Title: Centered Isotonic Regression: Point and Interval Estimation for Dose-Response Studies,
Abstract: 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.