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

Univariate isotonic regression (IR) has been used for nonparametric estimation in dose–response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the dose–response function is usually assumed to be strictly increasing. We propose a simple modification to IR, called centered isotonic regression (CIR). CIR's estimates are strictly increasing in the interior of the dose range. In the absence of monotonicity violations, CIR and IR both return the original observations. Numerical examination indicates that for sample sizes typical of dose–response studies and with realistic dose–response curves, CIR provides a substantial reduction in estimation error compared with IR when monotonicity violations occur. We also develop analytical interval estimates for IR and CIR, with good coverage behavior. An R package implements these point and interval estimates. Supplementary materials for this article are available online.