequacy of standard (Wald) confidence intervals – which are the intervals provided by most software packages. Extensions to bivariate situations (such as those focusing on both efficacy and safety of drugs) and censored (survival) analysis are also provided, as are implications for experimental design. Implementation using the SAS^® statistical software package will be discussed, but references will be made to other packages as well.

COURSE OUTLINE

Brief review of simple and multiple linear regression; two-sample t-tests, ANOVA, ANOCOV (analysis of covariance); diagnostics and model checking; logistic regression.

Introduction to Gaussian nonlinear models; practical concerns (choosing a model, starting values); nonlinear contrasted with linear models and with generalized linear models; applications (substance dissolution and enzyme kinetics); confidence regions, intervals, and the impact of curvature (nonlinearity, asymmetry).

Diagnostics and model checking; examples involving ELISA’s (and other assays) and pharmacokinetics; extensions of classical methods including modelling variance functions and correlated responses; brief discussion of mixed and hierarchical nonlinear models.

Generalized nonlinear models and applications in bioassay, relative potency, and drug/similar compound synergy modelling; usefulness and limitations of the IML and NLMixed SAS^® procedures.

Experimental design strategies including benefits and limitations of optimal designs; robust ‘optimal’ design strategies; geometric designs.

Extensions to bivariate Gaussian and binomial responses and to censored data in the context of the detection of drug/similar compound synergy.

FURTHER INFORMATION ABOUT THE PRESENTER

Dr. Timothy E. O’Brien is a tenured associate professor with the graduate faculty in the Department of Mathematics and Statistics, Loyola University of Chicago. Dr. O’Brien received his Ph.D. in Statistics from North Carolina State University in 1993. His dissertation topic, "New Design Strategies for Parameter Estimation and Model Discrimination in Nonlinear Regression Models" focuses on optimal experimental design, generalized linear and nonlinear modeling, and computer intensive methods, with applications to drug synergy research. Dr. O’Brien also received an M.A. in Statistics from the University of Rochester (1987), an M.A. in Mathematics from Syracuse University (1985), and a B.A. in Mathematics and Economics from Pace University (1978). He is a member of ASA, ENAR, IASC, IASE, and ISI.

Dr. O’Brien has made several contributions to the theory and methods of optimal experimental design, particularly regarding nonlinear modeling. Some of his publications appear (or will appear) in Biometrika, Statistica Sinica, Journal of Statistical Planning and Inference, The American Statistician, Journal of Agricultural, Biological, and Environmental Statistics, the Journal of Chemical Ecology, Computational Statistics and Data Analysis, and the Journal of Data Science. Dr. O’Brien also published three book chapters on optimal design, robust design, and lack of fit, for nonlinear regression models, as well as several refereed conference proceedings (e.g., Proceedings of the 15^th Conference on Applied Statistics in Agriculture, Proceedings of Agro-Industrie et Methodes Statistiques) and collaborative papers in refereed biomedical journals (e.g., Development, Annals of Neurology, Cell and Tissue Research), which illustrate the immediate application of his theoretical work. Dr. O’Brien won a SUGI Best Contributed Paper Award for demonstrating how some of his metholdogical work on optimal designs for nonlinear regression models can be implemented with SAS®

Dr. O’Brien's has extensive industrial and academic work experience which includes two years as a biostatistical consultant at Janssen Pharmaceutics NV, two years as an internal statistical consultant and biostatistician at Novartis Pharma AG, and three years as an assistant statistician at Glaxo. Dr. O’Brien’s previous domestic academic experience includes Assistant Professor positions at Loyola University of Chicago, the University of Georgia, and Washington State University. Internationally, Dr. O’Brien has been a Visiting Professor at both Limburgs Universitair Centrum (Belgium) and Katholieke Universiteit Leuven (Belgium), a Visiting Lecturer at the University of Natal at Pietermaritzburg (South Africa), and he was awarded two postdoctoral fellowships, one at the Universität Augsburg (Germany) and the other at INRA, Laboratorie de Biometrie (France).

Dr. O’Brien has a strong interest in and committment to statistical and mathematical education. He has developed and taught a wide range of theoretical and applied statistics, statistical computing, statistical programming, statistical consulting, and mathematics courses, at both the graduate and undergraduate levels, at both domestic and universities abroad.