Slide 1 winBUGS Oct2001 NOVARTISNOVARTIS WinBugs with some PK examples Peter Blood CP-Bios Novartis...

Slide 1winBUGS

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WinBugs with some PK examples

Peter Blood

CP-Bios

Novartis Horsham Research Centre

Slide 2winBUGS

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Examples

• IV dose - Cadralazine

• Oral 1 compartment– Theophylline

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A Simple Hierarchical Structure

f o r ( i I N 1 : 1 2 )

f o r ( j I N 1 : 1 1 )

e t a 2t h e t ae t a 1p h i

l o g ( V)l o g ( Cl )

mu

c o n c

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IV - Cadralazine

• Taken IV by patients for cardiac failure

• Data consisted of 10 patients on 30mg

• Original Bayesian analysis by Wakefield, Racine-Poon et al

• (Applied Statistics 43,No 1, pp201-221,1994)

• Analysed in BUGS with a linearised model– See version 0.6 manual addendum

• Can now be analysed with nonlinear Model in PkBUGS

• Will consider a non-linear model with winBUGS

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Cadralazine Data (from Wakefield et al)

0 5 10 15 20 25 30Time (h)

-0.1

0.4

0.9

1.4

1.9

Co

nce

ntr

atio

n (

mg

/L)

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IV Cadralazine Equation

)Cllog();Vlog(

ngsubstituti

)V

Cltexp(

V

DConc

)btexp(AConc

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Cadralazine Models

• Analysed in BUGS v0.6 as product formulation of the bivariate nomal

• Log V ~ N(ua, a) I (La,Ua)

• Log Cl | log V ~ N(k0+k1(Log V - c), b) I(Lb,Ub)

• Could now analyse in winBUGS 1.3 as multivariate

• muab [1:2] ~ dmnorm(mean[1:2], prec[1:2,1:2])

• tauab[1:2,1:2] ~ dwish(R[1:2], 1:2],2)

• Could now use PKBUGS (see David Lunn’s example)

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Cadralazine Doodle

f o r ( j I N 1 : N)

f o r ( i I N 1 : K)

Do s e t a u C

t a u . c lp . l g c lt a u . v o lp . l g v o l

l g c l [ i ]l g v o l [ i ]

Y[ i , j ]

mn [ i , j ]mn [ i , j ]

n a me : mn [ i , j ] t y p e : l o g i c a l l i n k : i d e n t i t y

v a l u e : ( Do s e / e x p ( l g v o l [ i ] ) ) * e x p ( - t [ j ] * e x p ( l g c l [ i ] - l g v o l [ i ] ) )

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Cadralazine Results

Mean

(sd)

BUGS 0.6 winBUGS PKBUGS

p.lgcl 1.051(0.147) 1.061 (0.131) 1.054 (0.129)

p.lgvol 2.838 (0.072) 2.669 (0.043) 2.683 (0.056)

tauC - 285.9 (52.96) 232.8 (51.18)

sigma - 0.060 (0.006) 0.066 (0.007)

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Theophylline Example

• Bronchodilator (methyl xanthine)

• Kinetics of drug’s anti-asthmatic properties

• 12 Subjects measured 11 times over 25 hours

• Oral first order one compartment model

• First Analysed by Sheiner and Beal with NONMEM

• Also by Pinherio and Bates in S+ using NLME

• And in SAS using proc NLMIXED

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References on Theophylline

• Davidian & Giltinan 1995– “Non linear Models for Repeated – Measurement Data”, pub Chapman & Hall.

• Pinheiro & Bates (1995)– Analysed in SAS (Proc Nlmixed)– Reanalysed in SPLUS (NLME)

• Boeckman, Sheiner & Beal 1992 – (Nonmem User’s Guide Part V)– Created with Body weight as a Cl covariate– Absorption assumed same for all subjects– 1 Compartment model – Volume in L/kg, Clearance in L/hr/kg

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Theophylline Example 12 adults from NONMEM file

0.1

1.0

10.0

100.0

0 5 10 15 20 25

time (hour)

1

10

11

12

2

3

4

5

6

7

8

9

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Theophylline Example

0.1

1.0

10.0

100.0

0.1 1.0 10.0 100.0

time (hour)

1

10

11

12

2

3

4

5

6

7

8

9

NONMEM dataset (12 adults)

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Open Oral Model for Theophylline

);Cllog();Vlog(

ngsubstituti

)}Katexp()V/Clt{exp()ClVka(

DkaConc

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Theophylline Central Code

• for(i in 1:nSUBJ){• for(j in 1:nTIME){• mu[i,j] <- Dose[i]*exp(logka)*• (exp((-Time[i,j])*exp(lgcl[i]-lgvol[i]))• - exp((-Time[i,j])*exp(logka)))• /(exp(lgvol[i]+logka)-exp(lgcl[i]))• Conc[i,j] ~ dnorm(mu[i,j], epsilon) • }# end of j time loop • }# end of i subject loop

• Conc[i,j] ~ dt(mu[i,j],epsilon,4)

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Prior Information

• phi ~ dnorm(-3.5, 500) # log(Cl)• theta ~ dnorm(-1,100000) # log(V)• logka ~ dnorm( 0.5, 150) • eta1 ~ dgamma(40, 1) # inter• eta2 ~ dgamma(12, 3) # inter • epsilon ~ dgamma(0.001,0.001) # intra

• for(i in 1:nSUBJ){• lgcl[i] ~ dnorm(phi,eta1) • lgvol[i] ~ dnorm(theta,eta2)•

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Initial Conditions (1st)

• # 1st set of initial start conditions• list(phi = -4.0,• theta = -1.5,• logka = 0.3, • eta1 = 24, • eta2 = 2,• epsilon= 0.7,• lgcl = c(-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,• -4.0,-4.0,-4.0,-4.0,-4.0,-4.0),• lgvol = c(-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,• -1.5,-1.5,-1.5,-1.5,-1.5,-1.5)• )

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Data Collection & Posterior Statistics

• for(i in 1:nSUBJ){• Dose[i] <- Z[i,1,4]• for(j in 1:nTIME){• Time[i,j] <- Z[i,j,5]• Conc[i,j] <- Z[i,j,6]

• lgcl.mn <- mean(lgcl[])• lgvol.mn <- mean(lgvol[])• mnCl <- exp(lgcl.mn)• mnVol <- exp(lgvol.mn)• Sigma <- 1.0/sqrt(epsilon)

• for(i in 1:nSUBJ){• Cl[i] <- exp(lgcl[i])• Vol[i] <- exp(lgvol[i])

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Theophylline Data-1st Subject

• list(nSUBJ = 12, nTIME = 11, • Z = structure(• .Data=c(• 1, 1, 79.60, 4.02, 0.00, 0.74,• 2, 1, 79.60, 4.02, 0.25, 2.84,• 3, 1, 79.60, 4.02, 0.57, 6.57,• 4, 1, 79.60, 4.02, 1.12,10.50,• 5, 1, 79.60, 4.02, 2.02, 9.66,• 6, 1, 79.60, 4.02, 3.82, 8.58,• 7, 1, 79.60, 4.02, 5.10, 8.36,• 8, 1, 79.60, 4.02, 7.03, 7.47,• 9, 1, 79.60, 4.02, 9.05, 6.89,• 10, 1, 79.60, 4.02,12.12, 5.94,• 11, 1, 79.60, 4.02,24.37, 3.28,• ............• 132,12, 60.50, 5.30,24.15, 1.17), .Dim=c(12,11,6)))

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Start of 2 chains for log(Cl) (Theophylline)

l g c l . mn c h a i n s 2 : 1

i t e r a t i o n5 00

- 4 . 0

- 3 . 5

- 3 . 0

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3rd Continuation of chains for log(Cl)(Theophylline)

l g c l . mn c h a i n s 2 : 1

i t e r a t i o n8 9 5 08 9 0 08 8 5 0

- 3 . 6 - 3 . 5 - 3 . 4 - 3 . 3 - 3 . 2

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History Chains (Theophylline)

l g c l . mn c h a i n 1

i t e r a t i o n4 0 0 1 5 0 0 0 7 5 0 0 1 0 0 0 0 1 2 5 0 0

- 3 . 6

- 3 . 5

- 3 . 4

- 3 . 3

- 3 . 2

l g c l . mn c h a i n 2

i t e r a t i o n4 0 0 1 5 0 0 0 7 5 0 0 1 0 0 0 0 1 2 5 0 0

- 3 . 6

- 3 . 5

- 3 . 4

- 3 . 3

- 3 . 2

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Results for Theophylline

• node mean sd MC err start sample• epsilon 0.891 0.124 0.0016 4001 20000

• eta1 36.34 6.035 0.0672 4001 20000

• eta2 4.734 1.124 0.0085 4001 20000

• Lgcl.mn -3.352 0.045 0.0011 4001 20000

• Lgvol.mn -0.719 0.028 0.0007 4001 20000

• Logka 0.483 0.056 0.0013 4001 20000

• Phi -3.432 0.039 0.0006 4001 20000

• Theta -0.999 0.003 0.00002 4001 20000

• sigma 1.067 0.075 0.0009 4001 20000

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Geweke & Cross-Correlation(chain 1)

Geweke (Z)

Variable Lgcl.mn Lgvol.mn Phi Theta Sigma

0.608 Lgcl.mn 1.000

-1.500 Lgvol.mn -0.488 1.000

1.080 Phi 0.525 -0.252 1.000

-0.882 Theta 0.002 -0.013 -0.001 1.000

-0.611 Sigma -0.211 0.125 -0.102 0.005 1.000

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Multivariate Theophylline

• # vague prior information• muab[1:2] ~ dmnorm(mean[1:2],precn[1:2,1:2])• tauab[1:2,1:2] ~ dwish(omega[1:2,1:2],2)

• # extra initial conditions• list(• mean = c(0,0),• precn = structure(.Data=c(1.0E-6,0,0,1.0E-.Dim=c(2,2)),• omega = structure(.Data=c(0.1,0,0,0.01), .Dim=c(2,2)))

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Results from Multi-variate Model (Theophylline)

• node mean sd MC err startsample

• epsilon 0.937 0.130 0.0018 4001 20000

• Logka 0.463 0.058 0.0014 4001 20000

• muab[1] -3.259 0.102 0.0015 4001 20000

• muab[2] -0.738 0.072 0.0009 4001 20000

• Sigma 1.041 0.073 0.0010 4001 20000

• tauab[1,1]17.740 11.30 0.2633 4001 20000

• tauab[1,2]-5.524 11.50 0.2628 4001 20000

• tauab[2,1]-5.524 11.50 0.2628 4001 20000

• tauab[2,2]32.080 21.60 0.4639 4001 20000

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Theophylline

Software Procedure RESULTS

Log(ka) Log(V) LOG(Cl) LOG(Ke)

winBUGS M-H 0.482 -0.999 -3.432

NONMEM Taylor 0.456 -0.802 -3.160

S+ NLME 0.453 -0.782 -3.214

SAS NLMIXED 0.453 -0.795 -3.169

SAS NLMIXED 0.481 -3.227 -2.459

Davidian & Giltian

GTS 0.265 -0.795 -3.207

“ V&C GLS 0.453 -0.748 -3.264

“ L&B GLS 0.329 -0.789 -3.214

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Conclusions

• Run some examples of PK models in winBUGS.

• IV and Oral One compartment examples.

• Cadralazine and Theophylline

• Compared with results from other sources

• Looked at convergence issues in CODA

• Perhaps you should now try PKBUGS (28models)!

• Plea for further development of PKBUGS

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The End

•Any

•Questions

• ?