Influence of the slope in percentile estimation through binary regression for dose-finding experiments

Dose-finding experiments aim to estimate the dose having a specified proportion of positive responses by collecting data in the vicinity of this unknown target dose. The importance of estimating the slope as well as a target dose has been recognized long ago in the literature. With large slopes at the target dose, a small error in the target dose estimate will be far from the target. Alternatively, with small slopes at the target, a large error conveys negligible changes on the associated response rate.  Thus a reasonably reliable estimate of the slope of the response function at the target dose should accompany every reported target dose estimate. Assuming a monotone increasing dose-response relationship, we work with a sizable catalogue of binary location-scale regression models parameterized by the target dose and the slope at the target. A compound design is proposed for the joint estimation of both features.