Use of sensitivity functions to characterise and compare the forgiveness of drugs.

In order to compare the capacity for forgiveness of different drugs, i.e. the sensitivity of their effects to sporadic noncompliance, we propose the use of 'sensitivity functions' for drugs acting through direct pharmacokinetic-pharmacodynamic relationships. This approach is based on the concept of the partial derivative dE/dC (with E corresponding to the pharmacodynamic effect and C to the concentration of drug at the effect site), and the study of the variation of this function in terms of its maximum and inflexion points. Values of sensitivity functions are given for the three common direct response models, i.e. the linear, maximum effect (hyperbolic) and Hill (sigmoid) models. The capacity for forgiveness of drugs differing only by one parameter in their pharmacokinetic-pharmacodynamic relationship is assessed using this approach and illustrated with theoretical simulated examples. Examples of clinical application are then proposed, dealing with the effect of nifedipine on heart rate and diastolic blood pressure, and loop diuretics on natriuretic response, in patients with and without liver cirrhosis. Although the study of sensitivity functions is proposed as a theoretical approach, the relationships between noncompliance and its consequences for pharmacodynamic effect remain highly complex and, in most cases, numerical simulation is still needed.