Dissolution stability of a modified release product

Transcription

1 Dissolution stility of modified relese product nd MBSW My 9, 9 Dvid.LeBlond@ott.com

2 Outline Multivrite dt set Mixed model (sttic view) Hierrchicl model (dynmic view) Why Byesin pproch? Selecting priors Model selection Prmeter estimtes Ltent prmeter ( BLUP ) estimtes Posterior prediction Estimting future tch filure nd level testing rtes

3 Dissolution profiles N=78 tlets from B= tches Men Btch Hour

4 Dissolution Instility Men Btch Month 4

5 FDA Guidnce Guidnce for Industry Extended Relese Orl Dosge Forms: Development, Evlution, nd Appliction of In Vitro/In Vivo Correltions CDER, Sept 997 VII.B. Setting Dissolution Specifictions A minimum of three time points should cover the erly, middle, nd lte stges of the dissolution profile. The lst time point t lest 8% of drug hs dissolved. [or] when the plteu of the dissolution profile hs een reched. 5

6 Proposed dissolution limits % Dissolution Hours + jitter 6

7 USP <74> Drug Relese L (n=6) L- L- L U U+ U+ X i L (n+6) X X i X 4 L (n+6+) X i #(X i ) < 7

8 Tlet residuls from fixed model: Correltion mong time points R= hr %LC 95 R=.79 6 R= hr %LC hr %LC 5 5 All p-vlues <. 8

9 Btch slopes: Correltions mong time points.... 8hr Slope hr Slope p=. R=.76 p=.57 p= hr Slope.6.5 R=. R=-.7 9

10 Btch intercepts: Correltions mong time points hr Initil hr Initil p=. R= hr Initil p=. R=.9 p=.4 R=.65

11 e Zu Xβ y + + = Mixed (sttic) modeling view N tlets (i) from B tches (j), testing t month x i = N N j B B B j j B N N i N N i N N i I x I I x I I x I I x I x I x I I I y y y ε ε ε Κ Κ Κ Κ Κ Κ Κ Κ Κ Κ ( ) B V u,i MVN u ~ ( ) N V e,i MVN ~ e

12 Hierrchicl (dynmic) Modeling view Dt: i tch i x i y i T... N Rndom intercept & slope for ech tch: j=:b ( ) α MVN V α j ~, Vα V MVN ( ) u = j ~, Vβ6 6 β V β Dissolution result for ech tlet: i=:n y i u, i ~ MVN V e α tch + tch x i i i + = β ( ) u i

13 HCS HCS 4 HAR HAR 4 = UN UN 6 Tlet residul covrince (V e )

14 PD Ve: Acceptle rnge of determinnt HCS HAR rho 4

15 Why Byesin pproch? Asymptotic pproximtions my not e vlid Allows quntifiction of prior informtion Properly ccounts for estimtion uncertinty Lends itself to dynmic modeling viewpoint Requires fewer mthemticl distrctions Estimtes quntities of interest esily Provides distriutionl estimtes Fewer emrrssments (e.g., negtive vrince estimtes) Is good complement to likelihood (only) methods WinBUGS is fun to use 5

16 Tlet residul covrince (V e ) Priors UN 6 prm sym ( I,) ~ InvWishrt HAR or HCS 4 prm k ~ InvGmm(.,.), k Unif ~ Unif (.5, + ) (.645, +.645) =,, for HCS for HAR 6

17 InvWishrt Prior Component mrginl prior distriutions sym ~ InvWishrt, ( c I ) c= c= , drws i c= c= ij c=

18 8 UN prms VC 6 prms Btch intercept & slope covrince (V u )

19 Btch intercept & slope Priors Process men 6 prm 4 ~ MVN 5, I, ~ MVN I 9 (, ) UN prm sym sym ~ InvWishrt ( c I,), ~ InvWishrt( c I,) VC 6 prm α k β k ~ ~ InvGmm(.,.) InvGmm(.,.), k =,, VC Common slope prm α k ~ InvGmm(.,.), k =,, 9

20 Effect of Covrince Choice: Devince Informtion Criterion Ve Vu DIC HCS VC HAR VC UN UN UN VC UN VC Common Slope

21 Prmeter Estimtes Proc MIXED vs WinBUGS 6.(.4).(5.7).(.) 4.(.9) 4.6(9.).(.) Vα.4(8.5).(.9).(.4).7(7.8) 4.6(4.6).(.8) Vβ 6.4(.).(.).(.4) 8.6(.4) 4.5(.4).7(.) 6.4(.) 9.8(.).(.4) 8.5(.4) 4.5(.4).8(.) Ve 94.(.9) 4.(.) 7.4(.5) 94.(.9) 4.(.) 7.4(.6) 7.5(4.) 6.7(.) 7.(.9) 8.(5.) 6.9(.9) 7.(.)

22 Posterior from Proc Mixed (SAS 8.) 9 proc mixed covtest; 9 clss tch tlet time; 9 model y= time time*month/ noint s; 94 rndom time time*month/ type=un() suject=tch G s; 95 repeted / type=un suject=tlet R; 96 prior /out=posterior nsmple=; NOTE: Convergence criteri met. WARNING: Posterior smpling is not performed ecuse the prmeter trnsformtion is not of full rnk. Runs in SAS 9., however SAS only strictly supports the posterior if rndom type=vc with no repeted, or rndom nd repeted types oth = VC

23 WinBUGS dynmic modeling # Prior InvVe[:T,:]~dwish(R[,],) cent[]~dnorm(.,.) cent[]~dnorm(5,.) cent[]~dnorm(,.) for ( j in :) { [ j ]~dnorm(.,.) gcent[ j ]~dgmm(.,.) g[ j ]~dgmm(.,.) } # Likelihood # Drw the T intercepts nd slopes for ech tch for ( i in :B) { for ( j in :) { lph[i, j] ~ dnorm(cent[ j ], gcent[ j ]) et[i, j] ~ dnorm([ j ], g[ j ]) } } # Drw vector of results from ech tlet for (os in :N){ for ( j in :){ mu[os,j]<-lph[btch[os],j]+et[btch[os],j]*(month[os]-xr)} y[os,:t ]~dmnorm(mu[os, ], InvVe[, ])}

24 Shrinkge of Byesin nd mixed model tch intercept nd slope estimtes Intercept (dissolution ner tch relese %LC) hr hr Byesin Fixed Model Mixed Model Estimtion Method Byesin Fixed Model Mixed Model Estimtion Method.5h.5h Byesin Fixed Model Mixed Model Estimtion Method Slope (rte of chnge in dissolution %LC/month) Byesin Fixed Model Mixed Model Estimtion Method 8hr 8hr Byesin Fixed Model Mixed Model Estimtion Method Byesin Fixed Model Mixed Model Estimtion Method 4

25 WinBUGS Btch intercept nd slope estimtes: Byesin BLUPs ox plot: Init[,] ox plot: Init[,] ox plot: Init[,] Intercepts [,] [,] [,] [4,] [5,] [6,] [7,] [8,] [9,] [,] [,] [,] [,] [4,] [5,] [6,] [7,] [8,] [9,] [,] [,] [,] [,] [4,] [5,] [6,] [7,] [8,] [9,] [,] ox plot: slope[,] ox plot: slope[,] ox plot: slope[,].5 [8,].4.4 [5,] [7,] Slopes..5 [,] [,] [,] [4,] [5,] [6,] [7,] [9,] [,].... [,] [,] [,] [4,] [5,] [6,] [7,] [8,] [9,] [,].. -. [,] [,] [,] [4,] [6,] [8,] [9,] [,]

26 Predicting future results Posterior smple Posterior predictive smple () V () α () V () β V () e : : : : : (d) V (d) α (d) V (d) β V (d) e : : : : : () V () α () V () β V () e α () fut β () fut : : α (d) fut β (d) fut : : α () fut β () fut y () fut, y () fut,4 : : : y (d) fut, y (d) fut,4 : : : y () fut, y () fut,4 y ( d ) ( d ) ( d ) ( α + xβ V ) ( d ) fut, i ~ MVN fut fut, e 6

27 WinBUGS posterior predictions # Predict int & slope for future tches for (j in :){ _str[ j ]~dnorm([ j ], g[ j ]) cent_pred[ j ]~dnorm(cent[ j ], gcent[ j ]) _str[ j ]<-cent[ j ] - [ j ]*xr} # Otin the Ve components Ve[:,:] <- invve[, ]) for (j in :){ sigm[ j ] <- sqrt(ve[j,j])} rho <- Ve[,]/sigm[]/sigm[] rho <- Ve[,]/sigm[]/sigm[] rho <- Ve[,]/sigm[]/sigm[] 7

28 Predicting testing results L) L) L) I(Fil) y () fut, y () fut,4 : : : y (d) fut, y (d) fut,4 : : : y () fut, y () fut,4 : : : : : : : : USP <74> Estimte Proilities L) L) L) Pr(Fil) L)/ L)/ L)/ #(Fil)/ 8

29 Semi-prmetric ootstrp prediction Fixed model prediction (no shrinkge) intercept nd slope vectors vi SLR 78 tlet residul vectors -or- Mixed model prediction (shrinkge) intercept vector BLUPs slope vector BLUPs 78 tlet residul vectors Smple with replcement to construct future results 9

30 Level testing nd filure rte predictions Proility of Pssing t Level (%) Mixed Model Fixed Model Byesin Months of Storge Proility of Pssing t Level (%) Mixed Model Fixed Model Byesin Months of Storge Proility of Pssing t Level (%) Mixed Model Fixed Model Byesin Proility of Filing Dissolution Testing Mixed Model Fixed Model Byesin Months of Storge Months of Storge

31 Summry A multivrite, hierrchicl, Byesin pproch to dissolution stility illustrted Some options for specifying the covrince priors Estimtion nd shrinkge of the ltent tch slope nd intercept prmeters Posterior prediction of future dt Prediction of future filure nd level testing rtes Fixed most pessimistic (no shrinkge?) Mixed lowest filure rte (non-symptotic?) Give WinBUGS try

32 Acknowledgements The invlule suggestions of, encourgement from, nd helpful discussions with John Peterson, GSK Oscr Go, J&J Jyh-Ming Shoung, J&J Stn Altn, J&J re gretly pprecited. Thnk You!