[R] nlminb( ) : one compartment open PK model

[Greg Tarpinian]

All,

I have been able to successfully use the optim( ) function with
"L-BFGS-B" to find reasonable parameters for a one-compartment
open pharmacokinetic model.  My loss function in this case was
squared error, and I made no assumptions about the distribution
of the plasma values.  The model appeared to fit pretty well.

Out of curiosity, I decided to try to use nlminb( ) applied to
a likelihood function that assumes the plasma values are normally
distributed on the semilog scale (ie, modeling log(conc) over
time).  nlminb( ) keeps telling me that it has converged, but 
the estimated parameters are always identical to the initial
values....  I am certain that I have committed "ein dummheit"
somewhere in the following code, but not sure what...  Any help
would be greatly appreciated.

Kind regards,

    Greg



model2 <- function(parms, dose, time, log.conc)
{
	exp1 <- exp(-parms[1]*time)
	exp2 <- exp(-parms[2]*time)
	right.hand <- log(exp1 - exp2)
	numerator <- dose*parms[1]*parms[2]
	denominator <- parms[3]*(parms[2] - parms[1])
	left.hand <- log(numerator/(denominator))
	pred <- left.hand + right.hand
	
	# defining the distribution of the values
	const <- 1/(sqrt(2*pi)*parms[4])
	exponent <- (-1/(2*(parms[4]^2)))*(log.conc - pred)^2
	likelihood <- const*exp(exponent)
	
	#defining the merit function
	-sum(log(likelihood))
}

deriv2
<- deriv( expr = ~   -log(1/(sqrt(2*pi)*S)*exp((-1/(2*(S^2)))*
                      (log.conc-(log(dose*Ke*Ka/(Cl*(Ka-Ke)))
                      +log(exp(-Ke*time)-exp(-Ka*time))))^2)),
	  namevec = c("Ke","Ka","Cl","S"),
	  function.arg = function(Ke, Ka, Cl, S, dose, time, log.conc) NULL )
		
gradient2.1compart <- function(parms, dose, time, log.conc)
{
Ke <- parms[1]; Ka <- parms[2]; Cl <- parms[3]; S <- parms[4]
colSums(attr(deriv2.1compart(Ke, Ka, Cl, S, dose, time, log.conc), "gradient"))
}

attach(foo.frame)
inits <- c(Ke = .5,
	   Ka = .5, 
	   Cl = 1,
	   S = 1)

#Trying out the code
nlminb(start = inits, 
	   objective = model2,
	   gradient = gradient2,
	   control = list(eval.max = 5000, iter.max = 5000),
	   lower = rep(0,4),
	   dose = DOSE,
	   time = TIME,
	   log.conc = log(RESPONSE))