dissolution stability of a modified release product 32 nd mbsw may 19, 2009 [email protected]

32
Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 [email protected]

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Page 1: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

Dissolution stabilityof a modified release product

32nd MBSWMay 19, 2009

[email protected]

Page 2: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

2

OutlineOutline• 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

Page 3: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

3Hour

Me

an

20

40

60

80

100

2 4 6 8

0 6

2 4 6 8

12

18 24

20

40

60

80

100

30

20

40

60

80

100

36

2 4 6 8

48

Batch12345678910

Dissolution profilesN=378 tablets from B=10 batches

Page 4: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

4Month

Me

an

20

40

60

80

100

0 10 20 30 40 50

1 2

0 10 20 30 40 50

3.5

5

0 10 20 30 40 50

20

40

60

80

100

8

Batch12345678910

Dissolution Instability

Page 5: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

5

FDA Guidance

“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.”

Guidance for IndustryExtended Release Oral Dosage Forms:

Development, Evaluation, andApplication of In Vitro/In Vivo

CorrelationsCDER, Sept 1997

Page 6: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

6

2 4 6 8

20

40

60

80

10

0

Hours + jitter

% D

isso

lutio

n

Proposed dissolution limits

14

2530

60

80

Page 7: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

7

USP <724> Drug Release

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

X12

#(Xi)<3

XiL1 (n1=6)

Xi

L2 (n2=n1+6)

Xi

X24

L3 (n3=n2+12)

Page 8: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

8

2hr %LC20

2520 25

15

20

15 20

3.5hr %LC50

6050 60

30

40

30 40

8hr %LC100

105

110100 105 110

85

90

95

85 90 95

All p-values < 0.0001

Tablet residuals from fixed model:Correlation among time points

r = 0.79

r = 0.36

r = 0.54

Page 9: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

9

2hr Slope0.07

0.080.07 0.08

0.05

0.06

0.05 0.06

3.5hr Slope

0.20

0.250.20 0.25

0.10

0.15

0.10 0.15

8hr Slope0.1

0.20.1 0.2

-0.1

0.0

-0.1 0.0

Batch slopes:Correlations among time points

r = 0.21

p = 0.57

r = -0.37

p = 0.30

r = 0.76

p = 0.01

Page 10: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

10

2hr Initial19

20

21

19 20 21

16

17

18

16 17 18

3.5hr Initial44

46

4844 46 48

38

40

42

38 40 42

8hr Initial

96

98

10096 98 100

90

92

94

90 92 94

Batch intercepts:Correlations among time points

r = 0.92

p = 0.0002

r = 0.65

p = 0.04

r = 0.83

p = 0.003

Page 11: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

11

eZuXβy

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

13

1

16

1

1

6333

33

313

16

633

3

31

3

3

3

13

1

0

0

0

0

0

0

0

0

0

0

0

0

NN

j

BB

B

j

j

BNN

i

NN

i

NN

i

b

a

ba

b

a

IxI

IxI

IxI

b

a

Ix

Ix

Ix

I

I

I

y

y

y

uB VI 0,MVN~u eN VI 0,MVN~e

Page 12: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

12

Hierarchical (dynamic) Modeling view

i batchi xi yiT

1 ● ● ● ● ●

2 ● ● ● ● ●

.

.

.

.

.

.

.

.

.

.

.

.

N ● ● ● ● ●

j=1:B VaMVNj ,~ 3

VbMVNj ,~ 3 660

0

V

VVu

Random intercept & slope for each batch:

iibatchbatchi exyii

ei VMVNe ,0~ 3i=1:N

Dissolution result for each tablet:

Data:

Page 13: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

13

3

2

1

3

2

1

00

00

00

1

1

1

00

00

00

HCSHCS

4 param4 param

3

2

1

2

2

3

2

1

00

00

00

1

1

1

00

00

00

HAR1HAR14 param

3

2

1

2313

2312

1312

3

2

1

232313

122212

231221

00

00

00

1

1

1

00

00

00

UNUN

6 param

Tablet residual covariance (Ve)

Page 14: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

14

PD Ve: Acceptable range of

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

rho

det

erm

inan

t

HCS

HAR1

Page 15: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

15

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

Page 16: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

16

HAR1for 999.0,999.0

HCSfor )999.0,499.0(~

3,2,1),001.0,001.0(~2

Unif

Unif

kInvGammak

HAR1 or HCS

4 param

3,30~ 3232313

2212

21

IInvWishart

sym

UN

6 param

Tablet residual covariance (Ve) Priors

Page 17: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

17

InvWishart PriorComponent marginal prior distributions

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 4 8 12 16 20 24 28 32 36 40

0 4 8 12 16 20 24 28 32 36 40

0 4 8 12 16 20 24 28 32 36 40

0 4 8 12 16 20 24 28 32 36 40

0 4 8 12 16 20 24 28 32 36 40

0.4-31

0.8-54

1.4-98

2.4-164

4.4-299

3,~ 32332233113

222112

21

IcInvWishart

sym

ij

c=1

c=3

c=10

c=30

c=100

i40,000 draws

Page 18: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

18

232313

232212

131221

232313

232212

131221

0

0

bbb

bbb

bbb

aaa

aaa

aaa

UN12 params

23

22

21

23

22

21

00

00

00

0

0

00

00

00

b

b

b

a

a

a

VC6 params

Batch intercept & slope covariance (Vu)

Page 19: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

19

Batch intercept & slope Priors

3,~,3,~ 3232313

2212

21

3232313

2212

21

IcInvWishart

sym

IcInvWishart

sym

bbb

bb

b

aaa

aa

a

UN12 param

3,2,1),001.0,001.0(~

)001.0,001.0(~2

2

kInvGamma

InvGamma

bk

ka

VC6 param

3,2,1),001.0,001.0(~2 kInvGammakaVC Common slope

3 param

33

334

3 10,0~,10,

90

50

20

~ IMVNbIMVNa

Process mean

6 param

Page 20: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

20

Ve Vu DICHCS VC 5476.17

HAR1 VC 5461.98

UN UN 5457.66

UN VC 5456.27

UN VCCommon

Slope

5499.46

Effect of Covariance Choice:Deviance Information Criterion

Page 21: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

21

Parameter Estimates Proc MIXED vs WinBUGS

)4.3(0.600

0)7.5(3.110

00)1.1(2.2

)9.2(1.400

0)1.9(6.140

00)2.2(3.3

V

310

)5.8(4.1300

0)9.1(2.10

00)4.0(3.0

310

)8.17(7.2300

0)6.4(6.40

00)8.0(0.1

V

)3.1(4.16)1.1(0.10)4.0(0.3

0)4.1(6.18)4.0(5.4

00)2.0(7.2

)2.1(4.16)1.1(8.9)4.0(0.3

0)4.1(5.18)4.0(5.4

00)2.0(8.2

Ve

)9.0(0.94

)1.1(3.41

)5.0(4.17

)9.0(0.94

)3.1(3.41

)6.0(4.17

a

210

)2.4(5.7

)3.2(7.16

)9.0(1.7

210

)2.5(2.8

)9.2(9.16

)3.1(2.7

b

Page 22: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

22

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

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

Page 23: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

23

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[ , ])}

Page 24: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

24

Shrinkage of Bayesian and mixed Shrinkage of Bayesian and mixed model batch intercept and slope model batch intercept and slope estimatesestimates

2h

r

15

16

17

18

19

20

21

Bayesian Fixed Model Mixed Model

Estimation Method

3.5

h36

39

42

45

48

Bayesian Fixed Model Mixed Model

Estimation Method

8h

r

85

90

95

100

105

Bayesian Fixed Model Mixed Model

Estimation Method

Intercept (dissolution near batch release %LC)

2h

r

0

0.02

0.04

0.06

0.08

0.1

0.12

Bayesian Fixed Model Mixed Model

Estimation Method

3.5

h

0

0.05

0.1

0.15

0.2

0.25

0.3

Bayesian Fixed Model Mixed Model

Estimation Method

8h

r

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Bayesian Fixed Model Mixed Model

Estimation Method

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

Page 25: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

25

WinBUGS Batch intercept and slope WinBUGS Batch intercept and slope estimates: Bayesian “BLUPs”estimates: Bayesian “BLUPs”

[1,1]

[2,1][3,1] [4,1]

[5,1]

[6,1]

[7,1]

[8,1]

[9,1]

[10,1]

box plot: Init[,1]

14.0

16.0

18.0

20.0

22.0[1,2]

[2,2]

[3,2] [4,2]

[5,2]

[6,2]

[7,2]

[8,2]

[9,2]

[10,2]

box plot: Init[,2]

35.0

40.0

45.0

50.0

[1,3]

[2,3] [3,3]

[4,3]

[5,3]

[6,3]

[7,3]

[8,3]

[9,3] [10,3]

box plot: Init[,3]

85.0

90.0

95.0

100.0

105.0

Inte

rcepts

[1,1]

[2,1]

[3,1]

[4,1]

[5,1][6,1]

[7,1]

[8,1]

[9,1]

[10,1]

box plot: slope[,1]

0.0

0.05

0.1

0.15

[1,2] [2,2]

[3,2] [4,2] [5,2]

[6,2][7,2]

[8,2]

[9,2]

[10,2]

box plot: slope[,2]

-0.1

0.0

0.1

0.2

0.3

0.4

[1,3]

[2,3]

[3,3]

[4,3]

[5,3]

[6,3]

[7,3]

[8,3]

[9,3] [10,3]

box plot: slope[,3]

-0.4

-0.2

0.0

0.2

0.4

Slo

pes

Page 26: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

26

Predicting future resultsPredicting future results

a(1) V(1) b(1) V

(1) Ve(1)

: : : : :

a(d) V(d) b(d) V

(d) Ve(d)

: : : : :

a(10000) V(10000) b(10000) V

(10000) Ve(10000)

fut(1) fut (1)

: :

fut (d) fut (d)

: :

fut (10000) fut (10000)

yfut,1(1) … yfut,24

(1)

: : :

yfut,1(d) … yfut,24

(d)

: : :

yfut,1(10000) … yfut,24

(10000)

Posterior sample Posterior predictive sample

)()()(3

)(, ,~ d

edfut

dfut

difut VxMVNy

Page 27: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

27

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]

Page 28: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

28

yfut,1(1) … yfut,24

(1)

: : :

yfut,1(d) … yfut,24

(d)

: : :

yfut,1(10000) … yfut,24

(10000)

I(Pass @ L1) I(Pass @ L2) I(Pass @ L3) I(Fail)

0 1 0 0

: : : :

1 0 0 0

: : : :

0 0 0 1

Pr(Pass @ L1) Pr(Pass @ L2) Pr(Pass @ L3) Pr(Fail)

#(Pass @ L1)/

10000

#(Pass @ L2)/

10000

#(Pass @ L3)/

10000

#(Fail)/

10000

USP <724>Estimate Probabilities

Predicting testing results

Page 29: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

29

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

Page 30: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

30

Level testing and failure rate predictionsLevel testing and failure rate predictions

60

65

70

75

80

85

90

95

100

0 6 12 18 24 30 36 42 48

Months of Storage

Pro

ba

bil

ity

of

Pa

ss

ing

at

Le

ve

l 1

(%

)

Mixed Model

Fixed Model

Bayesian

0

5

10

15

20

25

30

35

0 6 12 18 24 30 36 42 48

Months of Storage

Pro

bab

ilit

y o

f P

assi

ng

at

Lev

el 2

(%

)

Mixed Model

Fixed Model

Bayesian

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

0 6 12 18 24 30 36 42 48

Months of Storage

Pro

bab

ilit

y o

f P

assi

ng

at

Lev

el 3

(%

)

Mixed Model

Fixed Model

Bayesian

0

2

4

6

8

10

12

14

16

0 6 12 18 24 30 36 42 48

Months of Storage

Pro

bab

ilit

y o

f F

aili

ng

Dis

solu

tio

n

Tes

tin

g

Mixed Model

Fixed Model

Bayesian

Page 31: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

31

SummarySummary

• 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

Page 32: Dissolution stability of a modified release product 32 nd MBSW May 19, 2009 David.LeBlond@abbott.com

32

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

John Peterson, GSKOscar Go, J&JJyh-Ming Shoung, J&JStan Altan, J&J

are greatly appreciated.

AcknowledgementsAcknowledgements

[email protected]

Thankyou too!