Robust Non-inferiority Tests for Potency of a Test Drug Against a Reference Drug: (To appear in Statistics in Biopharmaceutical Research ).

In comparing test formulations of a drug product to reference formulations it is necessary to check that the test formulation has as much biologic activity as the reference within some indifference zone. A modern method for testing this relative potency is to fit a nonlinear model of the dose response curve, constrained such that the dose-response of the test is modeled with the same function as the reference except for a multiplicative parameter on the dose. This method works well as long as the nonlinear model fits the data. Although tests of this fit are mentioned in the literature, how relative potency should be measured when those tests fail has not been addressed. We study the use of the sandwich estimator of variance for this non-inferiority potency problem when the model does not fit the data. We focus on the simple linear model. Using the sandwich variance, the inferences are asymptotically valid even if the model does not hold. We discuss interpretation of the results under the misspecified linear model, and show by simulation that the method performs well in some practical cases. Finally, we give advice for designing a study that uses these methods.