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J Pharmacokinet Pharmacodyn. 2016 Jun;43(3):305-14. doi: 10.1007/s10928-016-9473-1. Epub 2016 May 10.

Approaches for modeling within subject variability in pharmacometric count data analysis: dynamic inter-occasion variability and stochastic differential equations.

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Department of Pharmaceutical Biosciences, Uppsala University, P.O. Box 591, 751 24, Uppsala, Sweden.
Pfizer (China) Research & Development Center, Shanghai, China.
Department of Pharmaceutical Biosciences, Uppsala University, P.O. Box 591, 751 24, Uppsala, Sweden.


Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data.


Count data; Dynamic inter-occasion variability; Stochastic differential equations; Within subject variability

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