Bronchial Allergen Challenge in Asthma: A Model for Inhaled Corticosteroids (ICS) and Montelukast using Literature Summary Data
F. Ezzet (1), J. Ribbing (2)
(1) Pharsight a Certara Company, St Louis, MO, USA; (2) Pfizer, Sandwich, UK
Objectives: To characterize effectiveness of anti-asthmatic treatments in studies using bronchial allergen challenge (AC)
Methods: Mean %FEV1 change from baseline following AC and treatment was modeled using data reported in 47 scientific publications. Studies were randomized placebo controlled cross-over investigating efficacy in mild asthmatic patients. Following AC, patients exhibit early asthmatic response (EAR) and late asthmatic response (LAR), within 30 minutes and 4-8 hours after inhalation of allergen, respectively [1]. EAR and LAR were modeled using a sum of 2 gamma density functions, if time =< or > t:
%FEV1(time) = - (time =a).Gamma(L1, K1, time) -
(time >t).S2 .(1-b).Gamma(L2, K2, time) (1)
The parameter S describes the magnitude of drop in %FEV1 due to AC. For a = b =0, equation (1) represents %FEV1 under placebo. Positive values of a and/or b represent %attenuation due to active treatment. Inter-trial random effects (proportional to S1 and S2) and an additive residual error were assumed normally distributed. The model was fitted using nlme, in Splus.
Results: Data set included 15 studies investigating ICS (6 compounds) and 7 investigating Montelukast. Equation (1) was found suitable in capturing %FEV1. S1 and S2, together with attenuation parameters a and b captured most of the differences in %FEV1 between treatments (while L and K were common to all treatments). For example, %attenuation in EAR and LAR for Montelukast (10 mg) was 58% and 65% respectively. For Fluticasone 250 mcg (an ICS) it was 16% and 58%. Budesonide was 11% and 62%. The value of t signifying end of EAR and beginning of LAR was between 2 and 3 hours. A similar value of objective function was achieved for t in this range. SD of residual error was small, 3%. Coefficient of variation of inter-study variability in S1 and S2 were 22% and 35%. Visual predictive checks and posterior predictive checks together with standard diagnostics indicated adequacy of the model fit. Model estimates were found invariant when subsets of the data used.
Conclusion: A sum of 2 gamma functions was found to be a flexible model to describing %FEV1 following AC. The attenuation parameters a and b captured most of the differences between treatments, allowing a simple and direct comparison. The literature model aids the interpretation of ongoing AC studies within Pfizer, as well as design of future AC studies, and can be updated with internal data from positive controls.
References:
[1] Gauvreau GM, Evans MY: Allergen Inhalation Challenge: A Human Model of Asthma Exacerbation. Sjobring U, Taylor JD (eds): Models of Exacerbation in Asthma and COPD. Contrib Microbiol. Basel, Karger, 2007, vol 14, pp 21-32
