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Paediatr Anaesth. 2011 Jun;21(6):691-8. doi: 10.1111/j.1460-9592.2011.03584.x.

Two-stage vs mixed-effect approach to pharmacodynamic modeling of propofol in children using state entropy.

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Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada.



To compare the population pharmacodynamic (PD) models of propofol in children derived using two-stage and mixed-effect modeling approaches.


Fifty-two ASA 1 and 2 children aged 6-15 years presenting for gastrointestinal endoscopy were administered a loading dose of 4 mg·kg(-1) of propofol intravenously at an infusion rate determined by a randomization schedule. Using the plasma concentration predicted by the Paedfusor pharmacokinetic (PK) model, the propofol effect on state entropy (SE) was modeled using the two-stage and the mixed-effect modeling approaches, and the final population PD models were compared with each other in terms of their prediction performance, using median percentage and absolute percentage errors as well as mean absolute weighted error as metrics. The effects of age and body weight as prospective covariates were examined.


The final population models were comparable with each other; the two-stage and the mixed-effect approaches resulted in a k(e0) of 2.38 and 2.66 min(-1), γ of 5.29 and 5.68, and EC(50) of 4.73 and 4.84 μg·ml(-1), respectively. The bootstrap estimates of the PD parameters were mean (SD) k(e0) = 2.38 (0.10), γ = 5.30 (0.30), and EC(50) = 4.73 (0.14). The PD parameters did not exhibit dependence on age and body weight. The parameters reported in this study in children were different from their adult counterparts reported in previous studies.


Models derived using different mathematical approaches produced consistent model parameters. By virtue of its relative computational efficiency, the two-stage approach can serve as an attractive alternative to the mixed-effect approach in situations where data are not sparse.

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