Douglas Eleveld (1), Pieter J. Colin (1,2)
(1) Department of Anesthesiology, University Medical Center Groningen, University of Groningen, The Netherlands; (2)Laboratory of Medical Biochemistry and Clinical Analysis, Faculty of Pharmaceutical Sciences, Ghent University, Belgium;
Objectives: In covariate analysis, age is often examined for its relationship with model parameters. An individual’s age is informative for characteristics of physiological mechanisms which we attempt to duplicate in PK and PD models. These can be gradual changes associated with aging as well as more abrupt changes in young children associated with maturation. There is no “theory of aging” to guide model development and current approaches are empirical. There is considerable diversity in age-adjustment functions1 in current literature, and researchers are not often challenged as to their choices. The purpose of this investigation is to apply techniques from reliability engineering2 to age-adjustment functions. The premise is the number of functional physiological units (and thus biological function) over time after ontogenesis is analogous to the number of remaining functional products over time after manufacture. Physiological units/ products may fail (or gain function) over time according to a hazard function. The Weibull cumulative distribution function (CDF) f(age)=1-exp(-(age/λ)**k) is used in reliability engineering to gain insight into product failure mechanisms. The value of k may indicate early-failure (k<1, “infant-mortality” or decreasing hazard) or aging (k>1, “wear-out” or increasing hazard) effects.
Methods: Two PK models and datasets were chosen with a wide age-range, for Propofol3 and Vancomycin4. The age- and maturation-correction functions in each model (3 for Propofol and 2 for Vancomycin) were plug-in replaced by Weibull CDF and the model re-estimated. Parameters λ and k were estimated, with k being fixed to 1 if supported.
Results: All 5 age- and maturation-adjustment function in the considered models could be approximated by the Weibull CDF with only moderate change in objective function (12.7 for Propofol and -7.78 for Vancomycin). Early maturation of clearance showed increasing hazard over time (k>1), suggesting positive feedback mechanisms drive maturation. Advanced age showed “wear-out” for vancomycin clearance (k>1), whereas the hazard for loss of propofol clearance appears independent of time (k=1).
Conclusion: Age- and maturation-correction functions showing diverse behaviors can be modelled in a unified framework with Weibull CDF functions with only moderate impact on the final model fit. The estimated k parameter determines whether the hazard increases, decreases or remains constant over time and this may be insightful for understanding physiological mechanisms. Use of the Weibull CDF for age-correction may reduce empiricism and help refine theoretical approaches for age- and maturation-correction functions in covariate analysis.
[1] http://holford.fmhs.auckland.ac.nz/docs/principles-of-covariate-modelling.pdf. Accessed 19/03/2019.
[2] https://www.weibull.com/. Accessed 19/03/2019.
[3] Eleveld DJ, Colin P, Absalom AR, Struys MM. Pharmacokinetic–pharmacodynamic model for propofol for broad application in anaesthesia and sedation. British journal of anaesthesia. 2018 May 31;120(5):942-59.
[4] Colin PJ, Allegaert K, Thomson AH, Touw DJ, Dolton M, de Hoog M, Roberts JA, Adane ED, Yamamoto M, Santos-Buelga D, Martín-Suarez A. Vancomycin Pharmacokinetics Throughout Life: Results from a Pooled Population Analysis and Evaluation of Current Dosing Recommendations. Clinical pharmacokinetics. 2019 Jan 17:1-4.
Reference: PAGE 28 (2019) Abstr 8846 [www.page-meeting.org/?abstract=8846]
Poster: Methodology - Covariate/Variability Models