The efficiency concept in pharmacodynamics

The classic approach to describe the pharmacological response to a drug is to analyse its concentration-effect relationship, using a variety of possible models such as maximum effect (Emax) models or sigmoid Emax models. The aim of this review is to discuss an alternative way of describing the pharmacological effect in terms of effect per unit of drug concentration, instead of simple effect. This variable is called efficiency, analogous with concepts used in other fields. The pharmacodynamic model for efficiency is derived from the sigmoid Emax model and is dependent on the same parameters. Since the sigmoid Emax model incorporates 'the law of diminishing returns', requiring ever higher concentrations to increase the effect by a given percentage, efficiency is bound to decrease with increasing concentrations. However, as a mathematical consequence of its derivation from the sigmoid Emax model, efficiency also has a maximum value, which can be expressed as a function of the slope factor (s) and drug concentration associated with half the maximum effect (C50), provided that the slope factor is greater than 1. The efficiency concept is potentially applicable to all drugs and particularly useful for those that follow concentration-effect relationships according to Emax or sigmoid Emax models. Most experience has been obtained with loop diuretics, especially with furosemide (frusemide). Slow administration of furosemide, leading to slow excretion of the drug, has been shown, in many studies, to significantly increase the total diuretic effect per amount of drug recovered in urine. In this review, some examples of the applicability of the efficiency concept to other drugs, such as antibacterials, opioids and antineoplastics, are discussed. In addition to pharmacodynamically varying efficiency, other saturable processes, such as the formation of active metabolites and saturable transport, may form a basis for the application of the efficiency concept. The efficiency of a drug dosage may also be influenced by tolerance and counter-regulation produced by the drug. All these factors contribute to schedule dependency. It is concluded that the shape of the time course of drug presentation to its site of action is an independent determinant of overall response. The possibility of adjusting the drug input profile to maximise therapeutic effect per dose and to separate cumulated therapeutic from cumulated adverse effects should be considered in designing administration schedules and in drug development.