L.E. Friberg, C. Dansirikul and S.B. Duffull
School of Pharmacy, University of Queensland, Brisbane, Australia
Objectives: The most common method to discriminate between nested models in frequentist analyses is the likelihood ratio test with some predefined level of significance. In addition to dichotomous model discrimination decisions, estimation methods, such as Markov chain Monte Carlo (MCMC), that are based on simulation platforms also allow for model discrimination to be based on predictive or posterior distributions. When using MCMC, competing models can be fitted simultaneously as a joint model with an added parameter to indicate which model is preferred.1,2 Quicker mixing has been found when competing models were linked with a common residual error.1 Here we examined the use of this approach to discriminate between population pharmacokinetic models.
Methods: Data sets, with 20 individuals in each, were simulated from 1- and 2-compartment models in MATLAB. The two competing models were simultaneously fit in WinBUGS as a mixture model with a mixing population parameter drawn from a uniform distribution. The posterior odds that one model was preferred over the other was calculated based on computation of the expectation of the mixing parameter. The mixture model was fit with both common and independent residual variances as well as with informative and low-information priors on the model parameters. The methodology was then applied in two examples, for citalopram and sirolimus.
Results: For all simulated data sets the mixing parameter supported the true model. The posterior odds were similar with and without a common residual variance. Parameter estimates for the true model were closer to the nominal simulation values when the models were not constrained to have a common residual variance, but chain mixing was slower. The posterior odds for the true model were higher and the autocorrelations lower with informative priors than with low-information priors. The mixing parameter showed that the 1-comparment model was preferred for the citalopram data (posterior odds=52) while the 2-compartment model was preferred for the sirolimus data (posterior odds=8.0).
Conclusion: Analysing two competing models simultaneously with a mixing parameter seems to be a promising tool for model discrimination in WinBUGS which can be performed on-the-fly.
References:
1. Carlin, BP, Chib S. J R Statist Soc B (1995) 57: 473-484.
2. Riley, SP. AAPS Workshop on Bayesian Primer Salt Lake City, Utah (2003).
Reference: PAGE 13 (2004) Abstr 493 [www.page-meeting.org/?abstract=493]
Poster: poster