A Semiparametric Sequential Algorithm for Estimation of Dose–Response Curve

Sequential designs for binary regression models are used for efficient estimation of quantiles of interest of the dose–response curve given by a link function. In many applications the link function is assumed to be known up to a location and a scale. We perform an empirical study to illustrate how the quantile estimates may be affected when the link function is misspecified. We propose nonparametric estimation of the link function via an isotonic smoothing spline estimator and incorporate the estimator into the sequential allocation scheme. This makes the procedure more robust against link function misspecification and at the same time maintains the objective of efficient estimation of the parameters.