2017/01/01 by Assaf P. Oron, Nancy Flournoy, Oron, Assaf P. +1
Decision Sciences · #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.1701.05964
Univariate isotonic regression (IR) has been used for nonparametric\nestimation in dose-response and dose-finding studies. One undesirable property\nof IR is the prevalence of piecewise-constant stretches in its estimates,\nwhereas the dose-response function is usually assumed to be strictly\nincreasing. We propose a simple modification to IR, called centered isotonic\nregression (CIR). CIR's estimates are strictly increasing in the interior of\nthe dose range. In the absence of monotonicity violations, CIR and IR both\nreturn the original observations. Numerical examination indicates that for\nsample sizes typical of dose-response studies and with realistic dose-response\ncurves, CIR provides a substantial reduction in estimation error compared with\nIR when monotonicity violations occur. We also develop analytical interval\nestimates for IR and CIR, with good coverage behavior. An R package implements\nthese point and interval estimates.\n