Solutions to reduce problems associated with experimental designs for nonlinear models: Conditional analyses and penalized optimal designs

Experimental design is a key feature of any study, as it directly influences the quality of inferences that can be drawn from the data. Inadequate experimental designs for nonlinear models can cause problems with the convergence of iterative algorithms used to estimate model parameters and contribute to correlated and/or imprecise parameter estimates. Fixing the maximum effect parameter in nonlinear, sigmoidal dose-response models permits the iterative algorithm to converge to estimates of the remaining unknown parameters and/or provide improved estimation properties. For this type of conditional analysis, it is shown that tests of significance are similar regardless of the value chosen for the maximum effect parameter given an adequate model fit. Statisticians have developed optimal design theory to generate experimental designs with optimal statistical properties related to the variance of model parameters or other estimation properties. However, optimal design theory may produce inappropriate designs from a practical perspective that conflict with common laboratory practice or other established guidelines. We propose a penalized optimal design technique to generate experimental designs that are both optimal in accordance with traditional design criteria and practical according to criteria imposed by an investigator through the use of desirability functions. This research suggests these solutions, conditional analyses and penalized optimal designs, to reduce problems associated with experimental designs for nonlinear models.