nmw-package {nmw}

Understanding Nonlinear Mixed Effects Modeling for Population Pharmacokinetics

Description

This shows how NONMEM(R) <http://www.iconplc.com/innovation/nonmem/> software works.

Details

This package explains 'First Order(FO) approximation' method, 'First Order Conditional Estimation(FOCE)' method, and 'Laplacian(LAPL)' method of NONMEM software.

Author(s)

Kyun-Seop Bae <[e-mail]>

References

1. NONMEM Users guide

2. Wang Y. Derivation of various NONMEM estimation methods. J Pharmacokinet Pharmacodyn. 2007.

3. Kang D, Bae K, Houk BE, Savic RM, Karlsson MO. Standard Error of Empirical Bayes Estimate in NONMEM(R) VI. K J Physiol Pharmacol. 2012.

4. Kim M, Yim D, Bae K. R-based reproduction of the estimation process hidden behind NONMEM Part 1: First order approximation method. 2015.

5. Bae K, Yim D. R-based reproduction of the estimation process hidden behind NONMEM Part 2: First order conditional estimation. 2016.

Examples

DataAll = Theoph
colnames(DataAll) = c("ID", "BWT", "DOSE", "TIME", "DV")
DataAll[,"ID"] = as.numeric(as.character(DataAll[,"ID"]))

nTheta = 3
nEta = 3
nEps = 2

THETAinit = c(2, 50, 0.1)
OMinit = matrix(c(0.2, 0.1, 0.1, 0.1, 0.2, 0.1, 0.1, 0.1, 0.2), nrow=nEta, ncol=nEta)
SGinit = diag(c(0.1, 0.1))

LB = rep(0, nTheta) # Lower bound
UB = rep(1000000, nTheta) # Upper bound

FGD = deriv(~DOSE/(TH2*exp(ETA2))*TH1*exp(ETA1)/(TH1*exp(ETA1) - TH3*exp(ETA3))*
             (exp(-TH3*exp(ETA3)*TIME)-exp(-TH1*exp(ETA1)*TIME)),
            c("ETA1","ETA2","ETA3"),
            function.arg=c("TH1", "TH2", "TH3", "ETA1", "ETA2", "ETA3", "DOSE", "TIME"),
            func=TRUE, hessian=TRUE)
H = deriv(~F + F*EPS1 + EPS2, c("EPS1", "EPS2"), function.arg=c("F", "EPS1", "EPS2"), func=TRUE)

PRED = function(THETA, ETA, DATAi)
{
  FGDres = FGD(THETA[1], THETA[2], THETA[3], ETA[1], ETA[2], ETA[3], DOSE=320, DATAi[,"TIME"]) 
  Gres = attr(FGDres, "gradient")
  Hres = attr(H(FGDres, 0, 0), "gradient")
  
  if (e$METHOD == "LAPL") {
    Dres = attr(FGDres, "hessian")
    Res = cbind(FGDres, Gres, Hres, Dres[,1,1], Dres[,2,1], Dres[,2,2], Dres[,3,])
    colnames(Res) = c("F", "G1", "G2", "G3", "H1", "H2", "D11", "D21", "D22", "D31", "D32", "D33") 
  } else {
    Res = cbind(FGDres, Gres, Hres)
    colnames(Res) = c("F", "G1", "G2", "G3", "H1", "H2") 
  }
  return(Res)
}

####### First Order Approximation Method # Commented out for the CRAN CPU time
#InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, LB=LB, UB=UB, 
#         Pred=PRED, METHOD="ZERO")
#(EstRes = EstStep())           # 4 sec
#(CovRes = CovStep())           # 2 sec
#PostHocEta() # Using e$FinalPara from EstStep()
#TabStep()    

######## First Order Conditional Estimation with Interaction Method
#InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, LB=LB, UB=UB, 
#         Pred=PRED, METHOD="COND")
#(EstRes = EstStep())           # 2 min
#(CovRes = CovStep())           # 1 min
#get("EBE", envir=e)
#TabStep()

######## Laplacian Approximation with Interacton Method
#InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, LB=LB, UB=UB, 
#         Pred=PRED, METHOD="LAPL")
#(EstRes = EstStep())           # 4 min
#(CovRes = CovStep())           # 1 min
#get("EBE", envir=e)
#TabStep()