Optimal designs for response functions with a downturn

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for this situation. A growth model is combined with a death model to allow for the downturn in mean doses. Several different objective functions are studied. When the number of treatments equals the number of parameters, Fisher information is found to be independent of the model of the treatment means and on the magnitudes of the treatments. A- and DA-optimal weights for estimating adjacent mean differences are found and results on c-optimality are obtained for estimating the peak dose and the EC50 (the treatment with response half way between the control and the peak response on the increasing portion of the response function). Also, D-optimal designs for estimating parameters in the response functions are studied and identify support points and weights to minimize the generalized variance of the parameter estimates. Finally, two stage approach to estimating the EC50 is evaluated using c-optimal design for estimating the EC50.