OPTIMAL DESIGN FOR NON-LINEAR MODEL WITH APPLICATION TO DRUG DEVELOPMENTIN CLINICAL TRIALS

Abstract

This research focuses on practical considerations for establishing efficient study design to estimate target dose of interest in treating hypertensive patients and we consider optimal design for the estimation of the minimum effective dose to the maximum treatment effect based on the data collected. We obtained this through sequential construction of optimal design, using D-optimality criterion.An optimal design of two drugs (Aldoment and Lisinopril) used in treating high blood pressure was constructed using D-optimality criterion along with a non-linear regression model. The relative efficiencies of other designs with respect to the optimal design were determined. Due to the nonlinearity of the model, we supplied initial values for the model parameters by using least square parameter estimates before running the algorithm. A 3 by 2 (3x2) starting design matrix was provided and the algorithm iterates until the stopping criterionwas satisfied, that is, when the standardized variance p, where p is the number of parameters in the model. The procedure typically iterates by mixing the current design with a specially selected point to form a new design, the selected point to introduce in the iteration is the point that maximizes the weighted variance function. The result shows that the optimal design is the design whose information matrix has the highest determinant leading to the design point (-1) and (1) with equal weight of 0.5.