A non-parametric method to analyse time-course of effect in the absence of pharmacokinetic data: Application to inhaled bronchodilators

Abstract

In spite of the extensive use of long-acting β 2-agonist (LABA) bronchodilators in asthma, the actual mechanism of their in vivo duration of action is not well understood, primarily due to limitations of standard pharmacokinetic–pharmacodynamic (PKPD) analysis methodologies. We have developed a novel method of analysing lung efficacy vs. time profiles for LABAs that can be used to provide comparative information on the lung PK. We hypothesised that for compounds that do not differ in their PK at the site of PD action, but differ in their in vivo potencies, the relationship between the area under the effect curve (AUEC) and the observed maximum effect (OME) at different doses is described by the same sigmoid curve. We have illustrated this property for standard PKPD models by obtaining analytical solution and through simulations. Anaesthetised dog in vivo effect vs. time profiles were gathered for six inhaled LABA candidates that differ in their in vitro potencies. Neither lung nor systemic PK was available for any compound. Analysis of the AUEC vs. OME data, derived from the efficacy profiles, using nonlinear mixed effects modelling indicated that for four compounds, the observed differences in in vivo duration of action was due to differences in their in vivo potencies and not because of lung PK differences. Therefore, it was concluded that for these compounds, characterisation of lung PK was unlikely to differentiate their PKPD characteristics. Thus, the proposed approach helped focus resources during translational research leading to lead candidate selection.