PSM.simulate: Create simulation data for multiple individuals

In PSM: Non-Linear Mixed-Effects Modelling using Stochastic Differential Equations

Description

Simulates data for multiple individuals in a mixed effects model based on stochastic differential equations using an euler scheme.

Usage

PSM.simulate(Model, Data, THETA, deltaTime, longX=TRUE) 

Arguments

Model	A list containing the model components either Linear or Non-Linear Model list.*
Data	List with elements described below. No Data$Y is needed as it is generated through the simulation. The number of individuals simulated is equal to length(Data). Time Time vector U Input list for the Model covar Covariates list
THETA	Vector of population parameters
deltaTime	Time Step in the Euler scheme
longX	Boolean. Toggles output of the entire simulated outcome of the states

* See description in PSM.estimate.

Details

The eta is drawn from the multivariate normal distribution N(0,OMEGA). The simulation is an euler based method but for every time interval dt the model is predicted and the states affected by system noise (SIG).

The measurements are added an normal error term belonging to N(0,S).

The function mvrnorm from the MASS pacakge is used to to generate random numbers fra multivariate normal distributions.

Value

The simulated outcome of the model is returned in a list, where each element is the data for an individual.

X	Simulated states sampled at time points for measurements
Y	Simulated measurements
Time	Time points for measurements
U	Input vector used in the simulation
eta	The random effects used in the simulation
Dose	The dose list used in the simulation
longX	Entire outcome of simulated states
longTime	Time points for longX.

Note

For further details please also read the package vignette pdf-document by writing vignette("PSM") in R.

Author(s)

Stig B. Mortensen and Soeren Klim

References

Please visit http://www.imm.dtu.dk/psm or refer to the help page for PSM.

See Also

PSM, PSM.estimate, PSM.smooth, PSM.plot, PSM.template

Examples

#specify pharmacokinetic model
#2 state equations, 1 observation equation, 1 random effect

mod = vector(mode="list")
mod$Matrices = function(phi) {
  list(
    matA=matrix(c(-phi$ka, 0, phi$ka, -phi$ke), nrow=2, ncol=2, byrow=TRUE),
    matC=matrix(c(0, 1), nrow=1, ncol=2)
  )
}
mod$h = function(eta, theta, covar) {
  phi = theta
  phi$dose = theta$dose * exp(eta[1])
  phi
}
mod$S = function(phi) {
  matrix(c(phi$sigma), nrow=1, ncol=1)
}
mod$SIG = function(phi) {
  matrix(c(0, 0, 0, phi$omega), nrow=2, ncol=2, byrow=TRUE)
}
mod$X0 = function(Time, phi, U) {
  matrix(c(phi$dose, 0), nrow=2, ncol=1)
}
mod$ModelPar = function(THETA) {
  list(theta=list(dose = THETA["dose"], ka = THETA["ka"], ke = THETA["ke"],
                  omega = THETA["omega"], sigma = THETA["sigma"]),
       OMEGA=matrix(c(THETA["BSV_dose"]), nrow=1, ncol=1)
  )
}


#specify sampling scheme and RNG

TheophPSM <- list()
TheophPSM[[1]] <- list(Time = seq(0,25,5))
set.seed(12345)

#simulate and visualize ODE model (no volatility)

parM <- c(ka = 1.58, ke = 0.08, dose = 9.54, omega = 0, sigma = 1.05, BSV_dose = 0)
TheophSim <- PSM.simulate(mod, TheophPSM, THETA = parM, deltaTime = 0.1)
plot(TheophSim[[1]]$longTime, TheophSim[[1]]$longX[2,],
     type="l", ylab="concentration", xlab="time")

#contrast it to SDE model

parM <- c(ka = 1.58, ke = 0.08, dose = 9.54, omega = 0.34, sigma = 1.05, BSV_dose = 0)
TheophSim <- PSM.simulate(mod, TheophPSM, THETA = parM, deltaTime = 0.1)
lines(TheophSim[[1]]$longTime, TheophSim[[1]]$longX[2,],
     ylab="concentration", xlab="time")

PSM documentation built on May 2, 2019, 9:47 a.m.