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Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 PowerPoint PPT Presentation


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Dissolution stability of a modified release product 32 nd MBSW May 19, 2009. [email protected] Outline. Multivariate data set Mixed model (static view) Hierarchical model (dynamic view) Why a Bayesian approach? Selecting priors Model selection Parameter estimates

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Dissolution stability of a modified release product 32 nd MBSW May 19, 2009

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Slide1 l.jpg

Dissolution stability

of a modified release product

32nd MBSW

May 19, 2009

[email protected]


Outline l.jpg

Outline

  • Multivariate data set

  • Mixed model (static view)

  • Hierarchical model (dynamic view)

  • Why a Bayesian approach?

  • Selecting priors

  • Model selection

  • Parameter estimates

  • Latent parameter (“BLUP”) estimates

  • Posterior prediction

  • Estimating future batch failure and level testing rates


Dissolution profiles n 378 tablets from b 10 batches l.jpg

Dissolution profilesN=378 tablets from B=10 batches


Dissolution instability l.jpg

Dissolution Instability


Fda guidance l.jpg

FDA Guidance

Guidance for Industry

Extended Release Oral Dosage Forms:

Development, Evaluation, and

Application of In Vitro/In Vivo

Correlations

CDER, Sept 1997

  • “VII.B. Setting Dissolution Specifications

  • A minimum of three time points …

  • … should cover the early, middle, and late stages of the dissolution profile.

  • The last time point … at least 80% of drug has dissolved …. [or] … when the plateau of the dissolution profile has been reached.”


Proposed dissolution limits l.jpg

Proposed dissolution limits

80

60

30

25

14


Usp 724 drug release l.jpg

L1 (n1=6)

Xi

X12

X24

L2 (n2=n1+6)

Xi

Xi

L3 (n3=n2+12)

#(Xi)<3

USP <724> Drug Release

L-20 L-10 L U U+10 U+20


Tablet residuals from fixed model correlation among time points l.jpg

Tablet residuals from fixed model:Correlation among time points

r = 0.36

r = 0.79

r = 0.54

All p-values < 0.0001


Batch slopes correlations among time points l.jpg

Batch slopes:Correlations among time points

r = 0.76

p = 0.01

r = 0.21

p = 0.57

r = -0.37

p = 0.30


Batch intercepts correlations among time points l.jpg

Batch intercepts:Correlations among time points

r = 0.92

p = 0.0002

r = 0.83

p = 0.003

r = 0.65

p = 0.04


Mixed static modeling view n tablets i from b batches j testing at month x i l.jpg

Mixed (static) modeling viewN tablets (i) from B batches (j), testing at month xi


Hierarchical dynamic modeling view l.jpg

Random intercept & slope for each batch:

j=1:B

Dissolution result for each tablet:

i=1:N

Hierarchical (dynamic) Modeling view

Data:


Tablet residual covariance v e l.jpg

UN

6 param

HAR1

4 param

HCS

4 param

Tablet residual covariance (Ve)


Pd ve acceptable range of r l.jpg

PD Ve: Acceptable range of r


Why a bayesian approach l.jpg

Why a Bayesian approach?

  • Asymptotic approximations may not be valid

  • Allows quantification of prior information

  • Properly accounts for estimation uncertainty

  • Lends itself to dynamic modeling viewpoint

  • Requires fewer mathematical distractions

  • Estimates quantities of interest easily

  • Provides distributional estimates

  • Fewer embarrassments (e.g., negative variance estimates)

  • Is a good complement to likelihood (only) methods

  • WinBUGS is fun to use


Tablet residual covariance v e priors l.jpg

UN

6 param

HAR1 or HCS

4 param

Tablet residual covariance (Ve) Priors


Invwishart prior component marginal prior distributions l.jpg

c=1

c=3

c=10

c=30

c=100

0.4-31

0.8-54

1.4-98

2.4-164

4.4-299

si

InvWishart PriorComponent marginal prior distributions

40,000 draws

rij


Batch intercept slope covariance v u l.jpg

UN

12 params

VC

6 params

Batch intercept & slope covariance (Vu)


Batch intercept slope priors l.jpg

Process mean

6 param

VC

6 param

VC Common slope

3 param

Batch intercept & slope Priors

UN

12 param


Effect of covariance choice deviance information criterion l.jpg

Effect of Covariance Choice:Deviance Information Criterion


Parameter estimates proc mixed vs winbugs l.jpg

a

b

Va

Vb

Ve

Parameter EstimatesProc MIXED vs WinBUGS


Posterior from proc mixed sas 8 2 l.jpg

WARNING: Posterior sampling is not performed because the parameter transformation is not of full rank.

Posterior from Proc Mixed(SAS 8.2)

391 proc mixed covtest;

392 class batch tablet time;

393 model y= time time*month/ noint s;

394 random time time*month/ type=un(1) subject=batch G s;

395 repeated / type=un subject=tablet R;

396 prior /out=posterior nsample=1000;

NOTE: Convergence criteria met.

  • Runs in SAS 9.2, however…

  • SAS only strictly “supports” the posterior if

  • random type=VC with no repeated, or

  • random and repeated types both = VC


Winbugs dynamic modeling l.jpg

WinBUGS dynamic modeling

# Prior

InvVe[1:T,1:3]~dwish(R[,],3)

acent[1]~dnorm(0.0,0.0001)

acent[2]~dnorm(50,0.0001)

acent[3]~dnorm(100,0.0001)

for ( j in 1:3) {

b[ j ]~dnorm(0.0,0.001)

gacent[ j ]~dgamma(0.001,0.001)

gb[ j ]~dgamma(0.001,0.001) }

# Likelihood

# Draw the T intercepts and slopes for each batch

for ( i in 1:B) {

for ( j in 1:3) {

alpha[i, j] ~ dnorm(acent[ j ], gacent[ j ])

beta[i, j] ~ dnorm(b[ j ], gb[ j ]) } }

# Draw vector of results from each tablet

for (obs in 1:N){

for ( j in 1:3){

mu[obs,j]<-alpha[Batch[obs],j]+beta[Batch[obs],j]*(Month[obs]-xbar)}

y[obs,1:T ]~dmnorm(mu[obs, ], InvVe[ , ])}


Shrinkage of bayesian and mixed model batch intercept and slope estimates l.jpg

Intercept (dissolution near batch release %LC)

Slope (rate of change in dissolution %LC/month)

Shrinkage of Bayesian and mixed model batch intercept and slope estimates


Winbugs batch intercept and slope estimates bayesian blups l.jpg

Intercepts

Slopes

WinBUGS Batch intercept and slope estimates: Bayesian “BLUPs”


Predicting future results l.jpg

Predicting future results

Posterior predictive sample

Posterior sample


Winbugs posterior predictions l.jpg

WinBUGS posterior predictions

# Predict int & slope for future batches

for (j in 1:3){

b_star[ j ]~dnorm(b[ j ], gb[ j ])

acent_pred[ j ]~dnorm(acent[ j ], gacent[ j ])

a_star[ j ]<-acent[ j ] - b[ j ]*xbar}

# Obtain the Ve components

Ve[1:3,1:3] <- invVe[ , ])

for (j in 1:3){

sigma[ j ] <- sqrt(Ve[j,j])}

rho12 <- Ve[1,2]/sigma[1]/sigma[2]

rho13 <- Ve[1,3]/sigma[1]/sigma[3]

rho23 <- Ve[2,3]/sigma[2]/sigma[3]


Predicting testing results l.jpg

Predicting testing results

Estimate Probabilities

USP <724>


Semi parametric bootstrap prediction l.jpg

Semi-parametric bootstrap prediction

  • “Fixed model” prediction (no shrinkage)

    • 10 intercept and 10 slope vectors via SLR

    • 378 tablet residual vectors

  • -or-

  • “Mixed model” prediction (shrinkage)

    • 10 intercept vector BLUPs

    • 10 slope vector BLUPs

    • 378 tablet residual vectors

  • Sample with replacement to construct future results


Level testing and failure rate predictions l.jpg

Level testing and failure rate predictions


Summary l.jpg

Summary

  • A multivariate, hierarchical, Bayesian approach to dissolution stability illustrated

  • Some options for specifying the covariance priors

  • Estimation and shrinkage of the latent batch slope and intercept parameters

  • Posterior prediction of future data

  • Prediction of future failure and level testing rates

    • “Fixed” most pessimistic… (no shrinkage?)

    • “Mixed” lowest failure rate… (non-asymptotic?)

    • Give WinBUGS a try


Acknowledgements l.jpg

Thank

you too!

[email protected]

Acknowledgements

The invaluable suggestions of, encouragement from, and helpful discussions with

John Peterson, GSK

Oscar Go, J&J

Jyh-Ming Shoung, J&J

Stan Altan, J&J

are greatly appreciated.


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