Within the realms of biological and medical research, toxicity studies which measure impaired reproduction are becoming more and more common, yet methods for efficiently designing experiments for these studies have received little attention. In this research, response surface design criteria are applied to four models for impaired reproduction data. The important role of control observations in impairment studies is discussed, and for one model, a normal error linear model, a design criterion is introduced for allocating a portion of the sample to the control. Special attention is focused on issues surrounding optimal design of experiments for two of the models, a Poisson exponential model and a Poisson linear model. As most of the optimal designs for these models are obtained via numerical methods rather than directly from criteria, equivalence theory is used to prove analytically that the numerically obtained designs are truly optimal. A further complication associated with designing experiments for Poisson regression is the need to know parameter values in order to implement the optimal designs. Thus, two stage design of experiments is investigated as one solution to this problem. Finally, since researchers frequently do not know the appropriate model for their data a priori, the optimal designs for these two different models are compared, and designs which are robust to model misspecification are highlighted. / Ph. D.