**Comparison of MCMC simulation results using NONMEM 7 or WinBUGS with the BUGSModelLibrary**

M.R. Gastonguay(1), W.R. Gillespie(1), R.J. Bauer(2)

(1)Metrum Research Group, Tariffville, CT; (2)ICON, Ellicott City, MD

**Objectives:** To compare the relative performance of the NONMEM 7 [1] BAYES MCMC method with WinBUGS [2] plus the BUGSModelLibrary [3] by applying them to simulated data for a range of PK and PKPD models.

**Methods:** For each of the following test cases, 100 data sets were simulated using NONMEM 6 (n = # subjects, nobs = # observations/subject): 1 compartment IV, n = 100, nobs = 10 (ad1tr2); 1 compartment IV, 2 sub-populations, n = 300, nobs = 8 (ad1tr2mixture); 1 compartment IV, inter-occasion variation, n = 250, nobs = 15 (ad1tr2occ); 1 compartment PO, n = 200, nobs = 3 (ad2tr2); 2 compartment IV, n = 100, nobs = 12 (ad3tr4); 2 compartment IV, CL & V1 dependent on age and gender, n = 400, nobs = 5 (ad3tr4covariate); 2 compartment IV, n = 1000, nobs = 2 (ad3tr4sparse); 2 compartment PO, n = 250, nobs = 3 (ad4tr4); 3 compartment IV, n = 200, nobs = 10 (ad11tr4); 1 compartment PO, binary PD, n = 72, nobs = 16 (fflag); Each set was analyzed with NONMEM 7 and WinBUGS using 3 chains of 10,000 MCMC iterations. The first 5,000 iterations from each chain were discarded. Results were compared w.r.t. summary statistics of the MCMC samples, computation time and "effective N", i.e., an approximate estimate of the equivalent number of independent samples from the posterior distribution [4,5].

**Results:** Summary statistics of NONMEM 7 and WinBUGS generated MCMC samples were generally comparable, an exception being ad11tr4 where WinBUGS over-estimated the inter-individual variances. For most examples effective N for the residual standard deviation was greater for NONMEM 7. NONMEM 7 also resulted in greater effective N for several parameters in the ad2tr2, ad3tr4covariate, ad3tr4sparse, ad4tr4, fflag and ad11tr4 examples. WinBUGS resulted in a greater effective N for the inter-occasion variance in the ad1tr2occ. The median NONMEM 7/WinBUGS ratios of computation times were 0.654, 1.91, 5.94, 1.08, 0.783, 1.90, 2.06, 0.729, 1.01 and 2.37 for ad11tr4, ad1tr2, ad1tr2mixture, ad1tr2occ, ad2tr2, ad3tr4, ad3tr4covariate, ad3tr4sparse, ad4tr4 and fflag, respectively.

**Conclusions:** MCMC simulations using NONMEM 7 and WinBUGS produce results with comparable accuracy. NONMEM 7 produced less auto-correlated residual standard deviation samples. WinBUGS required much less computation time to produce comparable MCMC results for a mixture model (ad1tr2mixture), and about half the computation time for the ad1tr2, ad3tr4, ad3tr4covariate and fflag examples. WinBUGS required more time to produce less precise results for the first order absorption model cases ad2tr2 and at4tr4.

**References:**

[1] ICON Development Solutions, Ellicott City, MD, [2] http://www.mrc-bsu.cam.ac.uk/bugs/ , [3] http://metruminstitute.org/ , [4] http://cran.r-project.org/web/packages/coda/ , [5] CP Robert & G Casella. Introducing Monte Carlo Methods with R. Springer, 2010. pp 255-256.