Distribution Kinetics in JAGS

Chapter 19 of Rowland and Tozer (Clinical pharmacokinetics and pharmacodynamics, 4th edition) has distribution kinetics. I am examining problem 3. It is fairly easy, especially since essentially all formulas are on the same page under 'key relationships'. The only difficulty is that the formulas are symmetrical in λ₁, c₁ and λ₂, c₂ and they are exchanged between chains. For this I forced λ₁>λ₂. In addition, I do not really believe concentrations in the 4000 range are as accurately measured as those in the 5 range (in the period 1/2 hour to 1 hour, the decrease is about 80 units per minute). The measurement error is now proportional to concentration.

Data and model

C19SP3 <- data.frame(
    time=c(0.5,1,1.5,2,3,4,5,8,12,16,24,36,48),
    conc=c(4211,1793,808,405,168,122,101,88,67,51,30,13,6))

library(R2jags)
datain <- list(
    time=C19SP3$time,
    lconc=log(C19SP3$conc),
    n=nrow(C19SP3),
    dose=30*1000)

model1 <- function() {
  tau <- 1/pow(sigma,2)
  sigma ~ dunif(0,100)
  llambda1 ~dlnorm(.4,.1)
  cc1 ~ dlnorm(1,.01)
  llambda2 ~dlnorm(.4,.1)
  cc2 ~ dlnorm(1,.01)
  choice <- llambda1>llambda2
  c1 <- choice*cc1+(1-choice)*cc2
  c2 <- choice*cc2+(1-choice)*cc1
  lambda1 <- choice*llambda1+(1-choice)*llambda2
  lambda2 <- choice*llambda2+(1-choice)*llambda1
  
  for (i in 1:n) {
    pred[i] <- log(c1*exp(-lambda1*time[i]) +c2*exp(-lambda2*time[i]))
    lconc[i] ~ dnorm(pred[i],tau)
  }
  V1 <- dose/(c1+c2)
  AUC <- c1/lambda1+c2/lambda2
  CL <- dose/AUC
  V <- CL/lambda2
  Vss <- dose*(c1/pow(lambda1,2)+c2/pow(lambda2,2))/pow(AUC,2)
  }

parameters <- c('c1','c2','lambda1','lambda2' ,
   'V1','CL','Vss','AUC','V')
inits <- function() 
  list(
      sigma=rnorm(1,1,.1),
      cc1=9000,
      cc2=150)

jagsfit <- jags(datain, model=model1, 
    inits=inits, 
    parameters=parameters,progress.bar="gui",
    n.chains=4,n.iter=14000,n.burnin=5000,n.thin=2)

Results

Results same as in the book:

Inference for Bugs model at "C:\...5a.txt", fit using jags,

 4 chains, each with 14000 iterations (first 5000 discarded), n.thin = 2

 n.sims = 18000 iterations saved

          mu.vect sd.vect     2.5%      25%      50%       75%     97.5%  Rhat n.eff

AUC      7752.778 130.145 7498.102 7670.443 7751.138  7831.068  8016.879 1.002  3000

CL          3.871   0.065    3.742    3.831    3.870     3.911     4.001 1.002  3000

V          57.971   1.210   55.650   57.215   57.956    58.708    60.401 1.002  4000

V1          2.980   0.104    2.776    2.915    2.978     3.044     3.192 1.002  2800

Vss        18.038   0.600   16.865   17.662   18.029    18.404    19.251 1.002  3900

c1       9933.578 352.138 9253.229 9709.652 9927.037 10145.611 10659.610 1.002  2800

c2        147.197   2.412  142.333  145.734  147.207   148.659   152.069 1.001  5000

lambda1     1.790   0.028    1.734    1.772    1.790     1.807     1.847 1.002  2800

lambda2     0.067   0.001    0.065    0.066    0.067     0.067     0.068 1.001 10000

deviance  -59.366   4.394  -65.150  -62.608  -60.275   -57.058   -48.524 1.001  4100

For each parameter, n.eff is a crude measure of effective sample size,

and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)

pD = 9.6 and DIC = -49.7

DIC is an estimate of expected predictive error (lower deviance is better).

Plot

The plot has narrow intervals, which is a reflection of the small intervals in the parameters.

Previous posts in this series:

Simple Pharmacokinetics with Jags

PK calculation of IV and oral dosing in JAGS Translated in Stan by Bob Carpenter here: Stan Model of the Week: PK Calculation of IV and Oral Dosing
PK calculations for infusion at constant rate