M. Simeoni(1), P. H. Van Der Graaf(2), P. Milligan(2), D. Verotta(3), G. De Nicolao(1), M. Rocchetti(4), I. Poggesi(4)
(1)Dep. of Computer Science and Systems Engineering, University of Pavia, Italy; (2)PGRD, Pfizer, Sandwich, Kent, UK; (3)Dep. of Biopharmaceutical Sciences, University of San Francisco, CA; (4)Nerviano Medical Sciences S.r.l., Milan, Italy
Objectives: In drug development, there are examples in which pharmacotoxicological or clinical endpoints are expressed in terms of counts (e.g., number of epileptic, vomiting or diahrrea episodes, neuronal firing, etc.). These events are typically described as arrivals in a Poisson process, the intensity of which can be modulated, depending on the cases, by pharmacological actions, disease progression or variations in external stimuli. Some examples of such analyses (1-3) made use of homogeneous Poisson processes, with constant intensity either in the whole observation interval or in a time interval. Whilst time-invariant intensity is correct in most cases, this approach cannot be easily applied to cases where large and rapid variations of intensity are expected (e.g., those obtained following a single, rapid, pharmacokinetic impulse). In these conditions an inhomogeneous Poisson process may be considered. In this study we compared the outcomes obtained using the homogeneous and inhomogeneous Poisson approaches.
Methods: We interpreted our count data as arrivals of a non-homogeneous Poisson process with a non-linear intensity function whose parameters were estimated by NONMEM. Firstly we used as objective function -2 log-likelihood of the Poisson density function, assuming a homogeneous Poisson process within a defined time interval. Secondly we used -2 log-likelihood of an inhomogeneous Poisson process where the intensity varies instantaneously.
Results: Provided that the time interval is appropriately chosen, the intensity profile obtained with the first approach is consistent with the more accurate estimate of the second approach. This approach can also be useful for optimizing the experimental design with the appropriate choice of the time interval that allows the application of the homogeneous approach.
References:
(1) Gupta SK, Sathyan G, Lindemulder EA, Ho PL, Sheiner LB, Aarons L. Quantitative characterization of therapeutic index: application of mixed-effects modeling to evaluate oxybutynin dose-efficacy and dose-side effect relationships. Clin Pharmacol Ther.65:672-84, 1999.
(2) Frame B, Miller R, Lalonde RL. Evaluation of mixture modeling with count data using NONMEM. J Pharmacokinet Pharmacodyn.30:167-83, 2003
(3) Jonker DM, van de Mheen C, Eilers PH, Kruk MR, Voskuyl RA, Danhof M. Anticonvulsant drugs differentially suppress individual ictal signs: a pharmacokinetic/pharmacodynamic analysis in the cortical stimulation model in the rat. Behav Neurosci. 117:1076-85, 2003.
Reference: PAGE 14 (2005) Abstr 789 [www.page-meeting.org/?abstract=789]
Poster: poster