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Searching for an optimal AUC estimation method: a never-ending task?

Jawień W - J Pharmacokinet Pharmacodyn (2014)

Bottom Line: An effective method of construction of a linear estimator of AUC in the finite interval, optimal in the minimax sense, is developed and demonstrated for five PK models.The difference between the optimal estimator and other methods becomes more pronounced with a decrease in sample size or decrease in the variability.It is indicated that many alternative approaches are also possible.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Pharmacy, Jagiellonian University in Kraków, ul. Medyczna 9, 30-688, Kraków, Poland, wojciech.jawien@uj.edu.pl.

ABSTRACT
An effective method of construction of a linear estimator of AUC in the finite interval, optimal in the minimax sense, is developed and demonstrated for five PK models. The models may be given as an explicit C(t) relationship or defined by differential equations. For high variability and rich sampling the optimal method is only moderately advantageous over optimal trapezoid or standard numerical approaches (Gauss-Legendre or Clenshaw-Curtis quadratures). The difference between the optimal estimator and other methods becomes more pronounced with a decrease in sample size or decrease in the variability. The described estimation method may appear useful in development of limited-sampling strategies for AUC determination, as an alternative to the widely used regression-based approach. It is indicated that many alternative approaches are also possible.

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Related in: MedlinePlus

Performance of the investigated methods for Model 1 with n=6 and . Panels depict true vs estimated AUC by (a) optimal, (b) optimal trapezoid, and (c) Gauss-Legendre methods. Panel (d) displays knots and weights of these methods (one bar of optimal method is hidden behind bars of other methods)
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Fig1: Performance of the investigated methods for Model 1 with n=6 and . Panels depict true vs estimated AUC by (a) optimal, (b) optimal trapezoid, and (c) Gauss-Legendre methods. Panel (d) displays knots and weights of these methods (one bar of optimal method is hidden behind bars of other methods)

Mentions: A few representative plots showing the quality of the predictions can be found in Figs. 1, 2, and 3. These plots show each simulated case as a small gray dot. Its abscissa equals to the true AUC value, i.e. calculated based on PK parameters values assumed in the simulation, and its ordinate represents the result of estimation. As it is quite common that maximum risk is reached at the extremal values of some or all parameters the special points simulated for these extremal values are indicated by open square symbols (). Open triangles indicate those points at which the maximum estimation error appeared: and are for maximum relative under- and overestimates, respectively; while and are for maximum absolute under- and overestimated results in a plot. In these figures, on separate plots, the knots and weights of all three methods are also depicted. The position of each bar is that of a knot while its height represents a value of weight.Fig. 1


Searching for an optimal AUC estimation method: a never-ending task?

Jawień W - J Pharmacokinet Pharmacodyn (2014)

Performance of the investigated methods for Model 1 with n=6 and . Panels depict true vs estimated AUC by (a) optimal, (b) optimal trapezoid, and (c) Gauss-Legendre methods. Panel (d) displays knots and weights of these methods (one bar of optimal method is hidden behind bars of other methods)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4225057&req=5

Fig1: Performance of the investigated methods for Model 1 with n=6 and . Panels depict true vs estimated AUC by (a) optimal, (b) optimal trapezoid, and (c) Gauss-Legendre methods. Panel (d) displays knots and weights of these methods (one bar of optimal method is hidden behind bars of other methods)
Mentions: A few representative plots showing the quality of the predictions can be found in Figs. 1, 2, and 3. These plots show each simulated case as a small gray dot. Its abscissa equals to the true AUC value, i.e. calculated based on PK parameters values assumed in the simulation, and its ordinate represents the result of estimation. As it is quite common that maximum risk is reached at the extremal values of some or all parameters the special points simulated for these extremal values are indicated by open square symbols (). Open triangles indicate those points at which the maximum estimation error appeared: and are for maximum relative under- and overestimates, respectively; while and are for maximum absolute under- and overestimated results in a plot. In these figures, on separate plots, the knots and weights of all three methods are also depicted. The position of each bar is that of a knot while its height represents a value of weight.Fig. 1

Bottom Line: An effective method of construction of a linear estimator of AUC in the finite interval, optimal in the minimax sense, is developed and demonstrated for five PK models.The difference between the optimal estimator and other methods becomes more pronounced with a decrease in sample size or decrease in the variability.It is indicated that many alternative approaches are also possible.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Pharmacy, Jagiellonian University in Kraków, ul. Medyczna 9, 30-688, Kraków, Poland, wojciech.jawien@uj.edu.pl.

ABSTRACT
An effective method of construction of a linear estimator of AUC in the finite interval, optimal in the minimax sense, is developed and demonstrated for five PK models. The models may be given as an explicit C(t) relationship or defined by differential equations. For high variability and rich sampling the optimal method is only moderately advantageous over optimal trapezoid or standard numerical approaches (Gauss-Legendre or Clenshaw-Curtis quadratures). The difference between the optimal estimator and other methods becomes more pronounced with a decrease in sample size or decrease in the variability. The described estimation method may appear useful in development of limited-sampling strategies for AUC determination, as an alternative to the widely used regression-based approach. It is indicated that many alternative approaches are also possible.

Show MeSH
Related in: MedlinePlus