Pharmaceutical Research

, Volume 31, Issue 3, pp 649–659 | Cite as

Bayesian Approach to Estimate AUC, Partition Coefficient and Drug Targeting Index for Studies with Serial Sacrifice Design

  • Tianli Wang
  • Kyle Baron
  • Wei Zhong
  • Richard Brundage
  • William Elmquist
Research Paper
First Online:
Received:
Accepted:
  • 396 Downloads

ABSTRACT

Purpose

The current study presents a Bayesian approach to non-compartmental analysis (NCA), which provides the accurate and precise estimate of AUC 0 ∞ and any AUC 0 ∞ -based NCA parameter or derivation.

Methods

In order to assess the performance of the proposed method, 1,000 simulated datasets were generated in different scenarios. A Bayesian method was used to estimate the tissue and plasma AUC 0 ∞ s and the tissue-to-plasma AUC 0 ∞ ratio. The posterior medians and the coverage of 95% credible intervals for the true parameter values were examined. The method was applied to laboratory data from a mice brain distribution study with serial sacrifice design for illustration.

Results

Bayesian NCA approach is accurate and precise in point estimation of the AUC 0 ∞ and the partition coefficient under a serial sacrifice design. It also provides a consistently good variance estimate, even considering the variability of the data and the physiological structure of the pharmacokinetic model. The application in the case study obtained a physiologically reasonable posterior distribution of AUC, with a posterior median close to the value estimated by classic Bailer-type methods.

Conclusions

This Bayesian NCA approach for sparse data analysis provides statistical inference on the variability of AUC 0 ∞ -based parameters such as partition coefficient and drug targeting index, so that the comparison of these parameters following destructive sampling becomes statistically feasible.

KEY WORDS

Bayesian approach drug targeting index NCA partition coefficient variance estimation 

ABBREVIATIONS

AUC

Area under the concentration-time curve

AUC0t

AUC from time zero to the last time point

AUC0∞

AUC from time zero to infinity

a, b, c

Large positive numbers in the prior settings indicating vague priors

BAV

Between-animal coefficient of variation

BCRP

Breast cancer resistance protein

BCRPKO

BCRP gene knockout (Bcrp1 (-/-))

br

The brain or any other tissue

C.I.

Credible interval

C.I.*

Confidence interval

\( {\overset{\rightharpoonup }{C}}_i{}_j \)

Plasma and tissue concentrations of the i th animal at the j th time point

Cj

Concentration at the j th time point

Cj*

Concentrations at the last three sampling time points

Ct

Concentration at the last sampling time point

d

Degree of freedom

DTI

Drug targeting index

i

Animal indicator

j

Time point indicator

k, θ

Superparameters of an Inverse-Gamma distribution

MVN (·,·)

Multivariate normal distribution

m

The total number of sampling time points

n

Number of animals at each time point

N (·,·)

Normal distribution

NCA

Noncompartmental analysis

P-gp

P-glycoprotein

PgpKO

P-gp gene knockout (Mdr1a/b (-/-))

pl

The plasma

R

Two-dimensional scale matric for Inverse-Wishart distribution

SD

Standard deviation

SEj

Standard error of C j

tj

Time corresponding to the j th time point

tj *

Time corresponding to the last three time points in a concentration-time profile

TKO

Triple knockout (Mdr1a/b (-/-)Bcrp1 (-/-))

Unif

Uniform distribution

WAV

Within-animal variability

WT

Wild-type

λz

The terminal elimination rate constant

μj

Mean of the log-transformed concentrations at the jth time point

\( {\overset{\rightharpoonup }{\mu}}_j \)

The vector (μpl,j μbr,j )T

Σj

Within-animal precision variance-covariance matrix of concentrations at time j

σj

Variance or covariance of the plasma and brain concentrations at the jth time point

σ*

Standard deviation of the log-normal distribution of concentrations at the last three time points of a concentration-time profile

α

The intercept for the terminal phase regression

β

The slope for the terminal phase regression

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Notes

ACKNOWLEDGMENTS AND DISCLOSURES

This work was supported by National Institutes of Health grants CA 138437, and NS 077921.

Supplementary material

11095_2013_1187_MOESM1_ESM.txt (3 kb)
ESM 1 (TXT 2 kb)

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tianli Wang
    • 1
  • Kyle Baron
    • 2
  • Wei Zhong
    • 2
  • Richard Brundage
    • 2
  • William Elmquist
    • 1
  1. 1.Department of PharmaceuticsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Experimental and Clinical PharmacologyUniversity of MinnesotaMinneapolisUSA

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