Adaptive Regression for Modeling Nonlinear Relationships

This book presents methods for investigating whether relationships are linear or nonlinear and for fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables in regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and require adaptive regression. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible.

A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on power transformations of primary predictor variables using real-valued powers. The book also covers how to formulate and conduct such adaptive fractional polynomial modeling in the standard, logistic, and Poisson regression contexts with univariate or multivariate outcomes, and the book provides for a comparison of adaptive modeling to generalized additive modeling (GAM) and multiple adaptive regression splines (MARS) for univariate outcomes.

The authors have created customized SAS macros for use with adaptive regression modeling. These macros and code for conducting the analyses discussed in the book are available through the first author's website and online via the book’s Springer website. Detailed descriptions of how to use these macros and their output appear throughout the book, though the methodology can be applied to other programs.

George Knafl is Professor and Biostatistician in the School of Nursing of the University of North Carolina at Chapel Hill where he teaches statistics courses to doctoral nursing students, consults with graduate students and faculty on their research, and conducts his own research. He has over 35 years of experience in teaching, consulting, and research in statistics. His research involves development of methods for searching through alternative models for data to identify an effective choice for modeling those data and the application of those methods to the analysis of health science data sets. He is also Professor Emeritus in the College of Computing and Digital Media at DePaul University and has also taught in Schools of Nursing at Yale University and the Oregon Health and Sciences University.

Kai Ding is Assistant Professor, Department of Biostatistics and Epidemiology at the University of Oklahoma (OU) Health Sciences Center. He is also Associated Member of the Peggy and Charles Stephenson Cancer Center (SCC) of OU Medicine. Dr. Ding received his Ph.D. in Biostatistics from the University of North Carolina at Chapel Hill in 2010. His research has focuses on survival analysis and semiparametric inference. He has been involved in the design and analysis of numerous research studies in cancer and ophthalmology and currently serves on the Scientific Review Committee and the Protocol Monitoring Committee of the SCC.?