A comparative study of the dose-response analysis with application to the target dose estimation

With a quantal response, the dose-response relation is summarized by the response probability function (RPF) that provides probabilities of the response being reacted as a function of dose levels. In the dose-response analysis (DRA), it is often of primary interest to find a dose at which targeted response probability is attained, which we call target dose (TD). The estimation of the TD clearly depends on the underlying RPF structure. In this article, we provide a comparative analysis of some of the existing and newly proposed RPF estimation methods with particular emphasis on TD estimation. Empirical performances based on simulated data are presented to compare the existing and newly proposed methods. Nonparametric models based on a sequence of Bernstein polynomials are found to be robust against model misspecification. The methods are also illustrated using data obtained from a toxicological study.