<p>Optimal design issues have been investigated in the literature for active controlled dose-finding trials with univariate outcome arising from an explicit distribution. The primary goal of these trials is to accurately estimate the minimum dose that produces the same treatment effect as the active control. This article takes a broader perspective to deal with such design problems. In particular, we utilize optimal design theory to develop locally optimal designs under the maximum quasi-likelihood estimator (MqLE), which relies on less restrictive assumptions compared to those of the maximum likelihood estimation method. Locally optimal designs are determined for commonly used dose-response models under different variance functions, which are then illustrated with examples.</p>