Modeling Nonmonotonic Dose-Response Curves

Abstract

Abstract : A number of procedures have been used to analyze nonmonotonic binary data to predict the probability of response. Some classical procedures are the Up and Down strategy, the Robbins-Monro procedure, and other sequential optimization designs. Recently, nonparametric procedures such as kernel regression and local linear regression have been applied to this type of data. It is well known that kernel regression has problems fitting the data near the boundaries, and a drawback with local linear regression is that it may be too linear when fitting data from a curvilinear function. This report introduces a procedure called local logistic regression, which fits a logistic regression function at each of the data points. United States Army projectile data are used in an example that supports the use of local logistic regression for analyzing nonmonotonic binary data for certain response curves. Properties of local logistic regression are presented along with simulation results that indicate some of the strengths of the procedure.