An Effective and Small Sample-Size Valid Confidence Interval for Isotonic Dose–Response Curves by Inverting a Partial Likelihood Ratio Test

A dose–response curve is essential for determining the safe dosage of a drug and is widely used in bioassay and in phase 1 clinical trials. It is generally accepted that the probability of death or the probability of dose-limiting toxicity is a nondecreasing function of the dose. This article proposes and develops an effective point-wise confidence interval for an isotonic dose–response curve, a problem without a satisfactory solution so far. We show that one subset of the observations informs the lower limit while the other subset informs the upper limit. A partial likelihood ratio test using these subsets of observations is fully investigated. The resulting confidence interval is compared to three existing methods (Morris, Meyer, and Oron) in an extensive simulation study. The new method produces tight intervals while maintaining coverage. It is therefore preferred when maintaining an actual coverage probability is crucial as often in a regulatory environment. The new method extends to one-way ANOVA of a continuous response variable in a straightforward way. An R function is provided.