RE: [Fwd: CLIN PHAR STAT: Mixed Vs Fixed]

From: "Stephen Duffull" <sduffull@pharmacy.uq.edu.au> Subject: RE: [Fwd: CLIN PHAR STAT: Mixed Vs Fixed] Date: Wed, 9 Aug 2000 09:37:35 +1000 Nick Here is a simple example of the prior setup for the WinBUGS code for implementing a Bayesian PK analysis: ...the model bit goes here... z[j,i] ~ dnorm(c[j,i],tau[j]) # likelihood function } # Individual priors theta[j,1:2] ~ dmnorm(mu.theta[1:2],omega.theta[1:2,1:2]) tau[j] ~ dgamma(0.001,0.001) } # Population Priors mu.theta[1] ~ dnorm(.05,0.1)#I(0,) mu.theta[2] ~ dnorm(1,0.1)#I(0,) omega.theta[1:2,1:2] ~ dwish(R[1:2,1:2],2) In this example z[j,i] is the ith observed concentration for the jth individual, and c[j,i] is the expected concentration; there are 2 parameters (thetas say CL and V) in the model. I have used mu.theta[x] to represent the population value (sometimes in NONMEM TV is used) of the parameter. Note that tau[j] is the precision of the residual error (precision = 1/variance] and there is one for each individual. It is of course possible to put a population prior on tau[j] to allow the individual estimates of RUV to be conditional on the population. Nick wrote: > I had suggested using the NONMEM Bayesian prior > approach earlier in this > thread. NONMEM allows one to put a normal (or > lognormal) prior on > structural model parameters (THETA), an inverse > Wishart prior on random > effects parameters (OMEGA) and normal/lognormal > prior on residual error > parameters (SIGMA) (by indirection using THETA). > How well does this > approach your definition of "fully" Bayesian? The difficulty I have lies in not knowing exactly what NONMEM does when it does the NONMEM Bayesian approach (please note that I have never used this feature of NONMEM and indeed don't know how too). In contrast WinBUGS is quite transparent about both its hierarchical structure and about methodology it uses to get around nasty integration problems. IMHO I think that if a Bayesian method is desirable then a Bayesian program should be used - but I may be biased :-). Regards Steve ================= Stephen Duffull School of Pharmacy University of Queensland Brisbane, QLD 4072 Australia Ph +61 7 3365 8808 Fax +61 7 3365 1688 http://www.uq.edu.au/pharmacy/duffull.htm