WinBugs with some PK examples

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WinBugs with some PK examples

• Peter Blood
• CP-Bios
• Novartis Horsham Research Centre

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Examples

• IV dose
• Cadralazine
• Oral 1 compartment
• Theophylline

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A Simple Hierarchical Structure
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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)
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IV Cadralazine Equation
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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(k0k1(Log V - c), ?b) I(Lb,Ub)
• Could now analyse in winBUGS 1.3 as multivariate
• muab 12 dmnorm(mean12, prec12,12)
• tauab12,12 dwish(R12, 12,2)
• Could now use PKBUGS (see David Lunns example)

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Cadralazine Doodle
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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 drugs 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 Users 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
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Theophylline Example
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Open Oral Model for Theophylline
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Theophylline Central Code

• for(i in 1nSUBJ)
• for(j in 1nTIME)
• mui,j lt- Doseiexp(logka)
• (exp((-Timei,j)exp(lgcli-lgvol
  i))
• - exp((-Timei,j)exp(logka)))
• /(exp(lgvolilogka)-exp(lgcli))
• Conci,j dnorm(mui,j, epsilon)
• end of j time loop
• end of i subject loop
• Conci,j dt(mui,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 1nSUBJ)
• lgcli dnorm(phi,eta1)
• lgvoli 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 1nSUBJ)
• Dosei lt- Zi,1,4
• for(j in 1nTIME)
• Timei,j lt- Zi,j,5
• Conci,j lt- Zi,j,6
• lgcl.mn lt- mean(lgcl)
• lgvol.mn lt- mean(lgvol)
• mnCl lt- exp(lgcl.mn)
• mnVol lt- exp(lgvol.mn)
• Sigma lt- 1.0/sqrt(epsilon)
• for(i in 1nSUBJ)
• Cli lt- exp(lgcli)
• Voli lt- exp(lgvoli)

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Theophylline Data-1st Subject

• list(nSUBJ 12, nTIME 11,
• Z structure(
• .Datac(
• 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),
  .Dimc(12,11,6)))

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Start of 2 chains for log(Cl) (Theophylline)
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3rd Continuation of chains for log(Cl)(Theophylli
ne)
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History Chains (Theophylline)
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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
• muab12 dmnorm(mean12,precn12,12)
• tauab12,12 dwish(omega12,12,2)
• extra initial conditions
• list(
• mean c(0,0),
• precn structure(.Datac(1.0E-6,0,0,1.0E-.Dimc(
  2,2)),
• omega structure(.Datac(0.1,0,0,0.01),
  .Dimc(2,2)))

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Results from Multi-variate Model (Theophylline)

• node mean sd MC err start sample
• epsilon 0.937 0.130 0.0018 4001 20000
• Logka 0.463 0.058 0.0014 4001 20000
• muab1 -3.259 0.102 0.0015 4001 20000
• muab2 -0.738 0.072 0.0009 4001 20000
• Sigma 1.041 0.073 0.0010 4001 20000
• tauab1,1 17.740 11.30 0.2633 4001 20000
• tauab1,2 -5.524 11.50 0.2628 4001 20000
• tauab2,1 -5.524 11.50 0.2628 4001 20000
• tauab2,2 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
VC GLS 0.453 -0.748 -3.264
LB 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
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