Hi,
I was wondering if the following model can be fitted by nlme/lme4. The difficult
part is that the error term is combined with other parameters.
The model that we need to fit is as below and the R codes to generate data is
provided as well. Many thanks!!!
# Y_{ijk} = (E_0 + Emax*dose_i/(ED_50+dose_i) + S_{ij} +
e_{ijk})*(1-exp(k*X_{ijk}))/(1-exp(k*d));
## Parameters to be estimated E0, Emax, ED50, sigma_S, sigma_e, kn
Patients <- 100; # 100 patients
nVisit <- 12; # total 12 visit
d <- 6; # 6 month study
dose <- c(0,5,10,20,40,100,200);
visits <- seq(6/12,6,by = 6/12);
# true parameters
E0 <- 2;
Emax <- 20;
ED50 <- 10;
sigma_S <- 5;
sigma_e <- 4;
k <- -1;
dataM <- matrix(NA, nrow = nPatients*nVisit, ncol= 4);
for(iter in 1:nPatients){
dose_i <- sample(dose,1);
S_i <- rep(rnorm(n=1, mean=0, sd=sigma_S),nVisit); # random effect for this
patients
e_i <- rnorm(n=nVisit, mean=0, sd=sigma_e);
response_i <-
(E0+Emax*dose_i/(ED50+dose_i)+S_i+e_i)*(1-exp(k*visits))/(1-exp(k*d));
patients_i <- cbind(rep(iter,nVisit),rep(dose_i,nVisit),visits,response_i);
dataM[(nVisit*(iter-1)+1):(nVisit*(iter-1)+nVisit),] <- patients_i;
}
colnames(dataM) <-
c("PatientID","Dose","VisitTime","Response")
Best,
Haoda