On Estimation for Monotone Dose—Response Curves

Abstract

Abstract Estimating monotone dose—response curves with independent, normal errors has been studied in detail in the literature. A simple procedure using a generalization of the studentized maximum modulus technique is proposed for constructing confidence bands for monotone regression functions. This procedure is shown to compare well with its predecessors. The center of this smooth and efficient confidence band is then used to estimate a smooth monotone regression function. Its pointwise mean squared errors compare favorably with the maximum likelihood estimate, a weighted average of the isotonic regression and the least squares line, and the rank-transformed regression. A numerical example of a binding inhibition assay is included to illustrate the proposed interval and point estimation procedures.