Centered Isotonic Regression: Point and Interval Estimation for Dose-Response Studies

• Activity Number: 701
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Assaf Oron* and Nancy Flournoy
• Companies: Seattle Children's Research Institute and University of Missouri - Columbia
• Keywords: isotonic regression ; nonparametric ; dose-finding ; dose-response ; up-and-down ; estimation

Abstract

Univariate isotonic regression (IR) with linear interpolation between point estimates, has been used for nonparametric estimation of dose-response and dose-finding studies. One undesirable property of IR is the presence of constant-response intervals. We develop a simple modification to IR, strictly increasing in the interior of the dose range. This modification, called centered isotonic regression (CIR), requires no tuning parameter. In the absence of monotonicity violations, CIR is identical to IR. Numerical examination indicates that for sample sizes typical of dose-response and dose-finding studies, CIR provides a substantial reduction in estimation error, except when the dose-response function itself is approximately piecewise-constant. In addition, we develop and present interval estimates for IR and CIR, with good coverage behavior. The R `cir' software package implements these point and interval estimates.